Bill Goodwine's Wiki - User contributions [en]

Engineering Differential Equations: Theory and Applications, Springer 2010

2015-11-09T21:11:48Z

Bill: /* Chapter 11 */

This page contains supplementary material for the book, ''Engineering Differential Equations: Theory and Applications'', by Bill Goodwine. 2010, Springer.

=Movies=
Chapter 11 considers solutions to partial differential equations.
==The One-Dimensional Wave Equation==
Section 11.1 considers the one-dimensional wave equation.

Some movies:
*String of length 3 plucked at L=1 (modeling a guitar):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode1.mpg The first (fundamental) mode of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15.mpg The first five modes of the plucked string plotted separately]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15sum.mpg The sum of the first five modes of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode50sum.mpg The sum of the first fifty modes of the plucked string]
*String of length 3 that is impacted near L=1 (modeling a piano):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact10sum.mpg The sum of the first ten modes of the impacted string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact50sum.mpg The sum of the first fifty modes of the impacted string]

==The One-Dimensional Heat Conduction Equation==
Section 11.3 considers the one-dimensional heat conduction equation.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinhomo.mpg The solution to the heat equation with inhomogeneous boundary conditions]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinsulated.mpg The solution to the heat equation with an insulated end]

==The Two-Dimensional Heat Equation==
Movie:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/twoheat.mpg Solution to the heat conduction equation in two dimensions]

==Vibrating Membranes==
Partial differential equations describing vibrating membranes in rectangular and polar coordinates are considered in Section 11.5.

Section 11.5.1 presents the two-dimensional wave equation in rectangular coordinates.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum11.mpg 1-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum21.mpg 2-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum22.mpg 2-2 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrumimpact.mpg Rectangular drum impacted near a corner]

Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum10.mpg 1-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum11.mpg 1-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum12.mpg 1-2 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum13.mpg 1-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum20.mpg 2-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum21.mpg 2-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum43.mpg 4-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drumimpact.mpg Circular drum that is impacted by a drum stick]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum.mpg Another drum impact movie]
*[http://www.youtube.com/watch?v=w8Gxut0odyc#t=4m10s Cool youtube movie of slow motion impact of drum head and cymbal]

=Errata=

==Chapter 1==
*[[p. 58, line -3, Equation 2.4]]: the ''c'' in the denominator should be the specific heat.

==Chapter 2==
*p. 61, second paragraph of Section 2.2, line 2: "and" should be "is".
*[[p. 89, line -7]]: the right hand side of the equation below equation 2.35 should be a function of t, not x.

==Chapter 3==
*[[p. 97, line -3]]: there is an extra closing parenthesis in the equation for the Wronskian.
*[[p. 105, line 12]]: both exponents should be <math>-\omega_n</math>.
*[[p. 117, Figure 3.5]]: the figure plots the solution to <math>\ddot x + \dot x + 10 x = 0</math> and not <math>2 \ddot x + \dot x + 10 x = 0</math> as stated. It really doesn't change the qualitative aspects of the problem, however.

==Chapter 4==
*[[p. 125, line 5]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line 8]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line -4]]: the coefficient of the x term in the differential equation should be squared.
*[[p. 128, Equation 4.8]]: the numerator of the coefficient of the sine term should be the initial velocity.
*[[p. 138, line 6 (large boxed equation)]]: the first zeta in the parentheses in the coefficient of the second exponential on the second line should be negative.
*[[p. 139, Equation 4.14]]: the second term should contain the derivative of x, not x.
*[[p. 142, Figure 4.16]]: the figure is incorrect in that the square root was not used to plot the curves.
*[[p. 156, Exercise 4.22]]: at this point in the book we don't know how to find the homogeneous solutions for these two systems.
*[[p. 158, Exercise 4.26, Figure 4.32]]: the variable x is not the distance along the beam, but rather the displacement at the end.
*[[p. 159, Exercise 4.27, Figure 4.33]]: the angle is incorrectly marked as the angular velocity.

==Chapter 5==
*[[p. 163, line 6]]: the first (n+1) term should be (n+2).
*[[p. 164, Equation 5.5]]: the first coefficient in the second series should be (n+2) not (n+1).
*[[p. 167, lines -4,-3 and -2]]: the expressions for the derivatives of the function are wrong.
* p. 170, line 6: at the end of the line "Table 5.2" should be "Table 5.1."
*[[p. 172, line -5]]: there should be a negative sign on the right hand side of the equation.
*[[p. 174, Equation 5.14]]: the first term in the numerator on the right hand side should be multiplied by 20.
*[[p. 181, line 16]]: the two terms on the right-hand side of the equation are switched, leading to the wrong answer for <math>a_2</math>. This wrong number then propagates to lines -1 and -6 on the same page.
*[[p. 182, line 14]]: in the first series for the second derivative, the exponent should be (n-2) not (n-1).
*[[p. 185, line 2]]: the recursion relation has two mistakes. The left hand side should be for a_{n+2} not {n+1}. Also, the negative sign should not be there.
*[[p. 186, line 6]]: the left hand side of the recursion relation should be for a_{n+2} not {n+1}.
*p. 188, Exercise 5.1, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*p. 189, Exercise 5.2, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*[[p. 190, Exercise 5.13]]: the middle term in the denominator of the second term should be "2 t" not "t2".
*[[p. 191, Exercise 5.16]]: the independent variable in the equation is x, so the derivative terms should be with respect to x.

==Chapter 6==
*[[p. 195, line 1]]: the third term in the vector on the right hand side should have a subscript of 4, not 3.
*[[p. 209, line -8]]: the exponential term should be multiplying the second term as well.
*[[p. 210, line 1]]: same error as on p. 209 carried through.
*[[p. 220, line -9]]: the superscript for the second term in the equation should be m-3.
*[[p. 244, line -11]]: the first component of the vector on the far right should contain t, not tau.
*[[p. 245, line 8]]: the matrix A7 does not have a set of n linearly-independent eigenvectors.
*[[p. 247, line -7]]: A3 should be A2.

==Chapter 7==
*p. 253, line 5: the word "of" is repeated.
*[[p. 265, Equation (7.16)]]: this equation has multiple typos. The last term in parentheses in the last line should be (1-k1-2 k3). Also the second line has misaligned parentheses.

==Chapter 8==
*[[p. 288, last line in Table 8.1]]: the exponent should be "-a t" and not "a t".
*p. 297, Example 8.14: the "3" multiplying the <math>t^2</math> term on the right hand side is dropped half way through the example. Because it scales the whole right hand side, it scales simply scales the solution by 3. Thus the final answer on p. 299 should be multiplied by 3, as should the equation on the top of page 299. Also the two equations in the middle of p. 298 involving X(s) should have the right hand side multiplied by 3.
*p. 326, line -10: "Figure 8.8" should be "Figure 8.37".
*p. 327: the pendulum in Figure 8.36 should indicate a length, ''l'', for the pendulum.

==Chapter 9==
*[[p. 348, line 4]]: the numerator for both expressions of G1 should be 5.
*[[p. 348, line 6]]: the numerator for both expressions of G1 should be 10.
*[[p. 349, caption to Figure 9.16]]: the numerator for G1 should be 4 in the numerator for G2 should be 9.
*p. 354, line 9: the word "row" should be "column".
*p. 368, line 4: "r=10, 1, -1, and 10" should be "r=10, 1, -1, -10".
*p. 368, line -4: "Systems with left half-plane zeros are called..." should be "Systems with right half-plane zeros are called...".
*[[p. 403, line -7]]: the arctan should be a ratio of the imaginary to real components of G(i \omega).

==Chapter 11==
*p. 496, Fig. 11.6: the label for abscissa should be "x" not "t".
*[[p. 513, line 2]]: the coefficient is alpha^2, not alpha.
*[[p. 515, line 6]]: the "x" should be outside, not inside, the square root.
*[[p. 524, line 1]]: the sine function should not equal n pi, the argument to it should.
*[[p. 525, Equation 11.43]]: the denominator in both exponentials should be <math>L_x</math>.
*[[p. 525, Equation 11.44]]: the first term in the denominator of the coefficient in front of the integral should be <math>L_x</math>, not <math>L</math>.
*[[p. 532, line 12]]: on the right-hand side of the equations, one of the terms should be the steady-state solution.
*[[p. 534, Equation 11.51]]: one of the partial derivatives should be with respect to x.
*[[p. 534, Equation 11.52]]: the frequency in the sine and cosine functions should be multiplied by t.
*p. 536, line 10: "right-hand side of Equation (11.51)" should be "left-hand side of Equation (11.51)".
*[[p. 539, Figure 11.28]]: in the label on the vertical axis, the subscript on z should be "0,n" not "1,n".
*[[p. 542, last boxed set of equations]]: the expressions for the ''c'' and ''d'' coefficients should be in terms of the function ''g'' not the function ''f''. Also, the ''d'' coefficient should have a sine function instead of cosine.
*[[p. 559, line -4]]: the tension and mass per unit length appearing in the frequency term should both be the square root of those terms.
*p. 561, line 1: the second word "subsection" should be "subsections".
*p. 570, Exercise 11.2: add to the problem statement "let <math>m=1, b=0</math> and <math>k = 9\pi^2</math>."
*[[p. 571, line 21]]: for Exercise 11.4, number 4, the initial condition should be for u(x,0) not the partial derivative of u with respect to t.
*[[p. 572, Exercise 11.9]]: in the "denominator" of the operators the partial sign is "squared" when it should be the x and y, respectively.

==Chapter 12==
* p. 580, line 16: the word "so" should be deleted near the end of the line.
* p. 580, line -14: the exact solution is cos(t), not -cos(t).
*[[p. 588, line 2]]: the middle term in the numerator should be evaluated at 2.0, not 1.5.
*[[p. 592, lines 11 and 12]]: the minus sign multiplying the cubed term was dropped. Also, it would be more complete if the expression for f(x(t),t) were substituted into the final expression.
*[[p. 600, line 10]]: the error term on the right-hand side should be at two time steps back, not one.
*[[p. 625, Exercise 12.2, number 6]]: the first derivative term should be a second derivative.

==Chapter 13==
*p. 662, Figure 13.24: the output Y(s) should be X(s) because that is what it is called in the text that refers to the figure.
*[[p. 662, line 8]]: the second equation on the page should have X(s) on the left hand side, not G_p(s).
*[[p. 664, line 1]]: the sine term inside the friction function should be multiplied by M.
*[[p. 654, line 1, Equation (13.23)]]: the second equilibrium point should be x=2, x'=0, not x=0, x'=2.
*[[p. 664, line 4]]: the term multiplying ''a'' on the left hand side of the equation should be the reciprocal of what is printed.
*[[p. 664, line 8]]: the term multiplying ''b'' on the left hand side of the equation should be the reciprocal of what is printed. Also, there should be an ''M'' multiplying the sine function that is the argument to the ''friction()'' function and no ''M'' multiplying the sine function outside the ''friction()'' function.
*[[p. 666, line 5]]: the "0.3" in the equation should be "-0.3".
*[[p. 679, exercise 13.12, number 2]]: "G(s) =" is missing from the left side of the equation.

==Appendix E==
*Various FORTRAN programs have semicolons terminating lines (always in the declaration statements): E.2.0.20, E.2.0.21, E2.0.22, E.2.0.23, E2.0.24, E2.0.25, E.2.0.26. These semicolons should not be there.
* p. 727, program in E.2.0.18, for Example 1.30: the program contains the variable n which does nothing. The declaration, initialization to zero and increment inside the do loop should be removed.
*[[p. 733, line 19]]: the equation to update x(2) should not have an x(1) in it, it should be copy(1). Also, while it will not affect how the program works, x(2) should be copy(2) for consistency.
*p. 737, line 5: The program in E.2.0.31 is for Example 12.17, not Example 12.16.

Main Page

2015-09-18T20:22:09Z

Bill: /* Papers */

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<td width=25%> [[Image:Bill5.jpeg|250px]]</td>
<td align=center>

Bill Goodwine 


Department of Aerospace and Mechanical Engineering 
University of Notre Dame 
Notre Dame, IN 46556 
bill@controls.ame.nd.edu 
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I have moved my homepage here. At least for the time being, my [http://controls.ame.nd.edu/~bill/oldindex.php old one] still exists.
=Publications=
==Papers==
# Kevin Leyden and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2015/icra_16.pdf Using Fractional-Order Differential Equations for Health Monitoring of a System of Cooperating Robots]. Submitted to the 2016 IEEE International Conference on Robotics and Automation.
# Bill Goodwine, Towards General Results in Bifurcations in Optimal Solutions for Symmetric Distributed Robotic Formation Control. Submitted to the 2015 IEEE International Symposium on System Integration.
# Baoyang Deng, Michael O'Connor and Bill Goodwine, Bifurcations and Symmetry in Two Optimal Formation Control Problems for Mobile Robotic Systems. Accepted for publication pending revisions in Robotica.
# Nicholas Turner, Bill Goodwine and Mihir Sen, A Review of Origami Applications in Mechanical Engineering, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science (2015): 0954406215597713.
# David C. Post, Bill Goodwine and James P. Schmiedeler, Quantifying Control Authority in Periodic Motions of Underactuated Mobile Robots, Proceedings of the ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2015, DETC2015-47666
#Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2015/icra2015.pdf Symmetries and Reduction for Multi-Agent Control], Proceedings of the 2015 IEEE International Conference on Robotics and Automation, pp 5390-5396
# Bill Goodwine and Kevin Leyden, Recent Results in Fractional-Order Modeling for Multi-Agent Systems and Linear Friction Welding, 8th Vienna International Conference on Mathematical Modelling - MATHMOD 2015, abstract submission
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icarcv2014.pdf Fractional-Order Dynamics in a Random, Approximately Scale-Free Network of Agents], Proceedings of the 2014 International Conference on Control, Automation, Robotics and Vision, pp 1581 - 1586
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/ifac14.pdf Nonlinear Stability of Approximately Symmetric Large-Scale Systems], Proceedings of the 2014 IFAC World Congress, Cape Town, South Africa, pp 845-850
# Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/mtns-282.pdf Symmetries of Multiagent Systems and Formation Stability], Proceedings of the 2014 International Symposium on Mathematical Theory of Networks and Systems (MTNS 14), pp 1340-1343 (extended abstract review)
# Bill Goodwine, [[Compositional Boundedness of Solutions for Symmetric Nonautonomous Control Systems]], Proceedings of the 2014 Mediterranean Conference on Control and Automation, pp 798 - 803
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icra-1441.pdf Modeling a Multi-Robot System with Fractional-Order Differential Equations], Proceedings of the 2014 IEEE International Conference on Robotics and Automation, Hong Kong, pp 1763-1768
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2013/automatica13.pdf Multi-agent compositional stability exploiting system symmetries], Automatica 49(11): 3158-3166, 2013
# Panos J Antsaklis,Bill Goodwine, Vijay Gupta, Michael J. McCourt, Yue Wang, Po Wu, Meng Xia, Han Yu, and Feng Zhu, [http://controls.ame.nd.edu/~bill/papers/2013/ejc13.pdf Control of cyberphysical systems using passivity and dissipativity based methods], European Journal of Control 19, no. 5 (2013): 379-388
# Bill Goodwine [http://controls.ame.nd.edu/~bill/papers/2013/med-2013a.pdf Compositional stability of approximately symmetric systems: Initial results], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED), pp. 1470-1476 IEEE, 2013
# Jason Nightingale and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2013/med-2013b.pdf An algorithm for stopping a class of underactuated nonlinear mechanical robotic systems], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED) pp. 531-536, 2013
# Alice M. Nightingale, Bill Goodwine, Michael Lemmon and Eric Jumper [http://controls.ame.nd.edu/~bill/papers/2013/aiaa13.pdf Phase-Locked-Loop Adaptive-Optic Controller and Simulated Shear Layer Correction], AIAA journal, 51(11), 2714-2726, 2013
# John Gallagher and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/cdio12.pdf CDIO-Oriented Inverted Pendulum Control Project for Undergraduate Engineering Students], 2012 CDIO International Conference, Brisbane, Australia, 2012
# Michael O'Connor and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/med12a.pdf Symmetry-Breaking in Bifurcations of Optimal Solutions for Coordinated Nonholonomic Robotic Control], Proceedings of the 2012 Mediterranean Conference on Control & Automation (MED), pp. 1554-1559, 2012
# Janos Sztipanovits, Xenofon Koutsoukos, Gabor Karsai, Nicholas Kottenstette, Panos Antsaklis, Vijay Gupta, Bill Goodwine, John Baras, and Shige Wang, [http://controls.ame.nd.edu/~bill/papers/2011/procieee11.pdf Toward a science of cyber–physical system integration], Proceedings of the IEEE 100, no. 1 (2012): 29-44
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2011/icra11.pdf Fault-Tolerant Multiagent Robotic Formation Control Exploiting System Symmetries], Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, pp. 2872-2877
# Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2011/ifac11.pdf Nonlinear Disturbance Decoupling for a Mobile Robotic Manipulator over Uneven Terrain], Proceedings of the 2011 International Federation of Automatic Control World Congress, Milan, Italy, Vol. 18, No. 1, pp. 6930-6936
# Dayu Lv and Bill Goodwine, "Pancreas Modeling by a Deterministic Optimization Method" 'International Journal of Data Mining and Bioinformatics,' Volume 5, Number 3, Pages 308-320 (2011).
# Goodwine, Bill, and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent coordination exploiting system symmetries], American Control Conference (ACC), 2010, pp. 830-835
# Baoyang Deng, Mihir Sen, and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/acc09.pdf Bifurcations and symmetries of optimal solutions for distributed robotic systems], Proceedings of the 2009 American Control Conference, St. Louis, MO, pp. 4127-4133
#Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icarcv10.pdf Nonlinear Disturbance Decoupling for a Nonholonomic Mobile Robotic Manipulation Platform], Proceedings of the Eleventh International Conference on Control, Automation, Robotics and Vision (ICARCV 2010), Singapore, pp. 1530-1535
#Neil Petroff and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/iros10.pdf Nonholonomic and Stratified Robotic Manipulation Supplemented with Fuzzy Control: Theory and Experiment], Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, pp. 1202-1208
#Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent Coordination Exploiting System Symmetries], Proceedings of the 2010 American Controls Conference, pp. 830-835
#Baoyang Deng, Andreas K. Valenzuela and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icra10a.pdf Bifurcations of Optimal Solutions for Coordinated Robotic Systems: Numerical and Homotopy Methods], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 4475-4480
#Bill Goodwine and Jason Nightingale, [http://controls.ame.nd.edu/~bill/papers/2010/icra10b.pdf The Effect of Dynamic Singularities on Robotic Control and Design], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 5213-5218
#Dayu Lv and Bill Goodwine, Modeling of glucose transport in skeletal muscle, Proceedings of the IEEE International Conference on Bioinformatics and Biomedicine Workshops (BIBMW), 2010, pp 833 - 833
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/bibm09.pdf Pancreas Modeling from IVGTT Data Using a Deterministic Optimal Search], Proceedings of the 2009 IEEE International Conference on Bioinformatics & Biomedicine, (35% acceptance rate) Washington, D.C.
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/wafr09.pdf A Stopping Algorithm for Mechanical Systems], Algorithmic Foundations of Robotics VIII, Gregory S. Chirikjian, et al., editors, Eighth International Workshop on the Algorithmic Foundations of Robotics, Guanajuato, Mexico, 2009, pp. 167-180
#Jason Nightingale, Richard Hind and Bill Goodwine, "Geometric analysis of a class of constrained mechanical control systems in the nonzero velocity setting,"Proceedings of the 17th International Federation of Automatic Control (IFAC) World Congress, Seoul, Korea July, 2008, pp 1171-1176
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/icra08.pdf Intrinsic Vector-Valued Symmetric Form for Simple Mechanical Control Systems in the Nonzero Velocity Setting], Proceedings of the 2008 IEEE International Conference on Robotics and Automation, (43.4% acceptance rate) Pasadena, CA, May, 2008, pp 2435 - 2440
# Alice Nightingale, Benson Mitchell, Bill Goodwine and Eric Jumper, "Feedforward" Adaptive-Optic Mitigation of Aero-Optic Disturbances, Proceedings of the AIAA Plasmadynamics and Lasers Conference, 2008
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/biodevices08.pdf A New Metabolism Model for Human Skeletal Muscle], Proceedings of the IEEE International Conference on Biomedical Electronics and Devices, January, 2008, Maderia, Portugal
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2007/ijrr07.pdf Motion Planning for Nonlinear Symmetric Distributed Robotic Formation], International Journal of Robotics Research, 2007, 26:10, pp. 1025-1042
#Alice Nightingale, Bill Goodwine, Michael Lemmon, and Eric Jumper, 2007, "Feedforward Adaptive-Optic System Identification Analysis for Mitigating Aero-Optic Disturbances," Proceedings of the AIAA 2007 Plasmadynamics and Lasers Conference.
#Alice Nightingale, Daniel D. Duffin, Michael Lemmon, Bill Goodwine and Eric Jumper, "Adaptive-Optic Correction of a Regularized Compressible Shear Layer," Proceedings of the 37th AIAA Plasmadynamics and Lasers Conference, San Francisco, CA, June, 2006.
#Alice Nightingale, Bill Goodwine and Eric Jumper, 2005, "Regularizing Shear Layer for Adaptive Optics Control Application," accepted for presentation at the 36th AIAA Plasmadynamics and Lasers Conference.
# Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2004/ra04.pdf Stratified motion planning on nonsmooth domains with robotic applications], IEEE Transactions on Robotics and Automation 20.1 (2004): 128-132
#Yejun Wei, Bill Goodwine and Steven B. Skaar, 2004, "Kinematics of Vision-Based Stratified Robotic Manipulation," Proceedings of the 11th IFToMM World Congress, Tianjin, China. Abstract review, pp 1900-1905.
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, "Flow-based control of temperature in long ducts," 2004, International Journal of Heat and Mass Transfer, 47:23, pp. 4995-5009.
# M. Brett McMickell and Bill Goodwine, 2003, "Reduction and Controllability of Nonlinear Symmetric Distributed Systems," International Journal of Control, 76:18, pp. 1809-1822, 2003.
#M. Brett McMickell and Bill Goodwine, 2003, [http://controls.ame.nd.edu/~bill/papers/2003/icra03a.pdf Reduced Order Motion Planning for Nonlinear Symmetric Distributed Robotic Systems], Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, 2004, "Controllability of Cross-Flow Heat Exchangers," International Journal of Heat and Mass Transfer, 47:5, pp. 913-924
#M. Brett McMickell and Bill Goodwine, 2003, MICAbot: A Platform for Large Scale Coordinated Distributed Mobile Robot Control, Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review. pp 1600-1605
#S. Alotaibi, J.W. Goodwine, M. Sen and K.T. Yang, 2003, Controllability of conductive-convective systems, Proceedings of the 6th ASME-JSME Thermal Engineering Joint Conference, Hawaii, Paper No. TED-AJ03-247, pp. 1-6.
#Antonio Cardenas, Bill Goodwine, Steven B. Skaar and Michael Seelinger, Vision-Based Control of a Mobile Base and On-Board Arm, The International Journal of Robotic Research, 22: 9, pp. 677-698, 2003
#Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/icarcv2002.pdf Vision-Based Non-Smooth Kinematic Stratified Object Manipulation], Proceedings of the 2002 Seventh Annual Conference on Control, Automation, Robotics and Vision, Singapore, 2002, pp 360 - 365
#Yejun Wei, S.B. Skaar and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/iros02.pdf Vision-Based Stratified Robotic Manipulation], Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, 2002 pp 1638-1644.
#S. Batill, S. Skaar, R. Nelson, B. Goodwine, J. Mason, and M. Sen, 2002, Development of a Curriculum for Mechanical Engineering Based Upon Intelligent Systems and Automation, Session 1526, Proceedings of the 2002 American Society for Engineering Education Annual Conference and Exposition, 2002
#S. Alotaibi, Mihir Sen, B. Goodwine, and K.T. Yang, Numerical Simulation of Thermal Control of Heat Exchangers, Numerical Heat Transfer Journal, Part A: Applications, 41:3, pp. 229-244, 2002
#Bill Goodwine and Joel Burdick, Motion planning for kinematic stratified systems with application to quasi-static legged locomotion and finger gaiting. IEEE Transactions on Robotics and Automation, 18:2, pp. 209-222, 2002
#M. Brett McMickell and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02b.pdf Reduction and Controllability of Symmetric Distributed Systems with Drift], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3454-3460, 2002. Full paper review.
#Yejun Wei and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02a.pdf Stratified Motion Planning on Non-Smooth Domains with Application to Robotic Legged Locomotion and Manipulation], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3546-3552. Full paper review.
#Bill Goodwine and Milos Zefran, 2002, Feedback Stabilization of a Class of Unstable Nonholonomic Systems, Transactions of the ASME, Journal of Dynamics Systems, Measurement, & Control, 124, pp. 221-230.
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2001/iros01.pdf Reduction and Controllability of Symmetric Distributed Systems with Robotic Applications], Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, Hawaii, pp. 1232-1237. Full paper review.
#S. Alotaibi, M. Sen, Bill Goodwine, and K.T. Yang, 2001, Thermal Control of Heat Exchangers, Proceedings of the 35th National Heat Transfer Conference, NHTC01-12517, Anaheim, CA.
#Yejun Wei and Bill Goodwine,, 2001, Theoretical and Experimental Investigation of Stratified Robotic Manipulation, Proceedings of the 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea. Full paper review.
#Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.
#Bill Goodwine and Gabor Stepan, 2000, "Controlling unstable Rolling Phenomena, Journal of Vibration and Control, 6:1, pp. 137-158, January 2000.
# Qun Ma, Antonio Cardenas, Mike Seelinger, Bill Goodwine and Steven Skaar, 2000, "Supervisory Control of a Mobile Robot Using Point-and-Click Mobile Camera-Space Manipulation," Proceedings of the 4th World Multiconference on Systemics, Cybernetics and Informatics SCI 2000 and The 6th International Conference on Information Systems, Analysis and Synthesis ISAS 2000, Orlando, Florida.
# Bill Goodwine and Yejun Wei, 2000, [http://controls.ame.nd.edu/~bill/papers/2000/allerton.pdf Theoretical and Experimental Investigation of Stratified Robotic Finger Gaiting and Manipulation], Proceedings of the 38th Annual Allerton Conference on Communication, Control and Computing, Allerton, Illinois
# Bill Goodwine and Joel Burdick, Motion Planning for Kinematic Stratified Systems with application to Quasi-Static Legged Locomotion and Finger Gaiting, Proceedings of the Workshop Algorithmic Foundations of Robotics.
# Bill Goodwine and Joel Burdick, [http://controls.ame.nd.edu/~bill/papers/1999/ifac99.pdf Stratified Motion Planning with Application to Robotic Finger Gaiting], Proceedings of the 1999 International Federation of Automatic Control, IFAC'99: 14th World Congress Beijing, China. Full paper review.
# Gabor Stepan and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/1999/ds99.pdf Analysis and Control of Unstable Rolling Wheel Dynamics], 1999 SIAM Conference on Applications of Dynamical Systems, Showbird, UT, 1999, abstract submission
# B. Goodwine, Michael Seelinger, John-David Yoder, Qun Ma and Steven Skaar, [http://controls.ame.nd.edu/~bill/papers/1999/fsr99.pdf Applications of mobile camera-space manipulation], Proceedings of FSR'99: Field and Service Robotics, pages 102-113, Pittsburg, 1999
# Bill Goodwine, 1999, Stratified Motion Planning with Application to Robotic Finger Gaiting, Proceedings of the 1999 IFToMM 10th World Congress, Oulu, Finland. Abstract review.
# Bill Goodwine and Gabor Stepan, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/misk98.pdf Stabilizing Switching Controllers], Proceedings of the 1998 Conference on Numerical Mathematics and Computational Mechanics, Miskolc, Hungary. Abstract review
# Bill Goodwine, Michael Seelinger, Steven B. Skaar and Qun Ma, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/spie98.pdf Nonholonomic Camera Space Manipulation using Cameras Mounted on a Mobile Base], Proceedings of the 1998 SPIE conference on Sensor Fusion and Decentralized Control in Robotic Systems, Boston, Massachusetts. Abstract review
# Bill Goodwine and Joel Burdick, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/icra98.pdf Gait Controllability for Legged Robots], Proceedings of the 1998 IEEE Conference on Robotics and Automation,Leuven, Belgium. Full paper review.
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/thesis.pdf Control of Stratified Systems with Robotic Applications], Ph.D Thesis, California Institute of Technology, 1997
# Bill Goodwine and Joel Burdick, 1997, [http://controls.ame.nd.edu/~bill/papers/1997/icra97.pdf Trajectory Generation for Legged Robotic Systems], Proceedings of the 1997 IEEE Conference on Robotics and Automation, Albuquerque, New Mexico. Full paper review
# Shuuji Kajita, Bill Goodwine and Joel Burdick, Walking Direction Control of a Biped Robot with Point Feet Using Dynamic Effects in 3-D Space, Proceedings of the 1997 Robotics Society of Japan Conference, Tokyo, Japan. 1997 (in Japanese).
# Bill Goodwine and Joel Burdick, [http://controls.ame.nd.edu/~bill/papers/1996/mtns96.pdf Controllability of Kinematic Control Systems on Stratified Configuration Spaces], Mathematical Theory of Networks and Systems, 1996, St. Louis
# Bill Goodwine and Joel Burdick, 1996, [http://controls.ame.nd.edu/~bill/papers/1996/cdc96.pdf Controllability with Unilateral Control Inputs], Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan. Full paper review, 1996, (Vol. 3, pp. 3394-3399
# Bill Goodwine and Gabor Stepan, [http://controls.ame.nd.edu/~bill/papers/1996/enoc96.pdf Stabilization of the Classical Shimmying Wheel], Proceedings of the 2nd European Nonlinear Oscillations Conference, Prague, Czech Republic, 1996
#Bill Goodwine, 1991, Abortion Parental Notification Statutes: Hodgson v. Minnesota, 110 S. Ct. 2926 (1990) and Ohio v. Akron Center for Reproductive Health, 110 S. Ct. 2972 (1990), Harvard Journal of Law & Public Policy, 14:1, pp. 237-247.

==Books and Chapters in Books==
# Bill Goodwine, [http://www.springer.com/mathematics/dynamical+systems/book/978-1-4419-7918-6 Engineering Differential Equations: Theory and Applications], Springer, 2010.
#* Some [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Movies movies] are available illustrating some of the more interesting solutions, generally for PDEs
#* A list of [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Errata errata] is also available
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849318047 Robotics and Automation Handbook], Chapter 3, Inverse Kinematics, Thomas R. Kurfess, Editor, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2001.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2001.

==Erdős Number==
# Erdős, P.; Shapiro, H. S.; Shields, A. L. Large and small subspaces of Hilbert space. Michigan Math. J. 12 1965 169--178.
# Shields, Allen L. Some problems in operator theory. Notes by Michael J. Hoffman. Lecture Notes in Math., 693, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977), pp. 157--167, Springer, Berlin, 1978.
# Marsden, Jerrold E.; Hoffman, Michael J. Basic complex analysis. Second edition. W. H. Freeman and Company, New York, 1987. xiv+604 pp. ISBN: 0-7167-1814-6
# Banavara N. Shashikanth, Jerrold E. Marsden, Joel W. Burdick and Scott D. Kelly, The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vorticesPhys. Fluids 14, 1214 (2002).
# Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.

=Students=

==PhD Students==
* Kevin Leyden, in progress
* Jason Nightingale, Ph.D. defended 8:00 am, June 4, 2012 [http://controls.ame.nd.edu/~bill/students/jason.pdf thesis]
* Dayu Lv, Ph.D. defended March 17, 2011, [http://controls.ame.nd.edu/~bill/students/dayu.pdf thesis]
* Baoyang Deng, Ph.D., defended March 11, 2011 [http://controls.ame.nd.edu/~bill/students/baoyang.pdf thesis]
* Alice Nightingale, Ph.D. defended November 3, 2010 [http://controls.ame.nd.edu/~bill/students/alice.pdf thesis]
* Neil Petroff, Ph.D. defended, October 6, 2006 [http://controls.ame.nd.edu/~bill/students/neil.pdf thesis]
* M. Brett McMickell, Ph.D. defended 2003
* Yejun Wei, Ph.D. defended 2002

==MS Students==
* Ashley Nettleman, M.S., November 2014 [http://controls.ame.nd.edu/~bill/students/ashley.pdf thesis]
* Nicholas Galati, July 15, 2013
* Michael O'Connor, Fall 2011
* Qun (Marc) Ma, M.S., 2000

==Undergraduate Research Projects==

* Patrick O’Meara, “Control and Dynamics of a Fleet of Automobiles,” spring, summer and fall 2013
* Nick Turner, “Mathematics and Theory of Origami,” summer 2013
* Catherine Bentzen, “Jellyfish Propulsion,” summer 2013
* Blair Rasmus, John Gallagher, Derek Wolf, “Development of Feedback Microcontroller for an Inverted Pendulum System for AME 30315” (all three, Fall 2011, John Gallagher continued through Spring 2012)
* Jeff O’Brien, “Synchronization and Limit Cycle Solutions for Coupled Hybrid Systems” (Fall and Spring, 2011)
* John Gallagher, “Describing Function Analysis with Non-Harmonic Basis Functions” (Spring 2012 – started in January)
* Adam Wojcik,. “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Paul Fleury, “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Robert Powers, “Energy storage technologies: a sustainable solution to electrical load shedding in rural Bangladesh,” Spring 2010
* “Raymond LeGrand, "Development of a Microprocessor controlled Inverted Pendulum Experiment,” , Summer and Fall 2010
* Steven Brus, “Homotopy Methods for Coordinated Robotic Systems,” Summer 2010
* Andres Valenzuela, “Bifurcation Measures for Nonlinear Boundary Value Problems in Optimal Control of Mobile Robot Formations,” Fall 2008 and Spring 2009. Undergraduate thesis in Spring 2009
* Blake Shilide, “Aero-Optic Shear Layer Control and Simulation,” Spring, 2005
* Tim Ronan, “MICAbot Programming and TinyOS,” Summer, 2003
* Timothy Kacmar, “Development of a Multi-Manipulator Path Planning Collision Avoidance System,” Fall, 2003
* Meaghan Perry-Eaton, “Investigation of Automotive Fuel Cell Energy System Usage and Feasibility,” Fall, 2003
* Peter Balough, “Development of a Mobile Multi-Robot Simulation Environment in Java and Hardware Development for the TagMote,” Summer and Fall, 2003
* Kristin Dormuth, “MICAbot Programming and TinyOS,” Summer, 2003
* John Aman, “MICAbot Programming and TinyOS,” Summer, 2003
* Denis Sullivan, “MICAbot Programming and TinyOS,” Summer and Fall, 2003
* Thomas Apker, “Investigation of the Efficacy of Switching Multi-Controller Systems,” Spring, 2003
* Daniel Luedtke, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Spring, 2003
* Tommy Ferrara, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Fall, 2003.
* Dennis Abdelnour, “Development Programming for a Mobile Robot,” Spring, 2001.
* Eric Shearer, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer 2000.
* Bethany Wilson, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer, 2000.
* Leonard Conapinski, “Investigation of the Presence of Chaos in a Hybrid Switching System, ” Fall, 2000.

=Research Summary=

===Cyber Physical Systems===

My research focuses primarily on theoretical nonlinear control with recent emphasis on Cyber Physical Systems. Cyber physical systems are systems with highly integrated physical and computational components (often involving the complication of networked communication). They tend to be very large and complex in scale. While many CPS systems exist in the real world, to date there are few general theoretical results available to guide both the design of such systems and the control of such systems. Most existing CPS systems are designed and controlled based upon accumulated real-world industrial knowledge that tends to be industry- or application-specific. My recent work has focused particularly on so-called ''symmetric systems.'' A symmetric system is comprised of many components with the restriction that the components be very closely related and connected together in a "regular" manner. With such restrictions, it is possible to formulate general models and then consider what types of properties remain invariant as components are added to or removed from the system. A related question is how the system behaves as components fail, which is a question of robustness.

===Stratified Systems===

Many interesting and important control systems evolve on
''stratified'' configuration spaces. Roughly speaking, we
will call a configuration manifold stratified if it contains
submanifolds upon which the system is subjected to additional
constraints or has different equations of state. For such
systems, the equations of motion on each submanifold may change
in a non-smooth, or even discontinuous manner, when the system
moves from one submanifold to another. In such cases,
traditional nonlinear control methodologies are inapplicable
because they generally rely upon differentiation in one form or
another. Yet it is the discontinuous nature of such systems
that is often their most important characteristic because the
system must cycle through different submanifolds to effectively
be controlled. Therefore, it is necessary to incorporate
explicitly into control methodologies the non-smooth or
discontinuous nature of these systems.

Robotic systems, in particular, are of this nature. A legged
robot has discontinuous equations of motion near points in the
configuration space where each of its ``feet'' come into contact
with the ground, and it is precisely the ability of the robot to
lift its feet off of the ground that enables it to move about.
Similarly, a robotic hand grasping an object often cannot
reorient the object without lifting its fingers off of the
object. Despite the obvious utility of such systems, however, a
comprehensive framework in which to consider control issues for
such systems does not exist.

The fundamental approach of this work has been to exploit the
physical geometric structure present in such problems to address
control issues such as nonlinear controllability, trajectory
generation and stabilization. The fundamental philosophy is to
generate ''general'' results, i.e., results
independent of a particular robot's number of legs, fingers or
morphology.

===Control of Mechanical Systems===

Most theoretical control results are based upon very generic dynamical systems formulations, such as
<math>\dot x = A x + B u</math> for linear systems or <math>\dot x =f(x) + g(x)u</math> for a nonlinear system. Of course this leads to the question of whether a more restrictive starting point can lead to valuable results. An important area of research along these lines is so-called control of mechanical systems where the equations of motion are not as general, but are assumed from the beginning to come from some first principle of mechanics. We have focused specifically on control of Lagrangian systems that are underactuated. Specifically, it is possible in such a framework to write general expressions for the relationship of the coupling between the controlled degree of freedoms and uncontrolled degrees of freedom, and given such expressions it is possible to know when there is close coupling between them and total decoupling between them. Furthermore, it is often the case that the coupling between the controlled and uncontrolled degrees of freedom is such that it may be only of one sign, ''i.e.'', no matter what is done with the control inputs, the uncontrolled degrees of freedom may only increase (or decrease) in magnitude. Such results have obvious important implications for control algorithms.

===Other Projects===

Other smaller projects include:
* control of aero-optic systems
* predictive biosimulation for human metabolism
* fuzzy logic-based robust control for stratified systems
* model-predictive control for marine navigation.

=Biographical Sketch=

* MS and PhD degrees in Applied Mechanics from the California Institute of Technology in 1993 and 1998, respectively.
* JD degree from Harvard Law School, 1991, ''cum laude''
* Instructor, Assistant Professor, Associate Professor, Department of Aerospace and Mechanical Engineering, University of Notre Dame, 1998 - present.
* Associate Department Chair, Department of Aerospace and Mechanical Engineering, University of Notre Dame, August 2008 - August 2012.
* Member of the Illinois Bar Association, 1991 - present.
* Registered Patent Attorney, 1998 - 2004 (not maintained).
* NSF CAREER Award Recipient.
* Boeing Welliver Faculty Fellow.
* Dockweiler Award for Excellence in Undergraduate Advising, May 2010.
* BP Foundation Outstanding Teacher of the Year, College of Engineering, Spring, 2008.
* Joyce Award (teaching), Spring, 2008.
* University of Notre Dame Kaneb teaching award, Spring, 2005.
* Department of Aerospace and Mechanical Engineering Ruth and Joel Spira Award for Excellence in Teaching, 2003 - 2004 and 2007 - 2008.
* American Society of Engineering Education Illinois/Indiana Section Outstanding Teaching Award, April, 2003.
* Department of Aerospace and Mechanical Engineering Faculty Award (teaching), 1998 - 1999.

=Courses=

* Fall 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=337 AME 30314: Differential Equations, Vibrations and Control I] (121 Students)
* Spring 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=323 AME 50652: Intermediate Controls] (7 Students) and AME 50650: Introduction to Nonlinear Analysis (9 Students)
* Fall 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=309 AME 30314, Differential Equations, Vibrations and Control I] (118 Students)
* Spring 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=304 AME 90951: Geometric Nonlinear Control] (8 students)
* Fall 2012: AME 30314: Differential Equations, Vibrations and Control I (86 Students)
* Spring 2012: [http://controls.ame.nd.edu/courses/viewforum.php?f=289 AME 30315: Differential Equations, Vibrations and Control II] (129 Students)
* Fall 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=274 AME 30314: Differential Equations, Vibrations and Control I] (112 Students)
* Summer 2011: [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Course_Syllabus,_Summer_2011 AME 40590: Intellectual Property for Engineers] [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Homework,_Summer_2011 (homeworks)]
* Spring 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=255 AME 30315: Differential Equations, Vibrations and Control II] (89 Students) and [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Intellectual_Property_for_Engineers AME 40590: Intellectual Property for Engineers] (56 Students) [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Homeworks,_Spring_2011 {homeworks)]
* Fall 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=227 AME 30314: Differential Equations, Vibrations and Control I] (81 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=228 AME 20214: Introduction to Engineering Computing] (131 Students)
* Spring 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=201 AME 30315: Differential Equations, Vibrations and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=202 AME 60652: Advanced Controls (now AME 50562: Intermediate Controls)]
* Fall 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=186 AME 30314: Differential Equations, Vibrations and Control I] (91 students)
* Spring 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=170 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=140 AME 30314: Differential Equations, Vibrations and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=141 AME 20214: Introduction to Engineering Computing]
* Spring 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=124 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=125 AME 30314: Differential Equations, Vibrations and Control I] (86 Students), [http://controls.ame.nd.edu/courses/viewforum.php?f=127 AME 60652: Advanced Controls] (11 Students) and AME 53591: Engineering Seminar Series.
* Spring 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=129 AME 30315: Differential Equations, Vibrations and Control II] (94 Students)
* Fall 2006: [http://controls.ame.nd.edu/courses/viewforum.php?f=130 AME 30314: Differential Equations, Vibrations and Control I] (79 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=131 AME 60611: Mathematical Methods I] (24 Students)
* Fall 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=132 AME 34314: Differential Equations, Vibrations and Control I (London)] and Intermediate Dynamics.
* Spring 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=133 AME 302: Modeling and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=134 Geometric Nonlinear Control]
* Fall 2004: [http://controls.ame.nd.edu/courses/viewforum.php?f=135 AME 301: Modeling and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=136 AME 550: Advanced Controls]
* Spring 2004: [http://controls.ame.nd.edu/courses/ame302/S2004 AME 302: Modeling and Control II] (72 students)
* Fall 2003: [http://controls.ame.nd.edu/courses/ame301/F2003/ AME 301: Modeling and Control I] (54 students) and AME 654: Geometric Nonlinear Control (2 students)
* Spring 2003: [http://controls.ame.nd.edu/courses/ame437/S2003/ AME 437: Control Systems Engineering] (68 students)
* Spring 2002: [http://controls.ame.nd.edu/courses/ame437/S2002/ AME 437: Control Systems Engineering] (64 students)
* Fall 2001: [http://controls.ame.nd.edu/courses/ame654/F2001/ AME 654: Geometric Nonlinear Control] (3 students)
* Spring 2001: [http://controls.ame.nd.edu/courses/ame469/S2001/ AME 469: Introduction to Robotics] (33 students)
* Spring 2000: [http://controls.ame.nd.edu/courses/ame469/S2000/ AME 469: Introduction to Robotics] (48 students), [http://controls.ame.nd.edu/courses/ame437/S2000/ AME 437: Control Systems Engineering] (50 students) and AME 598: Engineering Applications of Artificial Intelligence (5 students).
* Fall 1999: [http://controls.ame.nd.edu/courses/ame698/F1999/ AME 698: Geometric Nonlinear Control] (10 students)
* Spring 1999: [http://controls.ame.nd.edu/courses/ame469/S1999/ AME 469: Introduction to Robotics] (33 students)
* Fall 1998: [http://controls.ame.nd.edu/courses/ame469/F1998/ AME 469: Introduction to Robotics] (12 students)
* Spring 1998: [http://controls.ame.nd.edu/courses/ame437/S1998/ AME 437: Control Systems Engineering] (44 students)

===Course Blog===

In order to be able to interactively answer questions online, I've maintained a [http://controls.ame.nd.edu/courses course blog for all courses since 2002].

===AME 30315 Differential Equations, Vibrations and Control II===
*[[AME 30315 Pendulum Project]]

===AME 40590, Intellectual Property for Engineers===
*[[AME 44590 Course Syllabus, Summer 2011]]
*[[AME 44590 Homework, Summer 2011]]
*[[AME 40590 Intellectual Property for Engineers|AME 40590 Course Content]]
*[[AME 40590 Homeworks, Spring 2011]]

===AME 50652, Intermediate Controls===
*[[AME 50652 Pendulum Project]]

=[[Engineering Differential Equations: Theory and Applications, Springer 2010]]=

=[[Engineering China Summer Program]]=

=[[London CPS Workshop]]=

=[[CDIO Regional Meeting]]=

Main Page

2015-09-18T20:21:53Z

Bill: /* Papers */

<table border=0 width=100%>
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<td width=25%> [[Image:Bill5.jpeg|250px]]</td>
<td align=center>

Bill Goodwine 


Department of Aerospace and Mechanical Engineering 
University of Notre Dame 
Notre Dame, IN 46556 
bill@controls.ame.nd.edu 
</td>
</tr>
</table>

I have moved my homepage here. At least for the time being, my [http://controls.ame.nd.edu/~bill/oldindex.php old one] still exists.
=Publications=
==Papers==
# Kevin Leyden and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2016/icra_16.pdf Using Fractional-Order Differential Equations for Health Monitoring of a System of Cooperating Robots]. Submitted to the 2016 IEEE International Conference on Robotics and Automation.
# Bill Goodwine, Towards General Results in Bifurcations in Optimal Solutions for Symmetric Distributed Robotic Formation Control. Submitted to the 2015 IEEE International Symposium on System Integration.
# Baoyang Deng, Michael O'Connor and Bill Goodwine, Bifurcations and Symmetry in Two Optimal Formation Control Problems for Mobile Robotic Systems. Accepted for publication pending revisions in Robotica.
# Nicholas Turner, Bill Goodwine and Mihir Sen, A Review of Origami Applications in Mechanical Engineering, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science (2015): 0954406215597713.
# David C. Post, Bill Goodwine and James P. Schmiedeler, Quantifying Control Authority in Periodic Motions of Underactuated Mobile Robots, Proceedings of the ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2015, DETC2015-47666
#Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2015/icra2015.pdf Symmetries and Reduction for Multi-Agent Control], Proceedings of the 2015 IEEE International Conference on Robotics and Automation, pp 5390-5396
# Bill Goodwine and Kevin Leyden, Recent Results in Fractional-Order Modeling for Multi-Agent Systems and Linear Friction Welding, 8th Vienna International Conference on Mathematical Modelling - MATHMOD 2015, abstract submission
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icarcv2014.pdf Fractional-Order Dynamics in a Random, Approximately Scale-Free Network of Agents], Proceedings of the 2014 International Conference on Control, Automation, Robotics and Vision, pp 1581 - 1586
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/ifac14.pdf Nonlinear Stability of Approximately Symmetric Large-Scale Systems], Proceedings of the 2014 IFAC World Congress, Cape Town, South Africa, pp 845-850
# Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/mtns-282.pdf Symmetries of Multiagent Systems and Formation Stability], Proceedings of the 2014 International Symposium on Mathematical Theory of Networks and Systems (MTNS 14), pp 1340-1343 (extended abstract review)
# Bill Goodwine, [[Compositional Boundedness of Solutions for Symmetric Nonautonomous Control Systems]], Proceedings of the 2014 Mediterranean Conference on Control and Automation, pp 798 - 803
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icra-1441.pdf Modeling a Multi-Robot System with Fractional-Order Differential Equations], Proceedings of the 2014 IEEE International Conference on Robotics and Automation, Hong Kong, pp 1763-1768
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2013/automatica13.pdf Multi-agent compositional stability exploiting system symmetries], Automatica 49(11): 3158-3166, 2013
# Panos J Antsaklis,Bill Goodwine, Vijay Gupta, Michael J. McCourt, Yue Wang, Po Wu, Meng Xia, Han Yu, and Feng Zhu, [http://controls.ame.nd.edu/~bill/papers/2013/ejc13.pdf Control of cyberphysical systems using passivity and dissipativity based methods], European Journal of Control 19, no. 5 (2013): 379-388
# Bill Goodwine [http://controls.ame.nd.edu/~bill/papers/2013/med-2013a.pdf Compositional stability of approximately symmetric systems: Initial results], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED), pp. 1470-1476 IEEE, 2013
# Jason Nightingale and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2013/med-2013b.pdf An algorithm for stopping a class of underactuated nonlinear mechanical robotic systems], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED) pp. 531-536, 2013
# Alice M. Nightingale, Bill Goodwine, Michael Lemmon and Eric Jumper [http://controls.ame.nd.edu/~bill/papers/2013/aiaa13.pdf Phase-Locked-Loop Adaptive-Optic Controller and Simulated Shear Layer Correction], AIAA journal, 51(11), 2714-2726, 2013
# John Gallagher and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/cdio12.pdf CDIO-Oriented Inverted Pendulum Control Project for Undergraduate Engineering Students], 2012 CDIO International Conference, Brisbane, Australia, 2012
# Michael O'Connor and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/med12a.pdf Symmetry-Breaking in Bifurcations of Optimal Solutions for Coordinated Nonholonomic Robotic Control], Proceedings of the 2012 Mediterranean Conference on Control & Automation (MED), pp. 1554-1559, 2012
# Janos Sztipanovits, Xenofon Koutsoukos, Gabor Karsai, Nicholas Kottenstette, Panos Antsaklis, Vijay Gupta, Bill Goodwine, John Baras, and Shige Wang, [http://controls.ame.nd.edu/~bill/papers/2011/procieee11.pdf Toward a science of cyber–physical system integration], Proceedings of the IEEE 100, no. 1 (2012): 29-44
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2011/icra11.pdf Fault-Tolerant Multiagent Robotic Formation Control Exploiting System Symmetries], Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, pp. 2872-2877
# Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2011/ifac11.pdf Nonlinear Disturbance Decoupling for a Mobile Robotic Manipulator over Uneven Terrain], Proceedings of the 2011 International Federation of Automatic Control World Congress, Milan, Italy, Vol. 18, No. 1, pp. 6930-6936
# Dayu Lv and Bill Goodwine, "Pancreas Modeling by a Deterministic Optimization Method" 'International Journal of Data Mining and Bioinformatics,' Volume 5, Number 3, Pages 308-320 (2011).
# Goodwine, Bill, and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent coordination exploiting system symmetries], American Control Conference (ACC), 2010, pp. 830-835
# Baoyang Deng, Mihir Sen, and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/acc09.pdf Bifurcations and symmetries of optimal solutions for distributed robotic systems], Proceedings of the 2009 American Control Conference, St. Louis, MO, pp. 4127-4133
#Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icarcv10.pdf Nonlinear Disturbance Decoupling for a Nonholonomic Mobile Robotic Manipulation Platform], Proceedings of the Eleventh International Conference on Control, Automation, Robotics and Vision (ICARCV 2010), Singapore, pp. 1530-1535
#Neil Petroff and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/iros10.pdf Nonholonomic and Stratified Robotic Manipulation Supplemented with Fuzzy Control: Theory and Experiment], Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, pp. 1202-1208
#Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent Coordination Exploiting System Symmetries], Proceedings of the 2010 American Controls Conference, pp. 830-835
#Baoyang Deng, Andreas K. Valenzuela and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icra10a.pdf Bifurcations of Optimal Solutions for Coordinated Robotic Systems: Numerical and Homotopy Methods], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 4475-4480
#Bill Goodwine and Jason Nightingale, [http://controls.ame.nd.edu/~bill/papers/2010/icra10b.pdf The Effect of Dynamic Singularities on Robotic Control and Design], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 5213-5218
#Dayu Lv and Bill Goodwine, Modeling of glucose transport in skeletal muscle, Proceedings of the IEEE International Conference on Bioinformatics and Biomedicine Workshops (BIBMW), 2010, pp 833 - 833
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/bibm09.pdf Pancreas Modeling from IVGTT Data Using a Deterministic Optimal Search], Proceedings of the 2009 IEEE International Conference on Bioinformatics & Biomedicine, (35% acceptance rate) Washington, D.C.
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/wafr09.pdf A Stopping Algorithm for Mechanical Systems], Algorithmic Foundations of Robotics VIII, Gregory S. Chirikjian, et al., editors, Eighth International Workshop on the Algorithmic Foundations of Robotics, Guanajuato, Mexico, 2009, pp. 167-180
#Jason Nightingale, Richard Hind and Bill Goodwine, "Geometric analysis of a class of constrained mechanical control systems in the nonzero velocity setting,"Proceedings of the 17th International Federation of Automatic Control (IFAC) World Congress, Seoul, Korea July, 2008, pp 1171-1176
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/icra08.pdf Intrinsic Vector-Valued Symmetric Form for Simple Mechanical Control Systems in the Nonzero Velocity Setting], Proceedings of the 2008 IEEE International Conference on Robotics and Automation, (43.4% acceptance rate) Pasadena, CA, May, 2008, pp 2435 - 2440
# Alice Nightingale, Benson Mitchell, Bill Goodwine and Eric Jumper, "Feedforward" Adaptive-Optic Mitigation of Aero-Optic Disturbances, Proceedings of the AIAA Plasmadynamics and Lasers Conference, 2008
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/biodevices08.pdf A New Metabolism Model for Human Skeletal Muscle], Proceedings of the IEEE International Conference on Biomedical Electronics and Devices, January, 2008, Maderia, Portugal
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2007/ijrr07.pdf Motion Planning for Nonlinear Symmetric Distributed Robotic Formation], International Journal of Robotics Research, 2007, 26:10, pp. 1025-1042
#Alice Nightingale, Bill Goodwine, Michael Lemmon, and Eric Jumper, 2007, "Feedforward Adaptive-Optic System Identification Analysis for Mitigating Aero-Optic Disturbances," Proceedings of the AIAA 2007 Plasmadynamics and Lasers Conference.
#Alice Nightingale, Daniel D. Duffin, Michael Lemmon, Bill Goodwine and Eric Jumper, "Adaptive-Optic Correction of a Regularized Compressible Shear Layer," Proceedings of the 37th AIAA Plasmadynamics and Lasers Conference, San Francisco, CA, June, 2006.
#Alice Nightingale, Bill Goodwine and Eric Jumper, 2005, "Regularizing Shear Layer for Adaptive Optics Control Application," accepted for presentation at the 36th AIAA Plasmadynamics and Lasers Conference.
# Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2004/ra04.pdf Stratified motion planning on nonsmooth domains with robotic applications], IEEE Transactions on Robotics and Automation 20.1 (2004): 128-132
#Yejun Wei, Bill Goodwine and Steven B. Skaar, 2004, "Kinematics of Vision-Based Stratified Robotic Manipulation," Proceedings of the 11th IFToMM World Congress, Tianjin, China. Abstract review, pp 1900-1905.
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, "Flow-based control of temperature in long ducts," 2004, International Journal of Heat and Mass Transfer, 47:23, pp. 4995-5009.
# M. Brett McMickell and Bill Goodwine, 2003, "Reduction and Controllability of Nonlinear Symmetric Distributed Systems," International Journal of Control, 76:18, pp. 1809-1822, 2003.
#M. Brett McMickell and Bill Goodwine, 2003, [http://controls.ame.nd.edu/~bill/papers/2003/icra03a.pdf Reduced Order Motion Planning for Nonlinear Symmetric Distributed Robotic Systems], Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, 2004, "Controllability of Cross-Flow Heat Exchangers," International Journal of Heat and Mass Transfer, 47:5, pp. 913-924
#M. Brett McMickell and Bill Goodwine, 2003, MICAbot: A Platform for Large Scale Coordinated Distributed Mobile Robot Control, Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review. pp 1600-1605
#S. Alotaibi, J.W. Goodwine, M. Sen and K.T. Yang, 2003, Controllability of conductive-convective systems, Proceedings of the 6th ASME-JSME Thermal Engineering Joint Conference, Hawaii, Paper No. TED-AJ03-247, pp. 1-6.
#Antonio Cardenas, Bill Goodwine, Steven B. Skaar and Michael Seelinger, Vision-Based Control of a Mobile Base and On-Board Arm, The International Journal of Robotic Research, 22: 9, pp. 677-698, 2003
#Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/icarcv2002.pdf Vision-Based Non-Smooth Kinematic Stratified Object Manipulation], Proceedings of the 2002 Seventh Annual Conference on Control, Automation, Robotics and Vision, Singapore, 2002, pp 360 - 365
#Yejun Wei, S.B. Skaar and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/iros02.pdf Vision-Based Stratified Robotic Manipulation], Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, 2002 pp 1638-1644.
#S. Batill, S. Skaar, R. Nelson, B. Goodwine, J. Mason, and M. Sen, 2002, Development of a Curriculum for Mechanical Engineering Based Upon Intelligent Systems and Automation, Session 1526, Proceedings of the 2002 American Society for Engineering Education Annual Conference and Exposition, 2002
#S. Alotaibi, Mihir Sen, B. Goodwine, and K.T. Yang, Numerical Simulation of Thermal Control of Heat Exchangers, Numerical Heat Transfer Journal, Part A: Applications, 41:3, pp. 229-244, 2002
#Bill Goodwine and Joel Burdick, Motion planning for kinematic stratified systems with application to quasi-static legged locomotion and finger gaiting. IEEE Transactions on Robotics and Automation, 18:2, pp. 209-222, 2002
#M. Brett McMickell and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02b.pdf Reduction and Controllability of Symmetric Distributed Systems with Drift], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3454-3460, 2002. Full paper review.
#Yejun Wei and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02a.pdf Stratified Motion Planning on Non-Smooth Domains with Application to Robotic Legged Locomotion and Manipulation], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3546-3552. Full paper review.
#Bill Goodwine and Milos Zefran, 2002, Feedback Stabilization of a Class of Unstable Nonholonomic Systems, Transactions of the ASME, Journal of Dynamics Systems, Measurement, & Control, 124, pp. 221-230.
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2001/iros01.pdf Reduction and Controllability of Symmetric Distributed Systems with Robotic Applications], Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, Hawaii, pp. 1232-1237. Full paper review.
#S. Alotaibi, M. Sen, Bill Goodwine, and K.T. Yang, 2001, Thermal Control of Heat Exchangers, Proceedings of the 35th National Heat Transfer Conference, NHTC01-12517, Anaheim, CA.
#Yejun Wei and Bill Goodwine,, 2001, Theoretical and Experimental Investigation of Stratified Robotic Manipulation, Proceedings of the 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea. Full paper review.
#Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.
#Bill Goodwine and Gabor Stepan, 2000, "Controlling unstable Rolling Phenomena, Journal of Vibration and Control, 6:1, pp. 137-158, January 2000.
# Qun Ma, Antonio Cardenas, Mike Seelinger, Bill Goodwine and Steven Skaar, 2000, "Supervisory Control of a Mobile Robot Using Point-and-Click Mobile Camera-Space Manipulation," Proceedings of the 4th World Multiconference on Systemics, Cybernetics and Informatics SCI 2000 and The 6th International Conference on Information Systems, Analysis and Synthesis ISAS 2000, Orlando, Florida.
# Bill Goodwine and Yejun Wei, 2000, [http://controls.ame.nd.edu/~bill/papers/2000/allerton.pdf Theoretical and Experimental Investigation of Stratified Robotic Finger Gaiting and Manipulation], Proceedings of the 38th Annual Allerton Conference on Communication, Control and Computing, Allerton, Illinois
# Bill Goodwine and Joel Burdick, Motion Planning for Kinematic Stratified Systems with application to Quasi-Static Legged Locomotion and Finger Gaiting, Proceedings of the Workshop Algorithmic Foundations of Robotics.
# Bill Goodwine and Joel Burdick, [http://controls.ame.nd.edu/~bill/papers/1999/ifac99.pdf Stratified Motion Planning with Application to Robotic Finger Gaiting], Proceedings of the 1999 International Federation of Automatic Control, IFAC'99: 14th World Congress Beijing, China. Full paper review.
# Gabor Stepan and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/1999/ds99.pdf Analysis and Control of Unstable Rolling Wheel Dynamics], 1999 SIAM Conference on Applications of Dynamical Systems, Showbird, UT, 1999, abstract submission
# B. Goodwine, Michael Seelinger, John-David Yoder, Qun Ma and Steven Skaar, [http://controls.ame.nd.edu/~bill/papers/1999/fsr99.pdf Applications of mobile camera-space manipulation], Proceedings of FSR'99: Field and Service Robotics, pages 102-113, Pittsburg, 1999
# Bill Goodwine, 1999, Stratified Motion Planning with Application to Robotic Finger Gaiting, Proceedings of the 1999 IFToMM 10th World Congress, Oulu, Finland. Abstract review.
# Bill Goodwine and Gabor Stepan, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/misk98.pdf Stabilizing Switching Controllers], Proceedings of the 1998 Conference on Numerical Mathematics and Computational Mechanics, Miskolc, Hungary. Abstract review
# Bill Goodwine, Michael Seelinger, Steven B. Skaar and Qun Ma, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/spie98.pdf Nonholonomic Camera Space Manipulation using Cameras Mounted on a Mobile Base], Proceedings of the 1998 SPIE conference on Sensor Fusion and Decentralized Control in Robotic Systems, Boston, Massachusetts. Abstract review
# Bill Goodwine and Joel Burdick, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/icra98.pdf Gait Controllability for Legged Robots], Proceedings of the 1998 IEEE Conference on Robotics and Automation,Leuven, Belgium. Full paper review.
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/thesis.pdf Control of Stratified Systems with Robotic Applications], Ph.D Thesis, California Institute of Technology, 1997
# Bill Goodwine and Joel Burdick, 1997, [http://controls.ame.nd.edu/~bill/papers/1997/icra97.pdf Trajectory Generation for Legged Robotic Systems], Proceedings of the 1997 IEEE Conference on Robotics and Automation, Albuquerque, New Mexico. Full paper review
# Shuuji Kajita, Bill Goodwine and Joel Burdick, Walking Direction Control of a Biped Robot with Point Feet Using Dynamic Effects in 3-D Space, Proceedings of the 1997 Robotics Society of Japan Conference, Tokyo, Japan. 1997 (in Japanese).
# Bill Goodwine and Joel Burdick, [http://controls.ame.nd.edu/~bill/papers/1996/mtns96.pdf Controllability of Kinematic Control Systems on Stratified Configuration Spaces], Mathematical Theory of Networks and Systems, 1996, St. Louis
# Bill Goodwine and Joel Burdick, 1996, [http://controls.ame.nd.edu/~bill/papers/1996/cdc96.pdf Controllability with Unilateral Control Inputs], Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan. Full paper review, 1996, (Vol. 3, pp. 3394-3399
# Bill Goodwine and Gabor Stepan, [http://controls.ame.nd.edu/~bill/papers/1996/enoc96.pdf Stabilization of the Classical Shimmying Wheel], Proceedings of the 2nd European Nonlinear Oscillations Conference, Prague, Czech Republic, 1996
#Bill Goodwine, 1991, Abortion Parental Notification Statutes: Hodgson v. Minnesota, 110 S. Ct. 2926 (1990) and Ohio v. Akron Center for Reproductive Health, 110 S. Ct. 2972 (1990), Harvard Journal of Law & Public Policy, 14:1, pp. 237-247.

==Books and Chapters in Books==
# Bill Goodwine, [http://www.springer.com/mathematics/dynamical+systems/book/978-1-4419-7918-6 Engineering Differential Equations: Theory and Applications], Springer, 2010.
#* Some [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Movies movies] are available illustrating some of the more interesting solutions, generally for PDEs
#* A list of [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Errata errata] is also available
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849318047 Robotics and Automation Handbook], Chapter 3, Inverse Kinematics, Thomas R. Kurfess, Editor, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2001.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2001.

==Erdős Number==
# Erdős, P.; Shapiro, H. S.; Shields, A. L. Large and small subspaces of Hilbert space. Michigan Math. J. 12 1965 169--178.
# Shields, Allen L. Some problems in operator theory. Notes by Michael J. Hoffman. Lecture Notes in Math., 693, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977), pp. 157--167, Springer, Berlin, 1978.
# Marsden, Jerrold E.; Hoffman, Michael J. Basic complex analysis. Second edition. W. H. Freeman and Company, New York, 1987. xiv+604 pp. ISBN: 0-7167-1814-6
# Banavara N. Shashikanth, Jerrold E. Marsden, Joel W. Burdick and Scott D. Kelly, The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vorticesPhys. Fluids 14, 1214 (2002).
# Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.

=Students=

==PhD Students==
* Kevin Leyden, in progress
* Jason Nightingale, Ph.D. defended 8:00 am, June 4, 2012 [http://controls.ame.nd.edu/~bill/students/jason.pdf thesis]
* Dayu Lv, Ph.D. defended March 17, 2011, [http://controls.ame.nd.edu/~bill/students/dayu.pdf thesis]
* Baoyang Deng, Ph.D., defended March 11, 2011 [http://controls.ame.nd.edu/~bill/students/baoyang.pdf thesis]
* Alice Nightingale, Ph.D. defended November 3, 2010 [http://controls.ame.nd.edu/~bill/students/alice.pdf thesis]
* Neil Petroff, Ph.D. defended, October 6, 2006 [http://controls.ame.nd.edu/~bill/students/neil.pdf thesis]
* M. Brett McMickell, Ph.D. defended 2003
* Yejun Wei, Ph.D. defended 2002

==MS Students==
* Ashley Nettleman, M.S., November 2014 [http://controls.ame.nd.edu/~bill/students/ashley.pdf thesis]
* Nicholas Galati, July 15, 2013
* Michael O'Connor, Fall 2011
* Qun (Marc) Ma, M.S., 2000

==Undergraduate Research Projects==

* Patrick O’Meara, “Control and Dynamics of a Fleet of Automobiles,” spring, summer and fall 2013
* Nick Turner, “Mathematics and Theory of Origami,” summer 2013
* Catherine Bentzen, “Jellyfish Propulsion,” summer 2013
* Blair Rasmus, John Gallagher, Derek Wolf, “Development of Feedback Microcontroller for an Inverted Pendulum System for AME 30315” (all three, Fall 2011, John Gallagher continued through Spring 2012)
* Jeff O’Brien, “Synchronization and Limit Cycle Solutions for Coupled Hybrid Systems” (Fall and Spring, 2011)
* John Gallagher, “Describing Function Analysis with Non-Harmonic Basis Functions” (Spring 2012 – started in January)
* Adam Wojcik,. “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Paul Fleury, “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Robert Powers, “Energy storage technologies: a sustainable solution to electrical load shedding in rural Bangladesh,” Spring 2010
* “Raymond LeGrand, "Development of a Microprocessor controlled Inverted Pendulum Experiment,” , Summer and Fall 2010
* Steven Brus, “Homotopy Methods for Coordinated Robotic Systems,” Summer 2010
* Andres Valenzuela, “Bifurcation Measures for Nonlinear Boundary Value Problems in Optimal Control of Mobile Robot Formations,” Fall 2008 and Spring 2009. Undergraduate thesis in Spring 2009
* Blake Shilide, “Aero-Optic Shear Layer Control and Simulation,” Spring, 2005
* Tim Ronan, “MICAbot Programming and TinyOS,” Summer, 2003
* Timothy Kacmar, “Development of a Multi-Manipulator Path Planning Collision Avoidance System,” Fall, 2003
* Meaghan Perry-Eaton, “Investigation of Automotive Fuel Cell Energy System Usage and Feasibility,” Fall, 2003
* Peter Balough, “Development of a Mobile Multi-Robot Simulation Environment in Java and Hardware Development for the TagMote,” Summer and Fall, 2003
* Kristin Dormuth, “MICAbot Programming and TinyOS,” Summer, 2003
* John Aman, “MICAbot Programming and TinyOS,” Summer, 2003
* Denis Sullivan, “MICAbot Programming and TinyOS,” Summer and Fall, 2003
* Thomas Apker, “Investigation of the Efficacy of Switching Multi-Controller Systems,” Spring, 2003
* Daniel Luedtke, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Spring, 2003
* Tommy Ferrara, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Fall, 2003.
* Dennis Abdelnour, “Development Programming for a Mobile Robot,” Spring, 2001.
* Eric Shearer, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer 2000.
* Bethany Wilson, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer, 2000.
* Leonard Conapinski, “Investigation of the Presence of Chaos in a Hybrid Switching System, ” Fall, 2000.

=Research Summary=

===Cyber Physical Systems===

My research focuses primarily on theoretical nonlinear control with recent emphasis on Cyber Physical Systems. Cyber physical systems are systems with highly integrated physical and computational components (often involving the complication of networked communication). They tend to be very large and complex in scale. While many CPS systems exist in the real world, to date there are few general theoretical results available to guide both the design of such systems and the control of such systems. Most existing CPS systems are designed and controlled based upon accumulated real-world industrial knowledge that tends to be industry- or application-specific. My recent work has focused particularly on so-called ''symmetric systems.'' A symmetric system is comprised of many components with the restriction that the components be very closely related and connected together in a "regular" manner. With such restrictions, it is possible to formulate general models and then consider what types of properties remain invariant as components are added to or removed from the system. A related question is how the system behaves as components fail, which is a question of robustness.

===Stratified Systems===

Many interesting and important control systems evolve on
''stratified'' configuration spaces. Roughly speaking, we
will call a configuration manifold stratified if it contains
submanifolds upon which the system is subjected to additional
constraints or has different equations of state. For such
systems, the equations of motion on each submanifold may change
in a non-smooth, or even discontinuous manner, when the system
moves from one submanifold to another. In such cases,
traditional nonlinear control methodologies are inapplicable
because they generally rely upon differentiation in one form or
another. Yet it is the discontinuous nature of such systems
that is often their most important characteristic because the
system must cycle through different submanifolds to effectively
be controlled. Therefore, it is necessary to incorporate
explicitly into control methodologies the non-smooth or
discontinuous nature of these systems.

Robotic systems, in particular, are of this nature. A legged
robot has discontinuous equations of motion near points in the
configuration space where each of its ``feet'' come into contact
with the ground, and it is precisely the ability of the robot to
lift its feet off of the ground that enables it to move about.
Similarly, a robotic hand grasping an object often cannot
reorient the object without lifting its fingers off of the
object. Despite the obvious utility of such systems, however, a
comprehensive framework in which to consider control issues for
such systems does not exist.

The fundamental approach of this work has been to exploit the
physical geometric structure present in such problems to address
control issues such as nonlinear controllability, trajectory
generation and stabilization. The fundamental philosophy is to
generate ''general'' results, i.e., results
independent of a particular robot's number of legs, fingers or
morphology.

===Control of Mechanical Systems===

Most theoretical control results are based upon very generic dynamical systems formulations, such as
<math>\dot x = A x + B u</math> for linear systems or <math>\dot x =f(x) + g(x)u</math> for a nonlinear system. Of course this leads to the question of whether a more restrictive starting point can lead to valuable results. An important area of research along these lines is so-called control of mechanical systems where the equations of motion are not as general, but are assumed from the beginning to come from some first principle of mechanics. We have focused specifically on control of Lagrangian systems that are underactuated. Specifically, it is possible in such a framework to write general expressions for the relationship of the coupling between the controlled degree of freedoms and uncontrolled degrees of freedom, and given such expressions it is possible to know when there is close coupling between them and total decoupling between them. Furthermore, it is often the case that the coupling between the controlled and uncontrolled degrees of freedom is such that it may be only of one sign, ''i.e.'', no matter what is done with the control inputs, the uncontrolled degrees of freedom may only increase (or decrease) in magnitude. Such results have obvious important implications for control algorithms.

===Other Projects===

Other smaller projects include:
* control of aero-optic systems
* predictive biosimulation for human metabolism
* fuzzy logic-based robust control for stratified systems
* model-predictive control for marine navigation.

=Biographical Sketch=

* MS and PhD degrees in Applied Mechanics from the California Institute of Technology in 1993 and 1998, respectively.
* JD degree from Harvard Law School, 1991, ''cum laude''
* Instructor, Assistant Professor, Associate Professor, Department of Aerospace and Mechanical Engineering, University of Notre Dame, 1998 - present.
* Associate Department Chair, Department of Aerospace and Mechanical Engineering, University of Notre Dame, August 2008 - August 2012.
* Member of the Illinois Bar Association, 1991 - present.
* Registered Patent Attorney, 1998 - 2004 (not maintained).
* NSF CAREER Award Recipient.
* Boeing Welliver Faculty Fellow.
* Dockweiler Award for Excellence in Undergraduate Advising, May 2010.
* BP Foundation Outstanding Teacher of the Year, College of Engineering, Spring, 2008.
* Joyce Award (teaching), Spring, 2008.
* University of Notre Dame Kaneb teaching award, Spring, 2005.
* Department of Aerospace and Mechanical Engineering Ruth and Joel Spira Award for Excellence in Teaching, 2003 - 2004 and 2007 - 2008.
* American Society of Engineering Education Illinois/Indiana Section Outstanding Teaching Award, April, 2003.
* Department of Aerospace and Mechanical Engineering Faculty Award (teaching), 1998 - 1999.

=Courses=

* Fall 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=337 AME 30314: Differential Equations, Vibrations and Control I] (121 Students)
* Spring 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=323 AME 50652: Intermediate Controls] (7 Students) and AME 50650: Introduction to Nonlinear Analysis (9 Students)
* Fall 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=309 AME 30314, Differential Equations, Vibrations and Control I] (118 Students)
* Spring 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=304 AME 90951: Geometric Nonlinear Control] (8 students)
* Fall 2012: AME 30314: Differential Equations, Vibrations and Control I (86 Students)
* Spring 2012: [http://controls.ame.nd.edu/courses/viewforum.php?f=289 AME 30315: Differential Equations, Vibrations and Control II] (129 Students)
* Fall 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=274 AME 30314: Differential Equations, Vibrations and Control I] (112 Students)
* Summer 2011: [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Course_Syllabus,_Summer_2011 AME 40590: Intellectual Property for Engineers] [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Homework,_Summer_2011 (homeworks)]
* Spring 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=255 AME 30315: Differential Equations, Vibrations and Control II] (89 Students) and [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Intellectual_Property_for_Engineers AME 40590: Intellectual Property for Engineers] (56 Students) [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Homeworks,_Spring_2011 {homeworks)]
* Fall 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=227 AME 30314: Differential Equations, Vibrations and Control I] (81 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=228 AME 20214: Introduction to Engineering Computing] (131 Students)
* Spring 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=201 AME 30315: Differential Equations, Vibrations and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=202 AME 60652: Advanced Controls (now AME 50562: Intermediate Controls)]
* Fall 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=186 AME 30314: Differential Equations, Vibrations and Control I] (91 students)
* Spring 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=170 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=140 AME 30314: Differential Equations, Vibrations and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=141 AME 20214: Introduction to Engineering Computing]
* Spring 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=124 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=125 AME 30314: Differential Equations, Vibrations and Control I] (86 Students), [http://controls.ame.nd.edu/courses/viewforum.php?f=127 AME 60652: Advanced Controls] (11 Students) and AME 53591: Engineering Seminar Series.
* Spring 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=129 AME 30315: Differential Equations, Vibrations and Control II] (94 Students)
* Fall 2006: [http://controls.ame.nd.edu/courses/viewforum.php?f=130 AME 30314: Differential Equations, Vibrations and Control I] (79 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=131 AME 60611: Mathematical Methods I] (24 Students)
* Fall 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=132 AME 34314: Differential Equations, Vibrations and Control I (London)] and Intermediate Dynamics.
* Spring 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=133 AME 302: Modeling and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=134 Geometric Nonlinear Control]
* Fall 2004: [http://controls.ame.nd.edu/courses/viewforum.php?f=135 AME 301: Modeling and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=136 AME 550: Advanced Controls]
* Spring 2004: [http://controls.ame.nd.edu/courses/ame302/S2004 AME 302: Modeling and Control II] (72 students)
* Fall 2003: [http://controls.ame.nd.edu/courses/ame301/F2003/ AME 301: Modeling and Control I] (54 students) and AME 654: Geometric Nonlinear Control (2 students)
* Spring 2003: [http://controls.ame.nd.edu/courses/ame437/S2003/ AME 437: Control Systems Engineering] (68 students)
* Spring 2002: [http://controls.ame.nd.edu/courses/ame437/S2002/ AME 437: Control Systems Engineering] (64 students)
* Fall 2001: [http://controls.ame.nd.edu/courses/ame654/F2001/ AME 654: Geometric Nonlinear Control] (3 students)
* Spring 2001: [http://controls.ame.nd.edu/courses/ame469/S2001/ AME 469: Introduction to Robotics] (33 students)
* Spring 2000: [http://controls.ame.nd.edu/courses/ame469/S2000/ AME 469: Introduction to Robotics] (48 students), [http://controls.ame.nd.edu/courses/ame437/S2000/ AME 437: Control Systems Engineering] (50 students) and AME 598: Engineering Applications of Artificial Intelligence (5 students).
* Fall 1999: [http://controls.ame.nd.edu/courses/ame698/F1999/ AME 698: Geometric Nonlinear Control] (10 students)
* Spring 1999: [http://controls.ame.nd.edu/courses/ame469/S1999/ AME 469: Introduction to Robotics] (33 students)
* Fall 1998: [http://controls.ame.nd.edu/courses/ame469/F1998/ AME 469: Introduction to Robotics] (12 students)
* Spring 1998: [http://controls.ame.nd.edu/courses/ame437/S1998/ AME 437: Control Systems Engineering] (44 students)

===Course Blog===

In order to be able to interactively answer questions online, I've maintained a [http://controls.ame.nd.edu/courses course blog for all courses since 2002].

===AME 30315 Differential Equations, Vibrations and Control II===
*[[AME 30315 Pendulum Project]]

===AME 40590, Intellectual Property for Engineers===
*[[AME 44590 Course Syllabus, Summer 2011]]
*[[AME 44590 Homework, Summer 2011]]
*[[AME 40590 Intellectual Property for Engineers|AME 40590 Course Content]]
*[[AME 40590 Homeworks, Spring 2011]]

===AME 50652, Intermediate Controls===
*[[AME 50652 Pendulum Project]]

=[[Engineering Differential Equations: Theory and Applications, Springer 2010]]=

=[[Engineering China Summer Program]]=

=[[London CPS Workshop]]=

=[[CDIO Regional Meeting]]=

Main Page

2015-09-16T21:07:50Z

Bill: /* Publications */

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<td width=25%> [[Image:Bill5.jpeg|250px]]</td>
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Bill Goodwine 


Department of Aerospace and Mechanical Engineering 
University of Notre Dame 
Notre Dame, IN 46556 
bill@controls.ame.nd.edu 
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I have moved my homepage here. At least for the time being, my [http://controls.ame.nd.edu/~bill/oldindex.php old one] still exists.
=Publications=
==Papers==
# Kevin Leyden and Bill Goodwine, Using Fractional-Order Differential Equations for Health Monitoring of a System of Cooperating Robots. Submitted to the 2016 IEEE International Conference on Robotics and Automation.
# Bill Goodwine, Towards General Results in Bifurcations in Optimal Solutions for Symmetric Distributed Robotic Formation Control. Submitted to the 2015 IEEE International Symposium on System Integration.
# Baoyang Deng, Michael O'Connor and Bill Goodwine, Bifurcations and Symmetry in Two Optimal Formation Control Problems for Mobile Robotic Systems. Accepted for publication pending revisions in Robotica.
# Nicholas Turner, Bill Goodwine and Mihir Sen, A Review of Origami Applications in Mechanical Engineering, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science (2015): 0954406215597713.
# David C. Post, Bill Goodwine and James P. Schmiedeler, Quantifying Control Authority in Periodic Motions of Underactuated Mobile Robots, Proceedings of the ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2015, DETC2015-47666
#Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2015/icra2015.pdf Symmetries and Reduction for Multi-Agent Control], Proceedings of the 2015 IEEE International Conference on Robotics and Automation, pp 5390-5396
# Bill Goodwine and Kevin Leyden, Recent Results in Fractional-Order Modeling for Multi-Agent Systems and Linear Friction Welding, 8th Vienna International Conference on Mathematical Modelling - MATHMOD 2015, abstract submission
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icarcv2014.pdf Fractional-Order Dynamics in a Random, Approximately Scale-Free Network of Agents], Proceedings of the 2014 International Conference on Control, Automation, Robotics and Vision, pp 1581 - 1586
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/ifac14.pdf Nonlinear Stability of Approximately Symmetric Large-Scale Systems], Proceedings of the 2014 IFAC World Congress, Cape Town, South Africa, pp 845-850
# Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/mtns-282.pdf Symmetries of Multiagent Systems and Formation Stability], Proceedings of the 2014 International Symposium on Mathematical Theory of Networks and Systems (MTNS 14), pp 1340-1343 (extended abstract review)
# Bill Goodwine, [[Compositional Boundedness of Solutions for Symmetric Nonautonomous Control Systems]], Proceedings of the 2014 Mediterranean Conference on Control and Automation, pp 798 - 803
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icra-1441.pdf Modeling a Multi-Robot System with Fractional-Order Differential Equations], Proceedings of the 2014 IEEE International Conference on Robotics and Automation, Hong Kong, pp 1763-1768
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2013/automatica13.pdf Multi-agent compositional stability exploiting system symmetries], Automatica 49(11): 3158-3166, 2013
# Panos J Antsaklis,Bill Goodwine, Vijay Gupta, Michael J. McCourt, Yue Wang, Po Wu, Meng Xia, Han Yu, and Feng Zhu, [http://controls.ame.nd.edu/~bill/papers/2013/ejc13.pdf Control of cyberphysical systems using passivity and dissipativity based methods], European Journal of Control 19, no. 5 (2013): 379-388
# Bill Goodwine [http://controls.ame.nd.edu/~bill/papers/2013/med-2013a.pdf Compositional stability of approximately symmetric systems: Initial results], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED), pp. 1470-1476 IEEE, 2013
# Jason Nightingale and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2013/med-2013b.pdf An algorithm for stopping a class of underactuated nonlinear mechanical robotic systems], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED) pp. 531-536, 2013
# Alice M. Nightingale, Bill Goodwine, Michael Lemmon and Eric Jumper [http://controls.ame.nd.edu/~bill/papers/2013/aiaa13.pdf Phase-Locked-Loop Adaptive-Optic Controller and Simulated Shear Layer Correction], AIAA journal, 51(11), 2714-2726, 2013
# John Gallagher and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/cdio12.pdf CDIO-Oriented Inverted Pendulum Control Project for Undergraduate Engineering Students], 2012 CDIO International Conference, Brisbane, Australia, 2012
# Michael O'Connor and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/med12a.pdf Symmetry-Breaking in Bifurcations of Optimal Solutions for Coordinated Nonholonomic Robotic Control], Proceedings of the 2012 Mediterranean Conference on Control & Automation (MED), pp. 1554-1559, 2012
# Janos Sztipanovits, Xenofon Koutsoukos, Gabor Karsai, Nicholas Kottenstette, Panos Antsaklis, Vijay Gupta, Bill Goodwine, John Baras, and Shige Wang, [http://controls.ame.nd.edu/~bill/papers/2011/procieee11.pdf Toward a science of cyber–physical system integration], Proceedings of the IEEE 100, no. 1 (2012): 29-44
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2011/icra11.pdf Fault-Tolerant Multiagent Robotic Formation Control Exploiting System Symmetries], Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, pp. 2872-2877
# Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2011/ifac11.pdf Nonlinear Disturbance Decoupling for a Mobile Robotic Manipulator over Uneven Terrain], Proceedings of the 2011 International Federation of Automatic Control World Congress, Milan, Italy, Vol. 18, No. 1, pp. 6930-6936
# Dayu Lv and Bill Goodwine, "Pancreas Modeling by a Deterministic Optimization Method" 'International Journal of Data Mining and Bioinformatics,' Volume 5, Number 3, Pages 308-320 (2011).
# Goodwine, Bill, and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent coordination exploiting system symmetries], American Control Conference (ACC), 2010, pp. 830-835
# Baoyang Deng, Mihir Sen, and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/acc09.pdf Bifurcations and symmetries of optimal solutions for distributed robotic systems], Proceedings of the 2009 American Control Conference, St. Louis, MO, pp. 4127-4133
#Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icarcv10.pdf Nonlinear Disturbance Decoupling for a Nonholonomic Mobile Robotic Manipulation Platform], Proceedings of the Eleventh International Conference on Control, Automation, Robotics and Vision (ICARCV 2010), Singapore, pp. 1530-1535
#Neil Petroff and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/iros10.pdf Nonholonomic and Stratified Robotic Manipulation Supplemented with Fuzzy Control: Theory and Experiment], Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, pp. 1202-1208
#Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent Coordination Exploiting System Symmetries], Proceedings of the 2010 American Controls Conference, pp. 830-835
#Baoyang Deng, Andreas K. Valenzuela and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icra10a.pdf Bifurcations of Optimal Solutions for Coordinated Robotic Systems: Numerical and Homotopy Methods], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 4475-4480
#Bill Goodwine and Jason Nightingale, [http://controls.ame.nd.edu/~bill/papers/2010/icra10b.pdf The Effect of Dynamic Singularities on Robotic Control and Design], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 5213-5218
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/bibm09.pdf Pancreas Modeling from IVGTT Data Using a Deterministic Optimal Search], Proceedings of the 2009 IEEE International Conference on Bioinformatics & Biomedicine, (35% acceptance rate) Washington, D.C.
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/wafr09.pdf A Stopping Algorithm for Mechanical Systems], Algorithmic Foundations of Robotics VIII, Gregory S. Chirikjian, et al., editors, Eighth International Workshop on the Algorithmic Foundations of Robotics, Guanajuato, Mexico, 2009, pp. 167-180
#Jason Nightingale, Richard Hind and Bill Goodwine, "Geometric analysis of a class of constrained mechanical control systems in the nonzero velocity setting,"Proceedings of the 17th International Federation of Automatic Control (IFAC) World Congress, Seoul, Korea July, 2008, pp 1171-1176
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/icra08.pdf Intrinsic Vector-Valued Symmetric Form for Simple Mechanical Control Systems in the Nonzero Velocity Setting], Proceedings of the 2008 IEEE International Conference on Robotics and Automation, (43.4% acceptance rate) Pasadena, CA, May, 2008
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/biodevices08.pdf A New Metabolism Model for Human Skeletal Muscle], Proceedings of the IEEE International Conference on Biomedical Electronics and Devices, January, 2008, Maderia, Portugal
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2007/ijrr07.pdf Motion Planning for Nonlinear Symmetric Distributed Robotic Formation], International Journal of Robotics Research, 2007, 26:10, pp. 1025-1042
#Alice Nightingale, Bill Goodwine, Michael Lemmon, and Eric Jumper, 2007, "Feedforward Adaptive-Optic System Identification Analysis for Mitigating Aero-Optic Disturbances," Proceedings of the AIAA 2007 Plasmadynamics and Lasers Conference.
#Alice Nightingale, Daniel D. Duffin, Michael Lemmon, Bill Goodwine and Eric Jumper, 2005, "Adaptive-Optic Correction of a Regularized Compressible Shear Layer," Proceedings of the 37th AIAA Plasmadynamics and Lasers Conference, San Francisco, CA, June, 2006.
#Alice Nightingale, Bill Goodwine and Eric Jumper, 2005, "Regularizing Shear Layer for Adaptive Optics Control Application," accepted for presentation at the 36th AIAA Plasmadynamics and Lasers Conference.
# Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2004/ra04.pdf Stratified motion planning on nonsmooth domains with robotic applications], IEEE Transactions on Robotics and Automation 20.1 (2004): 128-132
#Yejun Wei, Bill Goodwine and Steven B. Skaar, 2004, "Kinematics of Vision-Based Stratified Robotic Manipulation," Proceedings of the 11th IFToMM World Congress, Tianjin, China. Abstract review.
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, "Flow-based control of temperature in long ducts," 2004, International Journal of Heat and Mass Transfer, 47,pp. 4995-5009.
# M. Brett McMickell and Bill Goodwine, 2003, "Reduction and Controllability of Nonlinear Symmetric Distributed Systems," International Journal of Control, 76:18, pp. 1809-1822, 2003.
#M. Brett McMickell and Bill Goodwine, 2003, [http://controls.ame.nd.edu/~bill/papers/2003/icra03a.pdf Reduced Order Motion Planning for Nonlinear Symmetric Distributed Robotic Systems], Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, 2003, "Controllability of Cross-Flow Heat Exchangers," International Journal of Heat and Mass Transfer, 47, pp. 913-924
#M. Brett McMickell and Bill Goodwine, 2003, MICAbot: A Platform for Large Scale Coordinated Distributed Mobile Robot Control, Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review.
#S. Alotaibi, J.W. Goodwine, M. Sen and K.T. Yang, 2003, Controllability of conductive-convective systems, Proceedings of the 6th ASME-JSME Thermal Engineering Joint Conference, Hawaii, Paper No. TED-AJ03-247, pp. 1-6.
#Antonio Cardenas, Bill Goodwine, Steven B. Skaar and Michael Seelinger, Vision-Based Control of a Mobile Base and On-Board Arm, The International Journal of Robotic Research, 22: 9, pp. 677-698, 2003
#Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/icarcv2002.pdf Vision-Based Non-Smooth Kinematic Stratified Object Manipulation], Proceedings of the 2002 Seventh Annual Conference on Control, Automation, Robotics and Vision, Singapore, 2002
#Yejun Wei, S.B. Skaar and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/iros02.pdf Vision-Based Stratified Robotic Manipulation], Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, 2002
#S. Batill, S. Skaar, R. Nelson, B. Goodwine, J. Mason, and M. Sen, 2002, Development of a Curriculum for Mechanical Engineering Based Upon Intelligent Systems and Automation, Session 1526, Proceedings of the 2002 American Society for Engineering Education Annual Conference and Exposition, 2002
#S. Alotaibi, Mihir Sen, B. Goodwine, and K.T. Yang, Numerical Simulation of Thermal Control of Heat Exchangers, Numerical Heat Transfer Journal, Part A: Applications, 41:3, pp. 229-244, 2002
#Bill Goodwine and Joel Burdick, A General Method for Motion Planning for Quasi-Static Legged Robotic Locomotion," IEEE International Journal of Robotics and Automation, 18:2, pp. 209-222, 2002
#M. Brett McMickell and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02b.pdf Reduction and Controllability of Symmetric Distributed Systems with Drift], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3454-3460, 2002. Full paper review.
#Yejun Wei and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02a.pdf Stratified Motion Planning on Non-Smooth Domains with Application to Robotic Legged Locomotion and Manipulation], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3546-3552. Full paper review.
#Bill Goodwine and Milos Zefran, 2002, Feedback Stabilization of a Class of Unstable Nonholonomic Systems, Transactions of the ASME, Journal of Dynamics Systems, Measurement, & Control, 124, pp. 221-230.
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2001/iros01.pdf Reduction and Controllability of Symmetric Distributed Systems with Robotic Applications], Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, Hawaii, pp. 1232-1237. Full paper review.
#S. Alotaibi, M. Sen, Bill Goodwine, and K.T. Yang, 2001, Thermal Control of Heat Exchangers, Proceedings of the 35th National Heat Transfer Conference, NHTC01-12517, Anaheim, CA.
#Yejun Wei and Bill Goodwine,, 2001, Theoretical and Experimental Investigation of Stratified Robotic Manipulation, Proceedings of the 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea. Full paper review.
#Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.
#Bill Goodwine and Gabor Stepan, 2000, "Controlling unstable Rolling Phenomena, Journal of Vibration and Control, 6:1, pp. 137-158, January 2000.
# Qun Ma, Antonio Cardenas, Mike Seelinger, Bill Goodwine and Steven Skaar, 2000, "Supervisory Control of a Mobile Robot Using Point-and-Click Mobile Camera-Space Manipulation," Proceedings of the 4th World Multiconference on Systemics, Cybernetics and Informatics SCI 2000 and The 6th International Conference on Information Systems, Analysis and Synthesis ISAS 2000, Orlando, Florida.
# Bill Goodwine and Yejun Wei, 2000, [http://controls.ame.nd.edu/~bill/papers/2000/allerton.pdf Theoretical and Experimental Investigation of Stratified Robotic Finger Gaiting and Manipulation], Proceedings of the 38th Annual Allerton Conference on Communication, Control and Computing, Allerton, Illinois
# Bill Goodwine and Joel Burdick, Motion Planning for Kinematic Stratified Systems with application to Quasi-Static Legged Locomotion and Finger Gaiting, Proceedings of the Workshop Algorithmic Foundations of Robotics.
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/1999/ifac99.pdf Stratified Motion Planning with Application to Robotic Finger Gaiting], Proceedings of the 1999 International Federation of Automatic Control, IFAC'99: 14th World Congress Beijing, China. Full paper review.
# Gabor Stepan and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/1999/ds99.pdf Analysis and Control of Unstable Rolling Wheel Dynamics], 1999 SIAM Conference on Applications of Dynamical Systems, Showbird, UT, 1999, abstract submission
# B. Goodwine, Michael Seelinger, John-David Yoder, Qun Ma and Steven Skaar, [http://controls.ame.nd.edu/~bill/papers/1999/fsr99.pdf Applications of mobile camera-space manipulation], Proceedings of FSR'99: Field and Service Robotics, pages 102-113, Pittsburg, 1999
# Bill Goodwine, 1999, Stratified Motion Planning with Application to Robotic Finger Gaiting, Proceedings of the 1999 IFToMM 10th World Congress, Oulu, Finland. Abstract review.
# Bill Goodwine and Gabor Stepan, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/misk98.pdf Stabilizing Switching Controllers], Proceedings of the 1998 Conference on Numerical Mathematics and Computational Mechanics, Miskolc, Hungary. Abstract review
# Bill Goodwine, Michael Seelinger, Steven B. Skaar and Qun Ma, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/spie98.pdf Nonholonomic Camera Space Manipulation using Cameras Mounted on a Mobile Base], Proceedings of the 1998 SPIE conference on Sensor Fusion and Decentralized Control in Robotic Systems, Boston, Massachusetts. Abstract review
# Bill Goodwine and Joel Burdick, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/icra98.pdf Gait Controllability for Legged Robots], Proceedings of the 1998 IEEE Conference on Robotics and Automation,Leuven, Belgium. Full paper review.
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/thesis.pdf Control of Stratified Systems with Robotic Applications], Ph.D Thesis, California Institute of Technology, 1997
# Bill Goodwine and Joel Burdick, 1997, [http://controls.ame.nd.edu/~bill/papers/1997/icra97.pdf Trajectory Generation for Legged Robotic Systems], Proceedings of the 1997 IEEE Conference on Robotics and Automation, Albuquerque, New Mexico. Full paper review
# Shuuji Kajita, Bill Goodwine and Joel Burdick, Walking Direction Control of a Biped Robot with Point Feet Using Dynamic Effects in 3-D Space, Proceedings of the 1997 Robotics Society of Japan Conference, Tokyo, Japan. 1997 (in Japanese).
# Bill Goodwine and Joel Burdick, [http://controls.ame.nd.edu/~bill/papers/1996/mtns96.pdf Controllability of Kinematic Control Systems on Stratified Configuration Spaces], Mathematical Theory of Networks and Systems, 1996, St. Louis
# Bill Goodwine and Joel Burdick, 1996, [http://controls.ame.nd.edu/~bill/papers/1996/cdc96.pdf Controllability with Unilateral Control Inputs], Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan. Full paper review, 1996, (Vol. 3, pp. 3394-3399
# Bill Goodwine and Gabor Stepan, [http://controls.ame.nd.edu/~bill/papers/1996/enoc96.pdf Stabilization of the Classical Shimmying Wheel], Proceedings of the 2nd European Nonlinear Oscillations Conference, Prague, Czech Republic, 1996
#Bill Goodwine, 1991, Abortion Parental Notification Statutes: Hodgson v. Minnesota, 110 S. Ct. 2926 (1990) and Ohio v. Akron Center for Reproductive Health, 110 S. Ct. 2972 (1990), Harvard Journal of Law & Public Policy, 14:1, pp. 237-247.

==Books and Chapters in Books==
# Bill Goodwine, [http://www.springer.com/mathematics/dynamical+systems/book/978-1-4419-7918-6 Engineering Differential Equations: Theory and Applications], Springer, 2010.
#* Some [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Movies movies] are available illustrating some of the more interesting solutions, generally for PDEs
#* A list of [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Errata errata] is also available
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849318047 Robotics and Automation Handbook], Chapter 3, Inverse Kinematics, Thomas R. Kurfess, Editor, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2001.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2001.

==Erdős Number==
# Erdős, P.; Shapiro, H. S.; Shields, A. L. Large and small subspaces of Hilbert space. Michigan Math. J. 12 1965 169--178.
# Shields, Allen L. Some problems in operator theory. Notes by Michael J. Hoffman. Lecture Notes in Math., 693, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977), pp. 157--167, Springer, Berlin, 1978.
# Marsden, Jerrold E.; Hoffman, Michael J. Basic complex analysis. Second edition. W. H. Freeman and Company, New York, 1987. xiv+604 pp. ISBN: 0-7167-1814-6
# Banavara N. Shashikanth, Jerrold E. Marsden, Joel W. Burdick and Scott D. Kelly, The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vorticesPhys. Fluids 14, 1214 (2002).
# Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.

=Students=

==PhD Students==
* Kevin Leyden, in progress
* Jason Nightingale, Ph.D. defended 8:00 am, June 4, 2012 [http://controls.ame.nd.edu/~bill/students/jason.pdf thesis]
* Dayu Lv, Ph.D. defended March 17, 2011, [http://controls.ame.nd.edu/~bill/students/dayu.pdf thesis]
* Baoyang Deng, Ph.D., defended March 11, 2011 [http://controls.ame.nd.edu/~bill/students/baoyang.pdf thesis]
* Alice Nightingale, Ph.D. defended November 3, 2010 [http://controls.ame.nd.edu/~bill/students/alice.pdf thesis]
* Neil Petroff, Ph.D. defended, October 6, 2006 [http://controls.ame.nd.edu/~bill/students/neil.pdf thesis]
* M. Brett McMickell, Ph.D. defended 2003
* Yejun Wei, Ph.D. defended 2002

==MS Students==
* Ashley Nettleman, M.S., November 2014 [http://controls.ame.nd.edu/~bill/students/ashley.pdf thesis]
* Nicholas Galati, July 15, 2013
* Michael O'Connor, Fall 2011
* Qun (Marc) Ma, M.S., 2000

==Undergraduate Research Projects==

* Patrick O’Meara, “Control and Dynamics of a Fleet of Automobiles,” spring, summer and fall 2013
* Nick Turner, “Mathematics and Theory of Origami,” summer 2013
* Catherine Bentzen, “Jellyfish Propulsion,” summer 2013
* Blair Rasmus, John Gallagher, Derek Wolf, “Development of Feedback Microcontroller for an Inverted Pendulum System for AME 30315” (all three, Fall 2011, John Gallagher continued through Spring 2012)
* Jeff O’Brien, “Synchronization and Limit Cycle Solutions for Coupled Hybrid Systems” (Fall and Spring, 2011)
* John Gallagher, “Describing Function Analysis with Non-Harmonic Basis Functions” (Spring 2012 – started in January)
* Adam Wojcik,. “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Paul Fleury, “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Robert Powers, “Energy storage technologies: a sustainable solution to electrical load shedding in rural Bangladesh,” Spring 2010
* “Raymond LeGrand, "Development of a Microprocessor controlled Inverted Pendulum Experiment,” , Summer and Fall 2010
* Steven Brus, “Homotopy Methods for Coordinated Robotic Systems,” Summer 2010
* Andres Valenzuela, “Bifurcation Measures for Nonlinear Boundary Value Problems in Optimal Control of Mobile Robot Formations,” Fall 2008 and Spring 2009. Undergraduate thesis in Spring 2009
* Blake Shilide, “Aero-Optic Shear Layer Control and Simulation,” Spring, 2005
* Tim Ronan, “MICAbot Programming and TinyOS,” Summer, 2003
* Timothy Kacmar, “Development of a Multi-Manipulator Path Planning Collision Avoidance System,” Fall, 2003
* Meaghan Perry-Eaton, “Investigation of Automotive Fuel Cell Energy System Usage and Feasibility,” Fall, 2003
* Peter Balough, “Development of a Mobile Multi-Robot Simulation Environment in Java and Hardware Development for the TagMote,” Summer and Fall, 2003
* Kristin Dormuth, “MICAbot Programming and TinyOS,” Summer, 2003
* John Aman, “MICAbot Programming and TinyOS,” Summer, 2003
* Denis Sullivan, “MICAbot Programming and TinyOS,” Summer and Fall, 2003
* Thomas Apker, “Investigation of the Efficacy of Switching Multi-Controller Systems,” Spring, 2003
* Daniel Luedtke, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Spring, 2003
* Tommy Ferrara, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Fall, 2003.
* Dennis Abdelnour, “Development Programming for a Mobile Robot,” Spring, 2001.
* Eric Shearer, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer 2000.
* Bethany Wilson, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer, 2000.
* Leonard Conapinski, “Investigation of the Presence of Chaos in a Hybrid Switching System, ” Fall, 2000.

=Research Summary=

===Cyber Physical Systems===

My research focuses primarily on theoretical nonlinear control with recent emphasis on Cyber Physical Systems. Cyber physical systems are systems with highly integrated physical and computational components (often involving the complication of networked communication). They tend to be very large and complex in scale. While many CPS systems exist in the real world, to date there are few general theoretical results available to guide both the design of such systems and the control of such systems. Most existing CPS systems are designed and controlled based upon accumulated real-world industrial knowledge that tends to be industry- or application-specific. My recent work has focused particularly on so-called ''symmetric systems.'' A symmetric system is comprised of many components with the restriction that the components be very closely related and connected together in a "regular" manner. With such restrictions, it is possible to formulate general models and then consider what types of properties remain invariant as components are added to or removed from the system. A related question is how the system behaves as components fail, which is a question of robustness.

===Stratified Systems===

Many interesting and important control systems evolve on
''stratified'' configuration spaces. Roughly speaking, we
will call a configuration manifold stratified if it contains
submanifolds upon which the system is subjected to additional
constraints or has different equations of state. For such
systems, the equations of motion on each submanifold may change
in a non-smooth, or even discontinuous manner, when the system
moves from one submanifold to another. In such cases,
traditional nonlinear control methodologies are inapplicable
because they generally rely upon differentiation in one form or
another. Yet it is the discontinuous nature of such systems
that is often their most important characteristic because the
system must cycle through different submanifolds to effectively
be controlled. Therefore, it is necessary to incorporate
explicitly into control methodologies the non-smooth or
discontinuous nature of these systems.

Robotic systems, in particular, are of this nature. A legged
robot has discontinuous equations of motion near points in the
configuration space where each of its ``feet'' come into contact
with the ground, and it is precisely the ability of the robot to
lift its feet off of the ground that enables it to move about.
Similarly, a robotic hand grasping an object often cannot
reorient the object without lifting its fingers off of the
object. Despite the obvious utility of such systems, however, a
comprehensive framework in which to consider control issues for
such systems does not exist.

The fundamental approach of this work has been to exploit the
physical geometric structure present in such problems to address
control issues such as nonlinear controllability, trajectory
generation and stabilization. The fundamental philosophy is to
generate ''general'' results, i.e., results
independent of a particular robot's number of legs, fingers or
morphology.

===Control of Mechanical Systems===

Most theoretical control results are based upon very generic dynamical systems formulations, such as
<math>\dot x = A x + B u</math> for linear systems or <math>\dot x =f(x) + g(x)u</math> for a nonlinear system. Of course this leads to the question of whether a more restrictive starting point can lead to valuable results. An important area of research along these lines is so-called control of mechanical systems where the equations of motion are not as general, but are assumed from the beginning to come from some first principle of mechanics. We have focused specifically on control of Lagrangian systems that are underactuated. Specifically, it is possible in such a framework to write general expressions for the relationship of the coupling between the controlled degree of freedoms and uncontrolled degrees of freedom, and given such expressions it is possible to know when there is close coupling between them and total decoupling between them. Furthermore, it is often the case that the coupling between the controlled and uncontrolled degrees of freedom is such that it may be only of one sign, ''i.e.'', no matter what is done with the control inputs, the uncontrolled degrees of freedom may only increase (or decrease) in magnitude. Such results have obvious important implications for control algorithms.

===Other Projects===

Other smaller projects include:
* control of aero-optic systems
* predictive biosimulation for human metabolism
* fuzzy logic-based robust control for stratified systems
* model-predictive control for marine navigation.

=Biographical Sketch=

* MS and PhD degrees in Applied Mechanics from the California Institute of Technology in 1993 and 1998, respectively.
* JD degree from Harvard Law School, 1991, ''cum laude''
* Instructor, Assistant Professor, Associate Professor, Department of Aerospace and Mechanical Engineering, University of Notre Dame, 1998 - present.
* Associate Department Chair, Department of Aerospace and Mechanical Engineering, University of Notre Dame, August 2008 - August 2012.
* Member of the Illinois Bar Association, 1991 - present.
* Registered Patent Attorney, 1998 - 2004 (not maintained).
* NSF CAREER Award Recipient.
* Boeing Welliver Faculty Fellow.
* Dockweiler Award for Excellence in Undergraduate Advising, May 2010.
* BP Foundation Outstanding Teacher of the Year, College of Engineering, Spring, 2008.
* Joyce Award (teaching), Spring, 2008.
* University of Notre Dame Kaneb teaching award, Spring, 2005.
* Department of Aerospace and Mechanical Engineering Ruth and Joel Spira Award for Excellence in Teaching, 2003 - 2004 and 2007 - 2008.
* American Society of Engineering Education Illinois/Indiana Section Outstanding Teaching Award, April, 2003.
* Department of Aerospace and Mechanical Engineering Faculty Award (teaching), 1998 - 1999.

=Courses=

* Fall 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=337 AME 30314: Differential Equations, Vibrations and Control I] (121 Students)
* Spring 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=323 AME 50652: Intermediate Controls] (7 Students) and AME 50650: Introduction to Nonlinear Analysis (9 Students)
* Fall 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=309 AME 30314, Differential Equations, Vibrations and Control I] (118 Students)
* Spring 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=304 AME 90951: Geometric Nonlinear Control] (8 students)
* Fall 2012: AME 30314: Differential Equations, Vibrations and Control I (86 Students)
* Spring 2012: [http://controls.ame.nd.edu/courses/viewforum.php?f=289 AME 30315: Differential Equations, Vibrations and Control II] (129 Students)
* Fall 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=274 AME 30314: Differential Equations, Vibrations and Control I] (112 Students)
* Summer 2011: [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Course_Syllabus,_Summer_2011 AME 40590: Intellectual Property for Engineers] [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Homework,_Summer_2011 (homeworks)]
* Spring 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=255 AME 30315: Differential Equations, Vibrations and Control II] (89 Students) and [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Intellectual_Property_for_Engineers AME 40590: Intellectual Property for Engineers] (56 Students) [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Homeworks,_Spring_2011 {homeworks)]
* Fall 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=227 AME 30314: Differential Equations, Vibrations and Control I] (81 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=228 AME 20214: Introduction to Engineering Computing] (131 Students)
* Spring 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=201 AME 30315: Differential Equations, Vibrations and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=202 AME 60652: Advanced Controls (now AME 50562: Intermediate Controls)]
* Fall 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=186 AME 30314: Differential Equations, Vibrations and Control I] (91 students)
* Spring 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=170 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=140 AME 30314: Differential Equations, Vibrations and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=141 AME 20214: Introduction to Engineering Computing]
* Spring 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=124 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=125 AME 30314: Differential Equations, Vibrations and Control I] (86 Students), [http://controls.ame.nd.edu/courses/viewforum.php?f=127 AME 60652: Advanced Controls] (11 Students) and AME 53591: Engineering Seminar Series.
* Spring 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=129 AME 30315: Differential Equations, Vibrations and Control II] (94 Students)
* Fall 2006: [http://controls.ame.nd.edu/courses/viewforum.php?f=130 AME 30314: Differential Equations, Vibrations and Control I] (79 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=131 AME 60611: Mathematical Methods I] (24 Students)
* Fall 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=132 AME 34314: Differential Equations, Vibrations and Control I (London)] and Intermediate Dynamics.
* Spring 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=133 AME 302: Modeling and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=134 Geometric Nonlinear Control]
* Fall 2004: [http://controls.ame.nd.edu/courses/viewforum.php?f=135 AME 301: Modeling and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=136 AME 550: Advanced Controls]
* Spring 2004: [http://controls.ame.nd.edu/courses/ame302/S2004 AME 302: Modeling and Control II] (72 students)
* Fall 2003: [http://controls.ame.nd.edu/courses/ame301/F2003/ AME 301: Modeling and Control I] (54 students) and AME 654: Geometric Nonlinear Control (2 students)
* Spring 2003: [http://controls.ame.nd.edu/courses/ame437/S2003/ AME 437: Control Systems Engineering] (68 students)
* Spring 2002: [http://controls.ame.nd.edu/courses/ame437/S2002/ AME 437: Control Systems Engineering] (64 students)
* Fall 2001: [http://controls.ame.nd.edu/courses/ame654/F2001/ AME 654: Geometric Nonlinear Control] (3 students)
* Spring 2001: [http://controls.ame.nd.edu/courses/ame469/S2001/ AME 469: Introduction to Robotics] (33 students)
* Spring 2000: [http://controls.ame.nd.edu/courses/ame469/S2000/ AME 469: Introduction to Robotics] (48 students), [http://controls.ame.nd.edu/courses/ame437/S2000/ AME 437: Control Systems Engineering] (50 students) and AME 598: Engineering Applications of Artificial Intelligence (5 students).
* Fall 1999: [http://controls.ame.nd.edu/courses/ame698/F1999/ AME 698: Geometric Nonlinear Control] (10 students)
* Spring 1999: [http://controls.ame.nd.edu/courses/ame469/S1999/ AME 469: Introduction to Robotics] (33 students)
* Fall 1998: [http://controls.ame.nd.edu/courses/ame469/F1998/ AME 469: Introduction to Robotics] (12 students)
* Spring 1998: [http://controls.ame.nd.edu/courses/ame437/S1998/ AME 437: Control Systems Engineering] (44 students)

===Course Blog===

In order to be able to interactively answer questions online, I've maintained a [http://controls.ame.nd.edu/courses course blog for all courses since 2002].

===AME 30315 Differential Equations, Vibrations and Control II===
*[[AME 30315 Pendulum Project]]

===AME 40590, Intellectual Property for Engineers===
*[[AME 44590 Course Syllabus, Summer 2011]]
*[[AME 44590 Homework, Summer 2011]]
*[[AME 40590 Intellectual Property for Engineers|AME 40590 Course Content]]
*[[AME 40590 Homeworks, Spring 2011]]

===AME 50652, Intermediate Controls===
*[[AME 50652 Pendulum Project]]

=[[Engineering Differential Equations: Theory and Applications, Springer 2010]]=

=[[Engineering China Summer Program]]=

=[[London CPS Workshop]]=

=[[CDIO Regional Meeting]]=

Main Page

2015-09-16T20:58:49Z

Bill: /* Papers */

<table border=0 width=100%>
<tr>
<td width=25%> [[Image:Bill5.jpeg|250px]]</td>
<td align=center>

Bill Goodwine 


Department of Aerospace and Mechanical Engineering 
University of Notre Dame 
Notre Dame, IN 46556 
bill@controls.ame.nd.edu 
</td>
</tr>
</table>

I have moved my homepage here. At least for the time being, my [http://controls.ame.nd.edu/~bill/oldindex.php old one] still exists.
=Publications=
==Papers==
# Kevin Leyden and Bill Goodwine, Using Fractional-Order Differential Equations for Health Monitoring of a System of Cooperating Robots. Submitted to the 2016 IEEE International Conference on Robotics and Automation.
# Bill Goodwine, Towards General Results in Bifurcations in Optimal Solutions for Symmetric Distributed Robotic Formation Control. Submitted to the 2015 IEEE International Symposium on System Integration.
# Baoyang Deng, Michael O'Connor and Bill Goodwine, Bifurcations and Symmetry in Two Optimal Formation Control Problems for Mobile Robotic Systems. Accepted for publication pending revisions in Robotica.
# Nicholas Turner, Bill Goodwine and Mihir Sen, A Review of Origami Applications in Mechanical Engineering, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science (2015): 0954406215597713.
# David C. Post, Bill Goodwine and James P. Schmiedeler, Quantifying Control Authority in Periodic Motions of Underactuated Mobile Robots, Proceedings of the ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2015, DETC2015-47666
#Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2015/icra2015.pdf Symmetries and Reduction for Multi-Agent Control], Proceedings of the 2015 IEEE International Conference on Robotics and Automation, pp 5390-5396
# Bill Goodwine and Kevin Leyden, Recent Results in Fractional-Order Modeling for Multi-Agent Systems and Linear Friction Welding, 8th Vienna International Conference on Mathematical Modelling - MATHMOD 2015, abstract submission
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icarcv2014.pdf Fractional-Order Dynamics in a Random, Approximately Scale-Free Network of Agents], Proceedings of the 2014 International Conference on Control, Automation, Robotics and Vision, pp 1581 - 1586
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/ifac14.pdf Nonlinear Stability of Approximately Symmetric Large-Scale Systems], Proceedings of the 2014 IFAC World Congress, Cape Town, South Africa, pp 845-850
# Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/mtns-282.pdf Symmetries of Multiagent Systems and Formation Stability], Proceedings of the 2014 International Symposium on Mathematical Theory of Networks and Systems (MTNS 14), pp 1340-1343 (extended abstract review)
# Bill Goodwine, [[Compositional Boundedness of Solutions for Symmetric Nonautonomous Control Systems]], Proceedings of the 2014 Mediterranean Conference on Control and Automation
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icra-1441.pdf Modeling a Multi-Robot System with Fractional-Order Differential Equations], Proceedings of the 2014 IEEE International Conference on Robotics and Automation, Hong Kong, pp 1763-1768
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2013/automatica13.pdf Multi-agent compositional stability exploiting system symmetries], Automatica 49(11): 3158-3166, 2013
# Panos J Antsaklis,Bill Goodwine, Vijay Gupta, Michael J. McCourt, Yue Wang, Po Wu, Meng Xia, Han Yu, and Feng Zhu, [http://controls.ame.nd.edu/~bill/papers/2013/ejc13.pdf Control of cyberphysical systems using passivity and dissipativity based methods], European Journal of Control 19, no. 5 (2013): 379-388
# Bill Goodwine [http://controls.ame.nd.edu/~bill/papers/2013/med-2013a.pdf Compositional stability of approximately symmetric systems: Initial results], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED), pp. 1470-1476 IEEE, 2013
# Jason Nightingale and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2013/med-2013b.pdf An algorithm for stopping a class of underactuated nonlinear mechanical robotic systems], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED) pp. 531-536, 2013
# Alice M. Nightingale, Bill Goodwine, Michael Lemmon and Eric Jumper [http://controls.ame.nd.edu/~bill/papers/2013/aiaa13.pdf Phase-Locked-Loop Adaptive-Optic Controller and Simulated Shear Layer Correction], AIAA journal, 51(11), 2714-2726, 2013
# John Gallagher and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/cdio12.pdf CDIO-Oriented Inverted Pendulum Control Project for Undergraduate Engineering Students], 2012 CDIO International Conference, Brisbane, Australia, 2012
# Michael O'Connor and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/med12a.pdf Symmetry-Breaking in Bifurcations of Optimal Solutions for Coordinated Nonholonomic Robotic Control], Proceedings of the 2012 Mediterranean Conference on Control & Automation (MED), pp. 1554-1559, 2012
# Janos Sztipanovits, Xenofon Koutsoukos, Gabor Karsai, Nicholas Kottenstette, Panos Antsaklis, Vijay Gupta, Bill Goodwine, John Baras, and Shige Wang, [http://controls.ame.nd.edu/~bill/papers/2011/procieee11.pdf Toward a science of cyber–physical system integration], Proceedings of the IEEE 100, no. 1 (2012): 29-44
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2011/icra11.pdf Fault-Tolerant Multiagent Robotic Formation Control Exploiting System Symmetries], Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, pp. 2872-2877
# Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2011/ifac11.pdf Nonlinear Disturbance Decoupling for a Mobile Robotic Manipulator over Uneven Terrain], Proceedings of the 2011 International Federation of Automatic Control World Congress, Milan, Italy, Vol. 18, No. 1, pp. 6930-6936
# Dayu Lv and Bill Goodwine, "Pancreas Modeling by a Deterministic Optimization Method" 'International Journal of Data Mining and Bioinformatics,' Volume 5, Number 3, Pages 308-320 (2011).
# Goodwine, Bill, and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent coordination exploiting system symmetries], American Control Conference (ACC), 2010, pp. 830-835
# Baoyang Deng, Mihir Sen, and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/acc09.pdf Bifurcations and symmetries of optimal solutions for distributed robotic systems], Proceedings of the 2009 American Control Conference, St. Louis, MO, pp. 4127-4133
#Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icarcv10.pdf Nonlinear Disturbance Decoupling for a Nonholonomic Mobile Robotic Manipulation Platform], Proceedings of the Eleventh International Conference on Control, Automation, Robotics and Vision (ICARCV 2010), Singapore, pp. 1530-1535
#Neil Petroff and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/iros10.pdf Nonholonomic and Stratified Robotic Manipulation Supplemented with Fuzzy Control: Theory and Experiment], Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, pp. 1202-1208
#Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent Coordination Exploiting System Symmetries], Proceedings of the 2010 American Controls Conference, pp. 830-835
#Baoyang Deng, Andreas K. Valenzuela and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icra10a.pdf Bifurcations of Optimal Solutions for Coordinated Robotic Systems: Numerical and Homotopy Methods], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 4475-4480
#Bill Goodwine and Jason Nightingale, [http://controls.ame.nd.edu/~bill/papers/2010/icra10b.pdf The Effect of Dynamic Singularities on Robotic Control and Design], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 5213-5218
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/bibm09.pdf Pancreas Modeling from IVGTT Data Using a Deterministic Optimal Search], Proceedings of the 2009 IEEE International Conference on Bioinformatics & Biomedicine, (35% acceptance rate) Washington, D.C.
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/wafr09.pdf A Stopping Algorithm for Mechanical Systems], Algorithmic Foundations of Robotics VIII, Gregory S. Chirikjian, et al., editors, Eighth International Workshop on the Algorithmic Foundations of Robotics, Guanajuato, Mexico, 2009, pp. 167-180
#Jason Nightingale, Richard Hind and Bill Goodwine, "Geometric analysis of a class of constrained mechanical control systems in the nonzero velocity setting,"Proceedings of the 17th International Federation of Automatic Control (IFAC) World Congress, Seoul, Korea July, 2008, pp 1171-1176
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/icra08.pdf Intrinsic Vector-Valued Symmetric Form for Simple Mechanical Control Systems in the Nonzero Velocity Setting], Proceedings of the 2008 IEEE International Conference on Robotics and Automation, (43.4% acceptance rate) Pasadena, CA, May, 2008
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/biodevices08.pdf A New Metabolism Model for Human Skeletal Muscle], Proceedings of the IEEE International Conference on Biomedical Electronics and Devices, January, 2008, Maderia, Portugal
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2007/ijrr07.pdf Motion Planning for Nonlinear Symmetric Distributed Robotic Formation], International Journal of Robotics Research, 2007, 26:10, pp. 1025-1042
#Alice Nightingale, Bill Goodwine, Michael Lemmon, and Eric Jumper, 2007, "Feedforward Adaptive-Optic System Identification Analysis for Mitigating Aero-Optic Disturbances," Proceedings of the AIAA 2007 Plasmadynamics and Lasers Conference.
#Alice Nightingale, Daniel D. Duffin, Michael Lemmon, Bill Goodwine and Eric Jumper, 2005, "Adaptive-Optic Correction of a Regularized Compressible Shear Layer," Proceedings of the 37th AIAA Plasmadynamics and Lasers Conference, San Francisco, CA, June, 2006.
#Alice Nightingale, Bill Goodwine and Eric Jumper, 2005, "Regularizing Shear Layer for Adaptive Optics Control Application," accepted for presentation at the 36th AIAA Plasmadynamics and Lasers Conference.
# Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2004/ra04.pdf Stratified motion planning on nonsmooth domains with robotic applications], IEEE Transactions on Robotics and Automation 20.1 (2004): 128-132
#Yejun Wei, Bill Goodwine and Steven B. Skaar, 2004, "Kinematics of Vision-Based Stratified Robotic Manipulation," Proceedings of the 11th IFToMM World Congress, Tianjin, China. Abstract review.
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, "Flow-based control of temperature in long ducts," 2004, International Journal of Heat and Mass Transfer, 47,pp. 4995-5009.
# M. Brett McMickell and Bill Goodwine, 2003, "Reduction and Controllability of Nonlinear Symmetric Distributed Systems," International Journal of Control, 76:18, pp. 1809-1822, 2003.
#M. Brett McMickell and Bill Goodwine, 2003, [http://controls.ame.nd.edu/~bill/papers/2003/icra03a.pdf Reduced Order Motion Planning for Nonlinear Symmetric Distributed Robotic Systems], Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, 2003, "Controllability of Cross-Flow Heat Exchangers," International Journal of Heat and Mass Transfer, 47, pp. 913-924
#M. Brett McMickell and Bill Goodwine, 2003, MICAbot: A Platform for Large Scale Coordinated Distributed Mobile Robot Control, Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review.
#S. Alotaibi, J.W. Goodwine, M. Sen and K.T. Yang, 2003, Controllability of conductive-convective systems, Proceedings of the 6th ASME-JSME Thermal Engineering Joint Conference, Hawaii, Paper No. TED-AJ03-247, pp. 1-6.
#Antonio Cardenas, Bill Goodwine, Steven B. Skaar and Michael Seelinger, Vision-Based Control of a Mobile Base and On-Board Arm, The International Journal of Robotic Research, 22: 9, pp. 677-698, 2003
#Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/icarcv2002.pdf Vision-Based Non-Smooth Kinematic Stratified Object Manipulation], Proceedings of the 2002 Seventh Annual Conference on Control, Automation, Robotics and Vision, Singapore, 2002
#Yejun Wei, S.B. Skaar and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/iros02.pdf Vision-Based Stratified Robotic Manipulation], Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, 2002
#S. Batill, S. Skaar, R. Nelson, B. Goodwine, J. Mason, and M. Sen, 2002, Development of a Curriculum for Mechanical Engineering Based Upon Intelligent Systems and Automation, Session 1526, Proceedings of the 2002 American Society for Engineering Education Annual Conference and Exposition, 2002
#S. Alotaibi, Mihir Sen, B. Goodwine, and K.T. Yang, Numerical Simulation of Thermal Control of Heat Exchangers, Numerical Heat Transfer Journal, Part A: Applications, 41:3, pp. 229-244, 2002
#Bill Goodwine and Joel Burdick, A General Method for Motion Planning for Quasi-Static Legged Robotic Locomotion," IEEE International Journal of Robotics and Automation, 18:2, pp. 209-222, 2002
#M. Brett McMickell and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02b.pdf Reduction and Controllability of Symmetric Distributed Systems with Drift], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3454-3460, 2002. Full paper review.
#Yejun Wei and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02a.pdf Stratified Motion Planning on Non-Smooth Domains with Application to Robotic Legged Locomotion and Manipulation], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3546-3552. Full paper review.
#Bill Goodwine and Milos Zefran, 2002, Feedback Stabilization of a Class of Unstable Nonholonomic Systems, Transactions of the ASME, Journal of Dynamics Systems, Measurement, & Control, 124, pp. 221-230.
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2001/iros01.pdf Reduction and Controllability of Symmetric Distributed Systems with Robotic Applications], Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, Hawaii, pp. 1232-1237. Full paper review.
#S. Alotaibi, M. Sen, Bill Goodwine, and K.T. Yang, 2001, Thermal Control of Heat Exchangers, Proceedings of the 35th National Heat Transfer Conference, NHTC01-12517, Anaheim, CA.
#Yejun Wei and Bill Goodwine,, 2001, Theoretical and Experimental Investigation of Stratified Robotic Manipulation, Proceedings of the 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea. Full paper review.
#Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.
#Bill Goodwine and Gabor Stepan, 2000, "Controlling unstable Rolling Phenomena, Journal of Vibration and Control, 6:1, pp. 137-158, January 2000.
# Qun Ma, Antonio Cardenas, Mike Seelinger, Bill Goodwine and Steven Skaar, 2000, "Supervisory Control of a Mobile Robot Using Point-and-Click Mobile Camera-Space Manipulation," Proceedings of the 4th World Multiconference on Systemics, Cybernetics and Informatics SCI 2000 and The 6th International Conference on Information Systems, Analysis and Synthesis ISAS 2000, Orlando, Florida.
# Bill Goodwine and Yejun Wei, 2000, [http://controls.ame.nd.edu/~bill/papers/2000/allerton.pdf Theoretical and Experimental Investigation of Stratified Robotic Finger Gaiting and Manipulation], Proceedings of the 38th Annual Allerton Conference on Communication, Control and Computing, Allerton, Illinois
# Bill Goodwine and Joel Burdick, Motion Planning for Kinematic Stratified Systems with application to Quasi-Static Legged Locomotion and Finger Gaiting, Proceedings of the Workshop Algorithmic Foundations of Robotics.
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/1999/ifac99.pdf Stratified Motion Planning with Application to Robotic Finger Gaiting], Proceedings of the 1999 International Federation of Automatic Control, IFAC'99: 14th World Congress Beijing, China. Full paper review.
# Gabor Stepan and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/1999/ds99.pdf Analysis and Control of Unstable Rolling Wheel Dynamics], 1999 SIAM Conference on Applications of Dynamical Systems, Showbird, UT, 1999, abstract submission
# B. Goodwine, Michael Seelinger, John-David Yoder, Qun Ma and Steven Skaar, [http://controls.ame.nd.edu/~bill/papers/1999/fsr99.pdf Applications of mobile camera-space manipulation], Proceedings of FSR'99: Field and Service Robotics, pages 102-113, Pittsburg, 1999
# Bill Goodwine, 1999, Stratified Motion Planning with Application to Robotic Finger Gaiting, Proceedings of the 1999 IFToMM 10th World Congress, Oulu, Finland. Abstract review.
# Bill Goodwine and Gabor Stepan, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/misk98.pdf Stabilizing Switching Controllers], Proceedings of the 1998 Conference on Numerical Mathematics and Computational Mechanics, Miskolc, Hungary. Abstract review
# Bill Goodwine, Michael Seelinger, Steven B. Skaar and Qun Ma, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/spie98.pdf Nonholonomic Camera Space Manipulation using Cameras Mounted on a Mobile Base], Proceedings of the 1998 SPIE conference on Sensor Fusion and Decentralized Control in Robotic Systems, Boston, Massachusetts. Abstract review
# Bill Goodwine and Joel Burdick, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/icra98.pdf Gait Controllability for Legged Robots], Proceedings of the 1998 IEEE Conference on Robotics and Automation,Leuven, Belgium. Full paper review.
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/thesis.pdf Control of Stratified Systems with Robotic Applications], Ph.D Thesis, California Institute of Technology, 1997
# Bill Goodwine and Joel Burdick, 1997, [http://controls.ame.nd.edu/~bill/papers/1997/icra97.pdf Trajectory Generation for Legged Robotic Systems], Proceedings of the 1997 IEEE Conference on Robotics and Automation, Albuquerque, New Mexico. Full paper review
# Shuuji Kajita, Bill Goodwine and Joel Burdick, Walking Direction Control of a Biped Robot with Point Feet Using Dynamic Effects in 3-D Space, Proceedings of the 1997 Robotics Society of Japan Conference, Tokyo, Japan. 1997 (in Japanese).
# Bill Goodwine and Joel Burdick, [http://controls.ame.nd.edu/~bill/papers/1996/mtns96.pdf Controllability of Kinematic Control Systems on Stratified Configuration Spaces], Mathematical Theory of Networks and Systems, 1996, St. Louis
# Bill Goodwine and Joel Burdick, 1996, [http://controls.ame.nd.edu/~bill/papers/1996/cdc96.pdf Controllability with Unilateral Control Inputs], Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan. Full paper review, 1996, (Vol. 3, pp. 3394-3399
# Bill Goodwine and Gabor Stepan, [http://controls.ame.nd.edu/~bill/papers/1996/enoc96.pdf Stabilization of the Classical Shimmying Wheel], Proceedings of the 2nd European Nonlinear Oscillations Conference, Prague, Czech Republic, 1996
#Bill Goodwine, 1991, Abortion Parental Notification Statutes: Hodgson v. Minnesota, 110 S. Ct. 2926 (1990) and Ohio v. Akron Center for Reproductive Health, 110 S. Ct. 2972 (1990), Harvard Journal of Law & Public Policy, 14:1, pp. 237-247.

==Books and Chapters in Books==
# Bill Goodwine, [http://www.springer.com/mathematics/dynamical+systems/book/978-1-4419-7918-6 Engineering Differential Equations: Theory and Applications], Springer, 2010.
#* Some [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Movies movies] are available illustrating some of the more interesting solutions, generally for PDEs
#* A list of [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Errata errata] is also available
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849318047 Robotics and Automation Handbook], Chapter 3, Inverse Kinematics, Thomas R. Kurfess, Editor, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2001.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2001.

==Erdős Number==
# Erdős, P.; Shapiro, H. S.; Shields, A. L. Large and small subspaces of Hilbert space. Michigan Math. J. 12 1965 169--178.
# Shields, Allen L. Some problems in operator theory. Notes by Michael J. Hoffman. Lecture Notes in Math., 693, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977), pp. 157--167, Springer, Berlin, 1978.
# Marsden, Jerrold E.; Hoffman, Michael J. Basic complex analysis. Second edition. W. H. Freeman and Company, New York, 1987. xiv+604 pp. ISBN: 0-7167-1814-6
# Banavara N. Shashikanth, Jerrold E. Marsden, Joel W. Burdick and Scott D. Kelly, The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vorticesPhys. Fluids 14, 1214 (2002).
# Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.

=Students=

==PhD Students==
* Kevin Leyden, in progress
* Jason Nightingale, Ph.D. defended 8:00 am, June 4, 2012 [http://controls.ame.nd.edu/~bill/students/jason.pdf thesis]
* Dayu Lv, Ph.D. defended March 17, 2011, [http://controls.ame.nd.edu/~bill/students/dayu.pdf thesis]
* Baoyang Deng, Ph.D., defended March 11, 2011 [http://controls.ame.nd.edu/~bill/students/baoyang.pdf thesis]
* Alice Nightingale, Ph.D. defended November 3, 2010 [http://controls.ame.nd.edu/~bill/students/alice.pdf thesis]
* Neil Petroff, Ph.D. defended, October 6, 2006 [http://controls.ame.nd.edu/~bill/students/neil.pdf thesis]
* M. Brett McMickell, Ph.D. defended 2003
* Yejun Wei, Ph.D. defended 2002

==MS Students==
* Ashley Nettleman, M.S., November 2014 [http://controls.ame.nd.edu/~bill/students/ashley.pdf thesis]
* Nicholas Galati, July 15, 2013
* Michael O'Connor, Fall 2011
* Qun (Marc) Ma, M.S., 2000

==Undergraduate Research Projects==

* Patrick O’Meara, “Control and Dynamics of a Fleet of Automobiles,” spring, summer and fall 2013
* Nick Turner, “Mathematics and Theory of Origami,” summer 2013
* Catherine Bentzen, “Jellyfish Propulsion,” summer 2013
* Blair Rasmus, John Gallagher, Derek Wolf, “Development of Feedback Microcontroller for an Inverted Pendulum System for AME 30315” (all three, Fall 2011, John Gallagher continued through Spring 2012)
* Jeff O’Brien, “Synchronization and Limit Cycle Solutions for Coupled Hybrid Systems” (Fall and Spring, 2011)
* John Gallagher, “Describing Function Analysis with Non-Harmonic Basis Functions” (Spring 2012 – started in January)
* Adam Wojcik,. “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Paul Fleury, “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Robert Powers, “Energy storage technologies: a sustainable solution to electrical load shedding in rural Bangladesh,” Spring 2010
* “Raymond LeGrand, "Development of a Microprocessor controlled Inverted Pendulum Experiment,” , Summer and Fall 2010
* Steven Brus, “Homotopy Methods for Coordinated Robotic Systems,” Summer 2010
* Andres Valenzuela, “Bifurcation Measures for Nonlinear Boundary Value Problems in Optimal Control of Mobile Robot Formations,” Fall 2008 and Spring 2009. Undergraduate thesis in Spring 2009
* Blake Shilide, “Aero-Optic Shear Layer Control and Simulation,” Spring, 2005
* Tim Ronan, “MICAbot Programming and TinyOS,” Summer, 2003
* Timothy Kacmar, “Development of a Multi-Manipulator Path Planning Collision Avoidance System,” Fall, 2003
* Meaghan Perry-Eaton, “Investigation of Automotive Fuel Cell Energy System Usage and Feasibility,” Fall, 2003
* Peter Balough, “Development of a Mobile Multi-Robot Simulation Environment in Java and Hardware Development for the TagMote,” Summer and Fall, 2003
* Kristin Dormuth, “MICAbot Programming and TinyOS,” Summer, 2003
* John Aman, “MICAbot Programming and TinyOS,” Summer, 2003
* Denis Sullivan, “MICAbot Programming and TinyOS,” Summer and Fall, 2003
* Thomas Apker, “Investigation of the Efficacy of Switching Multi-Controller Systems,” Spring, 2003
* Daniel Luedtke, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Spring, 2003
* Tommy Ferrara, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Fall, 2003.
* Dennis Abdelnour, “Development Programming for a Mobile Robot,” Spring, 2001.
* Eric Shearer, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer 2000.
* Bethany Wilson, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer, 2000.
* Leonard Conapinski, “Investigation of the Presence of Chaos in a Hybrid Switching System, ” Fall, 2000.

=Research Summary=

===Cyber Physical Systems===

My research focuses primarily on theoretical nonlinear control with recent emphasis on Cyber Physical Systems. Cyber physical systems are systems with highly integrated physical and computational components (often involving the complication of networked communication). They tend to be very large and complex in scale. While many CPS systems exist in the real world, to date there are few general theoretical results available to guide both the design of such systems and the control of such systems. Most existing CPS systems are designed and controlled based upon accumulated real-world industrial knowledge that tends to be industry- or application-specific. My recent work has focused particularly on so-called ''symmetric systems.'' A symmetric system is comprised of many components with the restriction that the components be very closely related and connected together in a "regular" manner. With such restrictions, it is possible to formulate general models and then consider what types of properties remain invariant as components are added to or removed from the system. A related question is how the system behaves as components fail, which is a question of robustness.

===Stratified Systems===

Many interesting and important control systems evolve on
''stratified'' configuration spaces. Roughly speaking, we
will call a configuration manifold stratified if it contains
submanifolds upon which the system is subjected to additional
constraints or has different equations of state. For such
systems, the equations of motion on each submanifold may change
in a non-smooth, or even discontinuous manner, when the system
moves from one submanifold to another. In such cases,
traditional nonlinear control methodologies are inapplicable
because they generally rely upon differentiation in one form or
another. Yet it is the discontinuous nature of such systems
that is often their most important characteristic because the
system must cycle through different submanifolds to effectively
be controlled. Therefore, it is necessary to incorporate
explicitly into control methodologies the non-smooth or
discontinuous nature of these systems.

Robotic systems, in particular, are of this nature. A legged
robot has discontinuous equations of motion near points in the
configuration space where each of its ``feet'' come into contact
with the ground, and it is precisely the ability of the robot to
lift its feet off of the ground that enables it to move about.
Similarly, a robotic hand grasping an object often cannot
reorient the object without lifting its fingers off of the
object. Despite the obvious utility of such systems, however, a
comprehensive framework in which to consider control issues for
such systems does not exist.

The fundamental approach of this work has been to exploit the
physical geometric structure present in such problems to address
control issues such as nonlinear controllability, trajectory
generation and stabilization. The fundamental philosophy is to
generate ''general'' results, i.e., results
independent of a particular robot's number of legs, fingers or
morphology.

===Control of Mechanical Systems===

Most theoretical control results are based upon very generic dynamical systems formulations, such as
<math>\dot x = A x + B u</math> for linear systems or <math>\dot x =f(x) + g(x)u</math> for a nonlinear system. Of course this leads to the question of whether a more restrictive starting point can lead to valuable results. An important area of research along these lines is so-called control of mechanical systems where the equations of motion are not as general, but are assumed from the beginning to come from some first principle of mechanics. We have focused specifically on control of Lagrangian systems that are underactuated. Specifically, it is possible in such a framework to write general expressions for the relationship of the coupling between the controlled degree of freedoms and uncontrolled degrees of freedom, and given such expressions it is possible to know when there is close coupling between them and total decoupling between them. Furthermore, it is often the case that the coupling between the controlled and uncontrolled degrees of freedom is such that it may be only of one sign, ''i.e.'', no matter what is done with the control inputs, the uncontrolled degrees of freedom may only increase (or decrease) in magnitude. Such results have obvious important implications for control algorithms.

===Other Projects===

Other smaller projects include:
* control of aero-optic systems
* predictive biosimulation for human metabolism
* fuzzy logic-based robust control for stratified systems
* model-predictive control for marine navigation.

=Biographical Sketch=

* MS and PhD degrees in Applied Mechanics from the California Institute of Technology in 1993 and 1998, respectively.
* JD degree from Harvard Law School, 1991, ''cum laude''
* Instructor, Assistant Professor, Associate Professor, Department of Aerospace and Mechanical Engineering, University of Notre Dame, 1998 - present.
* Associate Department Chair, Department of Aerospace and Mechanical Engineering, University of Notre Dame, August 2008 - August 2012.
* Member of the Illinois Bar Association, 1991 - present.
* Registered Patent Attorney, 1998 - 2004 (not maintained).
* NSF CAREER Award Recipient.
* Boeing Welliver Faculty Fellow.
* Dockweiler Award for Excellence in Undergraduate Advising, May 2010.
* BP Foundation Outstanding Teacher of the Year, College of Engineering, Spring, 2008.
* Joyce Award (teaching), Spring, 2008.
* University of Notre Dame Kaneb teaching award, Spring, 2005.
* Department of Aerospace and Mechanical Engineering Ruth and Joel Spira Award for Excellence in Teaching, 2003 - 2004 and 2007 - 2008.
* American Society of Engineering Education Illinois/Indiana Section Outstanding Teaching Award, April, 2003.
* Department of Aerospace and Mechanical Engineering Faculty Award (teaching), 1998 - 1999.

=Courses=

* Fall 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=337 AME 30314: Differential Equations, Vibrations and Control I] (121 Students)
* Spring 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=323 AME 50652: Intermediate Controls] (7 Students) and AME 50650: Introduction to Nonlinear Analysis (9 Students)
* Fall 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=309 AME 30314, Differential Equations, Vibrations and Control I] (118 Students)
* Spring 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=304 AME 90951: Geometric Nonlinear Control] (8 students)
* Fall 2012: AME 30314: Differential Equations, Vibrations and Control I (86 Students)
* Spring 2012: [http://controls.ame.nd.edu/courses/viewforum.php?f=289 AME 30315: Differential Equations, Vibrations and Control II] (129 Students)
* Fall 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=274 AME 30314: Differential Equations, Vibrations and Control I] (112 Students)
* Summer 2011: [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Course_Syllabus,_Summer_2011 AME 40590: Intellectual Property for Engineers] [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Homework,_Summer_2011 (homeworks)]
* Spring 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=255 AME 30315: Differential Equations, Vibrations and Control II] (89 Students) and [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Intellectual_Property_for_Engineers AME 40590: Intellectual Property for Engineers] (56 Students) [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Homeworks,_Spring_2011 {homeworks)]
* Fall 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=227 AME 30314: Differential Equations, Vibrations and Control I] (81 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=228 AME 20214: Introduction to Engineering Computing] (131 Students)
* Spring 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=201 AME 30315: Differential Equations, Vibrations and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=202 AME 60652: Advanced Controls (now AME 50562: Intermediate Controls)]
* Fall 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=186 AME 30314: Differential Equations, Vibrations and Control I] (91 students)
* Spring 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=170 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=140 AME 30314: Differential Equations, Vibrations and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=141 AME 20214: Introduction to Engineering Computing]
* Spring 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=124 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=125 AME 30314: Differential Equations, Vibrations and Control I] (86 Students), [http://controls.ame.nd.edu/courses/viewforum.php?f=127 AME 60652: Advanced Controls] (11 Students) and AME 53591: Engineering Seminar Series.
* Spring 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=129 AME 30315: Differential Equations, Vibrations and Control II] (94 Students)
* Fall 2006: [http://controls.ame.nd.edu/courses/viewforum.php?f=130 AME 30314: Differential Equations, Vibrations and Control I] (79 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=131 AME 60611: Mathematical Methods I] (24 Students)
* Fall 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=132 AME 34314: Differential Equations, Vibrations and Control I (London)] and Intermediate Dynamics.
* Spring 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=133 AME 302: Modeling and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=134 Geometric Nonlinear Control]
* Fall 2004: [http://controls.ame.nd.edu/courses/viewforum.php?f=135 AME 301: Modeling and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=136 AME 550: Advanced Controls]
* Spring 2004: [http://controls.ame.nd.edu/courses/ame302/S2004 AME 302: Modeling and Control II] (72 students)
* Fall 2003: [http://controls.ame.nd.edu/courses/ame301/F2003/ AME 301: Modeling and Control I] (54 students) and AME 654: Geometric Nonlinear Control (2 students)
* Spring 2003: [http://controls.ame.nd.edu/courses/ame437/S2003/ AME 437: Control Systems Engineering] (68 students)
* Spring 2002: [http://controls.ame.nd.edu/courses/ame437/S2002/ AME 437: Control Systems Engineering] (64 students)
* Fall 2001: [http://controls.ame.nd.edu/courses/ame654/F2001/ AME 654: Geometric Nonlinear Control] (3 students)
* Spring 2001: [http://controls.ame.nd.edu/courses/ame469/S2001/ AME 469: Introduction to Robotics] (33 students)
* Spring 2000: [http://controls.ame.nd.edu/courses/ame469/S2000/ AME 469: Introduction to Robotics] (48 students), [http://controls.ame.nd.edu/courses/ame437/S2000/ AME 437: Control Systems Engineering] (50 students) and AME 598: Engineering Applications of Artificial Intelligence (5 students).
* Fall 1999: [http://controls.ame.nd.edu/courses/ame698/F1999/ AME 698: Geometric Nonlinear Control] (10 students)
* Spring 1999: [http://controls.ame.nd.edu/courses/ame469/S1999/ AME 469: Introduction to Robotics] (33 students)
* Fall 1998: [http://controls.ame.nd.edu/courses/ame469/F1998/ AME 469: Introduction to Robotics] (12 students)
* Spring 1998: [http://controls.ame.nd.edu/courses/ame437/S1998/ AME 437: Control Systems Engineering] (44 students)

===Course Blog===

In order to be able to interactively answer questions online, I've maintained a [http://controls.ame.nd.edu/courses course blog for all courses since 2002].

===AME 30315 Differential Equations, Vibrations and Control II===
*[[AME 30315 Pendulum Project]]

===AME 40590, Intellectual Property for Engineers===
*[[AME 44590 Course Syllabus, Summer 2011]]
*[[AME 44590 Homework, Summer 2011]]
*[[AME 40590 Intellectual Property for Engineers|AME 40590 Course Content]]
*[[AME 40590 Homeworks, Spring 2011]]

===AME 50652, Intermediate Controls===
*[[AME 50652 Pendulum Project]]

=[[Engineering Differential Equations: Theory and Applications, Springer 2010]]=

=[[Engineering China Summer Program]]=

=[[London CPS Workshop]]=

=[[CDIO Regional Meeting]]=

Main Page

2015-09-16T20:50:45Z

Bill: /* Papers */

<table border=0 width=100%>
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<td width=25%> [[Image:Bill5.jpeg|250px]]</td>
<td align=center>

Bill Goodwine 


Department of Aerospace and Mechanical Engineering 
University of Notre Dame 
Notre Dame, IN 46556 
bill@controls.ame.nd.edu 
</td>
</tr>
</table>

I have moved my homepage here. At least for the time being, my [http://controls.ame.nd.edu/~bill/oldindex.php old one] still exists.
=Publications=
==Papers==
# Kevin Leyden and Bill Goodwine, Using Fractional-Order Differential Equations for Health Monitoring of a System of Cooperating Robots. Submitted to the 2016 IEEE International Conference on Robotics and Automation.
# Bill Goodwine, Towards General Results in Bifurcations in Optimal Solutions for Symmetric Distributed Robotic Formation Control. Submitted to the 2015 IEEE International Symposium on System Integration.
# Baoyang Deng, Michael O'Connor and Bill Goodwine, Bifurcations and Symmetry in Two Optimal Formation Control Problems for Mobile Robotic Systems. Accepted for publication pending revisions in Robotica.
# Nicholas Turner, Bill Goodwine and Mihir Sen, A Review of Origami Applications in Mechanical Engineering, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science (2015): 0954406215597713.
# David C. Post, Bill Goodwine and James P. Schmiedeler, Quantifying Control Authority in Periodic Motions of Underactuated Mobile Robots, Proceedings of the ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2015, DETC2015-47666
#Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2015/icra2015.pdf Symmetries and Reduction for Multi-Agent Control], Proceedings of the 2015 IEEE International Conference on Robotics and Automation, pp 5390-5396
# Bill Goodwine and Kevin Leyden, Recent Results in Fractional-Order Modeling for Multi-Agent Systems and Linear Friction Welding, 8th Vienna International Conference on Mathematical Modelling - MATHMOD 2015, abstract submission
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icarcv2014.pdf Fractional-Order Dynamics in a Random, Approximately Scale-Free Network of Agents], Proceedings of the 2014 International Conference on Control, Automation, Robotics and Vision, pp 1581 - 1586
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/ifac14.pdf Nonlinear Stability of Approximately Symmetric Large-Scale Systems], Proceedings of the 2014 IFAC World Congress, Cape Town, South Africa, pp 845-850
# Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/mtns-282.pdf Symmetries of Multiagent Systems and Formation Stability], Proceedings of the 2014 International Symposium on Mathematical Theory of Networks and Systems (MTNS 14), pp 1340-1343 (extended abstract review)
# Bill Goodwine, [[Compositional Boundedness of Solutions for Symmetric Nonautonomous Control Systems]], Proceedings of the 2014 Mediterranean Conference on Control and Automation
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icra-1441.pdf Modeling a Multi-Robot System with Fractional-Order Differential Equations], Proceedings of the 2014 IEEE International Conference on Robotics and Automation, Hong Kong, pp 1763-1768
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2013/automatica13.pdf Multi-agent compositional stability exploiting system symmetries], Automatica 49(11): 3158-3166, 2013
# Panos J Antsaklis,Bill Goodwine, Vijay Gupta, Michael J. McCourt, Yue Wang, Po Wu, Meng Xia, Han Yu, and Feng Zhu, [http://controls.ame.nd.edu/~bill/papers/2013/ejc13.pdf Control of cyberphysical systems using passivity and dissipativity based methods], European Journal of Control 19, no. 5 (2013): 379-388
# Bill Goodwine [http://controls.ame.nd.edu/~bill/papers/2013/med-2013a.pdf Compositional stability of approximately symmetric systems: Initial results], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED), pp. 1470-1476 IEEE, 2013
# Jason Nightingale and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2013/med-2013b.pdf An algorithm for stopping a class of underactuated nonlinear mechanical robotic systems], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED) pp. 531-536, 2013
# Alice M. Nightingale, Bill Goodwine, Michael Lemmon and Eric Jumper [http://controls.ame.nd.edu/~bill/papers/2013/aiaa13.pdf Phase-Locked-Loop Adaptive-Optic Controller and Simulated Shear Layer Correction], AIAA journal, 51(11), 2714-2726, 2013
# John Gallagher and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/cdio12.pdf CDIO-Oriented Inverted Pendulum Control Project for Undergraduate Engineering Students], 2012 CDIO International Conference, Brisbane, Australia, 2012
# Michael O'Connor and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/med12a.pdf Symmetry-Breaking in Bifurcations of Optimal Solutions for Coordinated Nonholonomic Robotic Control], Proceedings of the 2012 Mediterranean Conference on Control & Automation (MED), pp. 1554-1559, 2012
# Janos Sztipanovits, Xenofon Koutsoukos, Gabor Karsai, Nicholas Kottenstette, Panos Antsaklis, Vijay Gupta, Bill Goodwine, John Baras, and Shige Wang, [http://controls.ame.nd.edu/~bill/papers/2011/procieee11.pdf Toward a science of cyber–physical system integration], Proceedings of the IEEE 100, no. 1 (2012): 29-44
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2011/icra11.pdf Fault-Tolerant Multiagent Robotic Formation Control Exploiting System Symmetries], Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, pp. 2872-2877
# Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2011/ifac11.pdf Nonlinear Disturbance Decoupling for a Mobile Robotic Manipulator over Uneven Terrain], Proceedings of the 2011 International Federation of Automatic Control World Congress, Milan, Italy, Vol. 18, No. 1, pp. 6930-6936
# Dayu Lv and Bill Goodwine, "Pancreas Modeling by a Deterministic Optimization Method" 'International Journal of Data Mining and Bioinformatics,' Volume 5, Number 3, Pages 308-320 (2011).
# Goodwine, Bill, and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent coordination exploiting system symmetries], American Control Conference (ACC), 2010, pp. 830-835
# Baoyang Deng, Mihir Sen, and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/acc09.pdf Bifurcations and symmetries of optimal solutions for distributed robotic systems], Proceedings of the 2009 American Control Conference, St. Louis, MO, pp. 4127-4133
#Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icarcv10.pdf Nonlinear Disturbance Decoupling for a Nonholonomic Mobile Robotic Manipulation Platform], Proceedings of the Eleventh International Conference on Control, Automation, Robotics and Vision (ICARCV 2010), Singapore, pp. 1530-1535
#Neil Petroff and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/iros10.pdf Nonholonomic and Stratified Robotic Manipulation Supplemented with Fuzzy Control: Theory and Experiment], Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, pp. 1202-1208
#Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent Coordination Exploiting System Symmetries], Proceedings of the 2010 American Controls Conference, pp. 830-835
#Baoyang Deng, Andreas K. Valenzuela and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icra10a.pdf Bifurcations of Optimal Solutions for Coordinated Robotic Systems: Numerical and Homotopy Methods], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 4475-4480
#Bill Goodwine and Jason Nightingale, [http://controls.ame.nd.edu/~bill/papers/2010/icra10b.pdf The Effect of Dynamic Singularities on Robotic Control and Design], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 5213-5218
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/bibm09.pdf Pancreas Modeling from IVGTT Data Using a Deterministic Optimal Search], Proceedings of the 2009 IEEE International Conference on Bioinformatics & Biomedicine, (35% acceptance rate) Washington, D.C.
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/wafr09.pdf A Stopping Algorithm for Mechanical Systems], Algorithmic Foundations of Robotics VIII, Gregory S. Chirikjian, et al., editors, Eighth International Workshop on the Algorithmic Foundations of Robotics, Guanajuato, Mexico, 2009, pp. 167-180
#Jason Nightingale, Richard Hind and Bill Goodwine, "Geometric analysis of a class of constrained mechanical control systems in the nonzero velocity setting,"Proceedings of the 17th International Federation of Automatic Control (IFAC) World Congress, Seoul, Korea July, 2008.
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/icra08.pdf Intrinsic Vector-Valued Symmetric Form for Simple Mechanical Control Systems in the Nonzero Velocity Setting], Proceedings of the 2008 IEEE International Conference on Robotics and Automation, (43.4% acceptance rate) Pasadena, CA, May, 2008
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/biodevices08.pdf A New Metabolism Model for Human Skeletal Muscle], Proceedings of the IEEE International Conference on Biomedical Electronics and Devices, January, 2008, Maderia, Portugal
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2007/ijrr07.pdf Motion Planning for Nonlinear Symmetric Distributed Robotic Formation], International Journal of Robotics Research, 2007, 26:10, pp. 1025-1042
#Alice Nightingale, Bill Goodwine, Michael Lemmon, and Eric Jumper, 2007, "Feedforward Adaptive-Optic System Identification Analysis for Mitigating Aero-Optic Disturbances," Proceedings of the AIAA 2007 Plasmadynamics and Lasers Conference.
#Alice Nightingale, Daniel D. Duffin, Michael Lemmon, Bill Goodwine and Eric Jumper, 2005, "Adaptive-Optic Correction of a Regularized Compressible Shear Layer," Proceedings of the 37th AIAA Plasmadynamics and Lasers Conference, San Francisco, CA, June, 2006.
#Alice Nightingale, Bill Goodwine and Eric Jumper, 2005, "Regularizing Shear Layer for Adaptive Optics Control Application," accepted for presentation at the 36th AIAA Plasmadynamics and Lasers Conference.
# Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2004/ra04.pdf Stratified motion planning on nonsmooth domains with robotic applications], IEEE Transactions on Robotics and Automation 20.1 (2004): 128-132
#Yejun Wei, Bill Goodwine and Steven B. Skaar, 2004, "Kinematics of Vision-Based Stratified Robotic Manipulation," Proceedings of the 11th IFToMM World Congress, Tianjin, China. Abstract review.
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, "Flow-based control of temperature in long ducts," 2004, International Journal of Heat and Mass Transfer, 47,pp. 4995-5009.
# M. Brett McMickell and Bill Goodwine, 2003, "Reduction and Controllability of Nonlinear Symmetric Distributed Systems," International Journal of Control, 76:18, pp. 1809-1822, 2003.
#M. Brett McMickell and Bill Goodwine, 2003, [http://controls.ame.nd.edu/~bill/papers/2003/icra03a.pdf Reduced Order Motion Planning for Nonlinear Symmetric Distributed Robotic Systems], Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, 2003, "Controllability of Cross-Flow Heat Exchangers," International Journal of Heat and Mass Transfer, 47, pp. 913-924
#M. Brett McMickell and Bill Goodwine, 2003, MICAbot: A Platform for Large Scale Coordinated Distributed Mobile Robot Control, Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review.
#S. Alotaibi, J.W. Goodwine, M. Sen and K.T. Yang, 2003, Controllability of conductive-convective systems, Proceedings of the 6th ASME-JSME Thermal Engineering Joint Conference, Hawaii, Paper No. TED-AJ03-247, pp. 1-6.
#Antonio Cardenas, Bill Goodwine, Steven B. Skaar and Michael Seelinger, Vision-Based Control of a Mobile Base and On-Board Arm, The International Journal of Robotic Research, 22: 9, pp. 677-698, 2003
#Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/icarcv2002.pdf Vision-Based Non-Smooth Kinematic Stratified Object Manipulation], Proceedings of the 2002 Seventh Annual Conference on Control, Automation, Robotics and Vision, Singapore, 2002
#Yejun Wei, S.B. Skaar and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/iros02.pdf Vision-Based Stratified Robotic Manipulation], Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, 2002
#S. Batill, S. Skaar, R. Nelson, B. Goodwine, J. Mason, and M. Sen, 2002, Development of a Curriculum for Mechanical Engineering Based Upon Intelligent Systems and Automation, Session 1526, Proceedings of the 2002 American Society for Engineering Education Annual Conference and Exposition, 2002
#S. Alotaibi, Mihir Sen, B. Goodwine, and K.T. Yang, Numerical Simulation of Thermal Control of Heat Exchangers, Numerical Heat Transfer Journal, Part A: Applications, 41:3, pp. 229-244, 2002
#Bill Goodwine and Joel Burdick, A General Method for Motion Planning for Quasi-Static Legged Robotic Locomotion," IEEE International Journal of Robotics and Automation, 18:2, pp. 209-222, 2002
#M. Brett McMickell and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02b.pdf Reduction and Controllability of Symmetric Distributed Systems with Drift], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3454-3460, 2002. Full paper review.
#Yejun Wei and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02a.pdf Stratified Motion Planning on Non-Smooth Domains with Application to Robotic Legged Locomotion and Manipulation], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3546-3552. Full paper review.
#Bill Goodwine and Milos Zefran, 2002, Feedback Stabilization of a Class of Unstable Nonholonomic Systems, Transactions of the ASME, Journal of Dynamics Systems, Measurement, & Control, 124, pp. 221-230.
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2001/iros01.pdf Reduction and Controllability of Symmetric Distributed Systems with Robotic Applications], Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, Hawaii, pp. 1232-1237. Full paper review.
#S. Alotaibi, M. Sen, Bill Goodwine, and K.T. Yang, 2001, Thermal Control of Heat Exchangers, Proceedings of the 35th National Heat Transfer Conference, NHTC01-12517, Anaheim, CA.
#Yejun Wei and Bill Goodwine,, 2001, Theoretical and Experimental Investigation of Stratified Robotic Manipulation, Proceedings of the 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea. Full paper review.
#Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.
#Bill Goodwine and Gabor Stepan, 2000, "Controlling unstable Rolling Phenomena, Journal of Vibration and Control, 6:1, pp. 137-158, January 2000.
# Qun Ma, Antonio Cardenas, Mike Seelinger, Bill Goodwine and Steven Skaar, 2000, "Supervisory Control of a Mobile Robot Using Point-and-Click Mobile Camera-Space Manipulation," Proceedings of the 4th World Multiconference on Systemics, Cybernetics and Informatics SCI 2000 and The 6th International Conference on Information Systems, Analysis and Synthesis ISAS 2000, Orlando, Florida.
# Bill Goodwine and Yejun Wei, 2000, [http://controls.ame.nd.edu/~bill/papers/2000/allerton.pdf Theoretical and Experimental Investigation of Stratified Robotic Finger Gaiting and Manipulation], Proceedings of the 38th Annual Allerton Conference on Communication, Control and Computing, Allerton, Illinois
# Bill Goodwine and Joel Burdick, Motion Planning for Kinematic Stratified Systems with application to Quasi-Static Legged Locomotion and Finger Gaiting, Proceedings of the Workshop Algorithmic Foundations of Robotics.
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/1999/ifac99.pdf Stratified Motion Planning with Application to Robotic Finger Gaiting], Proceedings of the 1999 International Federation of Automatic Control, IFAC'99: 14th World Congress Beijing, China. Full paper review.
# Gabor Stepan and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/1999/ds99.pdf Analysis and Control of Unstable Rolling Wheel Dynamics], 1999 SIAM Conference on Applications of Dynamical Systems, Showbird, UT, 1999, abstract submission
# B. Goodwine, Michael Seelinger, John-David Yoder, Qun Ma and Steven Skaar, [http://controls.ame.nd.edu/~bill/papers/1999/fsr99.pdf Applications of mobile camera-space manipulation], Proceedings of FSR'99: Field and Service Robotics, pages 102-113, Pittsburg, 1999
# Bill Goodwine, 1999, Stratified Motion Planning with Application to Robotic Finger Gaiting, Proceedings of the 1999 IFToMM 10th World Congress, Oulu, Finland. Abstract review.
# Bill Goodwine and Gabor Stepan, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/misk98.pdf Stabilizing Switching Controllers], Proceedings of the 1998 Conference on Numerical Mathematics and Computational Mechanics, Miskolc, Hungary. Abstract review
# Bill Goodwine, Michael Seelinger, Steven B. Skaar and Qun Ma, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/spie98.pdf Nonholonomic Camera Space Manipulation using Cameras Mounted on a Mobile Base], Proceedings of the 1998 SPIE conference on Sensor Fusion and Decentralized Control in Robotic Systems, Boston, Massachusetts. Abstract review
# Bill Goodwine and Joel Burdick, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/icra98.pdf Gait Controllability for Legged Robots], Proceedings of the 1998 IEEE Conference on Robotics and Automation,Leuven, Belgium. Full paper review.
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/thesis.pdf Control of Stratified Systems with Robotic Applications], Ph.D Thesis, California Institute of Technology, 1997
# Bill Goodwine and Joel Burdick, 1997, [http://controls.ame.nd.edu/~bill/papers/1997/icra97.pdf Trajectory Generation for Legged Robotic Systems], Proceedings of the 1997 IEEE Conference on Robotics and Automation, Albuquerque, New Mexico. Full paper review
# Shuuji Kajita, Bill Goodwine and Joel Burdick, Walking Direction Control of a Biped Robot with Point Feet Using Dynamic Effects in 3-D Space, Proceedings of the 1997 Robotics Society of Japan Conference, Tokyo, Japan. 1997 (in Japanese).
# Bill Goodwine and Joel Burdick, [http://controls.ame.nd.edu/~bill/papers/1996/mtns96.pdf Controllability of Kinematic Control Systems on Stratified Configuration Spaces], Mathematical Theory of Networks and Systems, 1996, St. Louis
# Bill Goodwine and Joel Burdick, 1996, [http://controls.ame.nd.edu/~bill/papers/1996/cdc96.pdf Controllability with Unilateral Control Inputs], Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan. Full paper review, 1996, (Vol. 3, pp. 3394-3399
# Bill Goodwine and Gabor Stepan, [http://controls.ame.nd.edu/~bill/papers/1996/enoc96.pdf Stabilization of the Classical Shimmying Wheel], Proceedings of the 2nd European Nonlinear Oscillations Conference, Prague, Czech Republic, 1996
#Bill Goodwine, 1991, Abortion Parental Notification Statutes: Hodgson v. Minnesota, 110 S. Ct. 2926 (1990) and Ohio v. Akron Center for Reproductive Health, 110 S. Ct. 2972 (1990), Harvard Journal of Law & Public Policy, 14:1, pp. 237-247.

==Books and Chapters in Books==
# Bill Goodwine, [http://www.springer.com/mathematics/dynamical+systems/book/978-1-4419-7918-6 Engineering Differential Equations: Theory and Applications], Springer, 2010.
#* Some [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Movies movies] are available illustrating some of the more interesting solutions, generally for PDEs
#* A list of [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Errata errata] is also available
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849318047 Robotics and Automation Handbook], Chapter 3, Inverse Kinematics, Thomas R. Kurfess, Editor, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2001.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2001.

==Erdős Number==
# Erdős, P.; Shapiro, H. S.; Shields, A. L. Large and small subspaces of Hilbert space. Michigan Math. J. 12 1965 169--178.
# Shields, Allen L. Some problems in operator theory. Notes by Michael J. Hoffman. Lecture Notes in Math., 693, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977), pp. 157--167, Springer, Berlin, 1978.
# Marsden, Jerrold E.; Hoffman, Michael J. Basic complex analysis. Second edition. W. H. Freeman and Company, New York, 1987. xiv+604 pp. ISBN: 0-7167-1814-6
# Banavara N. Shashikanth, Jerrold E. Marsden, Joel W. Burdick and Scott D. Kelly, The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vorticesPhys. Fluids 14, 1214 (2002).
# Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.

=Students=

==PhD Students==
* Kevin Leyden, in progress
* Jason Nightingale, Ph.D. defended 8:00 am, June 4, 2012 [http://controls.ame.nd.edu/~bill/students/jason.pdf thesis]
* Dayu Lv, Ph.D. defended March 17, 2011, [http://controls.ame.nd.edu/~bill/students/dayu.pdf thesis]
* Baoyang Deng, Ph.D., defended March 11, 2011 [http://controls.ame.nd.edu/~bill/students/baoyang.pdf thesis]
* Alice Nightingale, Ph.D. defended November 3, 2010 [http://controls.ame.nd.edu/~bill/students/alice.pdf thesis]
* Neil Petroff, Ph.D. defended, October 6, 2006 [http://controls.ame.nd.edu/~bill/students/neil.pdf thesis]
* M. Brett McMickell, Ph.D. defended 2003
* Yejun Wei, Ph.D. defended 2002

==MS Students==
* Ashley Nettleman, M.S., November 2014 [http://controls.ame.nd.edu/~bill/students/ashley.pdf thesis]
* Nicholas Galati, July 15, 2013
* Michael O'Connor, Fall 2011
* Qun (Marc) Ma, M.S., 2000

==Undergraduate Research Projects==

* Patrick O’Meara, “Control and Dynamics of a Fleet of Automobiles,” spring, summer and fall 2013
* Nick Turner, “Mathematics and Theory of Origami,” summer 2013
* Catherine Bentzen, “Jellyfish Propulsion,” summer 2013
* Blair Rasmus, John Gallagher, Derek Wolf, “Development of Feedback Microcontroller for an Inverted Pendulum System for AME 30315” (all three, Fall 2011, John Gallagher continued through Spring 2012)
* Jeff O’Brien, “Synchronization and Limit Cycle Solutions for Coupled Hybrid Systems” (Fall and Spring, 2011)
* John Gallagher, “Describing Function Analysis with Non-Harmonic Basis Functions” (Spring 2012 – started in January)
* Adam Wojcik,. “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Paul Fleury, “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Robert Powers, “Energy storage technologies: a sustainable solution to electrical load shedding in rural Bangladesh,” Spring 2010
* “Raymond LeGrand, "Development of a Microprocessor controlled Inverted Pendulum Experiment,” , Summer and Fall 2010
* Steven Brus, “Homotopy Methods for Coordinated Robotic Systems,” Summer 2010
* Andres Valenzuela, “Bifurcation Measures for Nonlinear Boundary Value Problems in Optimal Control of Mobile Robot Formations,” Fall 2008 and Spring 2009. Undergraduate thesis in Spring 2009
* Blake Shilide, “Aero-Optic Shear Layer Control and Simulation,” Spring, 2005
* Tim Ronan, “MICAbot Programming and TinyOS,” Summer, 2003
* Timothy Kacmar, “Development of a Multi-Manipulator Path Planning Collision Avoidance System,” Fall, 2003
* Meaghan Perry-Eaton, “Investigation of Automotive Fuel Cell Energy System Usage and Feasibility,” Fall, 2003
* Peter Balough, “Development of a Mobile Multi-Robot Simulation Environment in Java and Hardware Development for the TagMote,” Summer and Fall, 2003
* Kristin Dormuth, “MICAbot Programming and TinyOS,” Summer, 2003
* John Aman, “MICAbot Programming and TinyOS,” Summer, 2003
* Denis Sullivan, “MICAbot Programming and TinyOS,” Summer and Fall, 2003
* Thomas Apker, “Investigation of the Efficacy of Switching Multi-Controller Systems,” Spring, 2003
* Daniel Luedtke, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Spring, 2003
* Tommy Ferrara, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Fall, 2003.
* Dennis Abdelnour, “Development Programming for a Mobile Robot,” Spring, 2001.
* Eric Shearer, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer 2000.
* Bethany Wilson, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer, 2000.
* Leonard Conapinski, “Investigation of the Presence of Chaos in a Hybrid Switching System, ” Fall, 2000.

=Research Summary=

===Cyber Physical Systems===

My research focuses primarily on theoretical nonlinear control with recent emphasis on Cyber Physical Systems. Cyber physical systems are systems with highly integrated physical and computational components (often involving the complication of networked communication). They tend to be very large and complex in scale. While many CPS systems exist in the real world, to date there are few general theoretical results available to guide both the design of such systems and the control of such systems. Most existing CPS systems are designed and controlled based upon accumulated real-world industrial knowledge that tends to be industry- or application-specific. My recent work has focused particularly on so-called ''symmetric systems.'' A symmetric system is comprised of many components with the restriction that the components be very closely related and connected together in a "regular" manner. With such restrictions, it is possible to formulate general models and then consider what types of properties remain invariant as components are added to or removed from the system. A related question is how the system behaves as components fail, which is a question of robustness.

===Stratified Systems===

Many interesting and important control systems evolve on
''stratified'' configuration spaces. Roughly speaking, we
will call a configuration manifold stratified if it contains
submanifolds upon which the system is subjected to additional
constraints or has different equations of state. For such
systems, the equations of motion on each submanifold may change
in a non-smooth, or even discontinuous manner, when the system
moves from one submanifold to another. In such cases,
traditional nonlinear control methodologies are inapplicable
because they generally rely upon differentiation in one form or
another. Yet it is the discontinuous nature of such systems
that is often their most important characteristic because the
system must cycle through different submanifolds to effectively
be controlled. Therefore, it is necessary to incorporate
explicitly into control methodologies the non-smooth or
discontinuous nature of these systems.

Robotic systems, in particular, are of this nature. A legged
robot has discontinuous equations of motion near points in the
configuration space where each of its ``feet'' come into contact
with the ground, and it is precisely the ability of the robot to
lift its feet off of the ground that enables it to move about.
Similarly, a robotic hand grasping an object often cannot
reorient the object without lifting its fingers off of the
object. Despite the obvious utility of such systems, however, a
comprehensive framework in which to consider control issues for
such systems does not exist.

The fundamental approach of this work has been to exploit the
physical geometric structure present in such problems to address
control issues such as nonlinear controllability, trajectory
generation and stabilization. The fundamental philosophy is to
generate ''general'' results, i.e., results
independent of a particular robot's number of legs, fingers or
morphology.

===Control of Mechanical Systems===

Most theoretical control results are based upon very generic dynamical systems formulations, such as
<math>\dot x = A x + B u</math> for linear systems or <math>\dot x =f(x) + g(x)u</math> for a nonlinear system. Of course this leads to the question of whether a more restrictive starting point can lead to valuable results. An important area of research along these lines is so-called control of mechanical systems where the equations of motion are not as general, but are assumed from the beginning to come from some first principle of mechanics. We have focused specifically on control of Lagrangian systems that are underactuated. Specifically, it is possible in such a framework to write general expressions for the relationship of the coupling between the controlled degree of freedoms and uncontrolled degrees of freedom, and given such expressions it is possible to know when there is close coupling between them and total decoupling between them. Furthermore, it is often the case that the coupling between the controlled and uncontrolled degrees of freedom is such that it may be only of one sign, ''i.e.'', no matter what is done with the control inputs, the uncontrolled degrees of freedom may only increase (or decrease) in magnitude. Such results have obvious important implications for control algorithms.

===Other Projects===

Other smaller projects include:
* control of aero-optic systems
* predictive biosimulation for human metabolism
* fuzzy logic-based robust control for stratified systems
* model-predictive control for marine navigation.

=Biographical Sketch=

* MS and PhD degrees in Applied Mechanics from the California Institute of Technology in 1993 and 1998, respectively.
* JD degree from Harvard Law School, 1991, ''cum laude''
* Instructor, Assistant Professor, Associate Professor, Department of Aerospace and Mechanical Engineering, University of Notre Dame, 1998 - present.
* Associate Department Chair, Department of Aerospace and Mechanical Engineering, University of Notre Dame, August 2008 - August 2012.
* Member of the Illinois Bar Association, 1991 - present.
* Registered Patent Attorney, 1998 - 2004 (not maintained).
* NSF CAREER Award Recipient.
* Boeing Welliver Faculty Fellow.
* Dockweiler Award for Excellence in Undergraduate Advising, May 2010.
* BP Foundation Outstanding Teacher of the Year, College of Engineering, Spring, 2008.
* Joyce Award (teaching), Spring, 2008.
* University of Notre Dame Kaneb teaching award, Spring, 2005.
* Department of Aerospace and Mechanical Engineering Ruth and Joel Spira Award for Excellence in Teaching, 2003 - 2004 and 2007 - 2008.
* American Society of Engineering Education Illinois/Indiana Section Outstanding Teaching Award, April, 2003.
* Department of Aerospace and Mechanical Engineering Faculty Award (teaching), 1998 - 1999.

=Courses=

* Fall 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=337 AME 30314: Differential Equations, Vibrations and Control I] (121 Students)
* Spring 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=323 AME 50652: Intermediate Controls] (7 Students) and AME 50650: Introduction to Nonlinear Analysis (9 Students)
* Fall 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=309 AME 30314, Differential Equations, Vibrations and Control I] (118 Students)
* Spring 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=304 AME 90951: Geometric Nonlinear Control] (8 students)
* Fall 2012: AME 30314: Differential Equations, Vibrations and Control I (86 Students)
* Spring 2012: [http://controls.ame.nd.edu/courses/viewforum.php?f=289 AME 30315: Differential Equations, Vibrations and Control II] (129 Students)
* Fall 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=274 AME 30314: Differential Equations, Vibrations and Control I] (112 Students)
* Summer 2011: [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Course_Syllabus,_Summer_2011 AME 40590: Intellectual Property for Engineers] [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Homework,_Summer_2011 (homeworks)]
* Spring 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=255 AME 30315: Differential Equations, Vibrations and Control II] (89 Students) and [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Intellectual_Property_for_Engineers AME 40590: Intellectual Property for Engineers] (56 Students) [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Homeworks,_Spring_2011 {homeworks)]
* Fall 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=227 AME 30314: Differential Equations, Vibrations and Control I] (81 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=228 AME 20214: Introduction to Engineering Computing] (131 Students)
* Spring 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=201 AME 30315: Differential Equations, Vibrations and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=202 AME 60652: Advanced Controls (now AME 50562: Intermediate Controls)]
* Fall 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=186 AME 30314: Differential Equations, Vibrations and Control I] (91 students)
* Spring 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=170 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=140 AME 30314: Differential Equations, Vibrations and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=141 AME 20214: Introduction to Engineering Computing]
* Spring 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=124 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=125 AME 30314: Differential Equations, Vibrations and Control I] (86 Students), [http://controls.ame.nd.edu/courses/viewforum.php?f=127 AME 60652: Advanced Controls] (11 Students) and AME 53591: Engineering Seminar Series.
* Spring 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=129 AME 30315: Differential Equations, Vibrations and Control II] (94 Students)
* Fall 2006: [http://controls.ame.nd.edu/courses/viewforum.php?f=130 AME 30314: Differential Equations, Vibrations and Control I] (79 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=131 AME 60611: Mathematical Methods I] (24 Students)
* Fall 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=132 AME 34314: Differential Equations, Vibrations and Control I (London)] and Intermediate Dynamics.
* Spring 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=133 AME 302: Modeling and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=134 Geometric Nonlinear Control]
* Fall 2004: [http://controls.ame.nd.edu/courses/viewforum.php?f=135 AME 301: Modeling and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=136 AME 550: Advanced Controls]
* Spring 2004: [http://controls.ame.nd.edu/courses/ame302/S2004 AME 302: Modeling and Control II] (72 students)
* Fall 2003: [http://controls.ame.nd.edu/courses/ame301/F2003/ AME 301: Modeling and Control I] (54 students) and AME 654: Geometric Nonlinear Control (2 students)
* Spring 2003: [http://controls.ame.nd.edu/courses/ame437/S2003/ AME 437: Control Systems Engineering] (68 students)
* Spring 2002: [http://controls.ame.nd.edu/courses/ame437/S2002/ AME 437: Control Systems Engineering] (64 students)
* Fall 2001: [http://controls.ame.nd.edu/courses/ame654/F2001/ AME 654: Geometric Nonlinear Control] (3 students)
* Spring 2001: [http://controls.ame.nd.edu/courses/ame469/S2001/ AME 469: Introduction to Robotics] (33 students)
* Spring 2000: [http://controls.ame.nd.edu/courses/ame469/S2000/ AME 469: Introduction to Robotics] (48 students), [http://controls.ame.nd.edu/courses/ame437/S2000/ AME 437: Control Systems Engineering] (50 students) and AME 598: Engineering Applications of Artificial Intelligence (5 students).
* Fall 1999: [http://controls.ame.nd.edu/courses/ame698/F1999/ AME 698: Geometric Nonlinear Control] (10 students)
* Spring 1999: [http://controls.ame.nd.edu/courses/ame469/S1999/ AME 469: Introduction to Robotics] (33 students)
* Fall 1998: [http://controls.ame.nd.edu/courses/ame469/F1998/ AME 469: Introduction to Robotics] (12 students)
* Spring 1998: [http://controls.ame.nd.edu/courses/ame437/S1998/ AME 437: Control Systems Engineering] (44 students)

===Course Blog===

In order to be able to interactively answer questions online, I've maintained a [http://controls.ame.nd.edu/courses course blog for all courses since 2002].

===AME 30315 Differential Equations, Vibrations and Control II===
*[[AME 30315 Pendulum Project]]

===AME 40590, Intellectual Property for Engineers===
*[[AME 44590 Course Syllabus, Summer 2011]]
*[[AME 44590 Homework, Summer 2011]]
*[[AME 40590 Intellectual Property for Engineers|AME 40590 Course Content]]
*[[AME 40590 Homeworks, Spring 2011]]

===AME 50652, Intermediate Controls===
*[[AME 50652 Pendulum Project]]

=[[Engineering Differential Equations: Theory and Applications, Springer 2010]]=

=[[Engineering China Summer Program]]=

=[[London CPS Workshop]]=

=[[CDIO Regional Meeting]]=

Main Page

2015-09-15T16:05:27Z

Bill: /* Publications */

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<td width=25%> [[Image:Bill5.jpeg|250px]]</td>
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Bill Goodwine 


Department of Aerospace and Mechanical Engineering 
University of Notre Dame 
Notre Dame, IN 46556 
bill@controls.ame.nd.edu 
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</table>

I have moved my homepage here. At least for the time being, my [http://controls.ame.nd.edu/~bill/oldindex.php old one] still exists.
=Publications=
==Papers==
#Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2015/icra2015.pdf Symmetries and Reduction for Multi-Agent Control], Proceedings of the 2015 IEEE International Conference on Robotics and Automation, pp 5390-5396
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icarcv2014.pdf Fractional-Order Dynamics in a Random, Approximately Scale-Free Network of Agents], Proceedings of the 2014 International Conference on Control, Automation, Robotics and Vision, pp 1581 - 1586
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/ifac14.pdf Nonlinear Stability of Approximately Symmetric Large-Scale Systems], Proceedings of the 2014 IFAC World Congress, Cape Town, South Africa
# Ashley Nettleman and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/mtns-282.pdf Symmetries of Multiagent Systems and Formation Stability], Proceedings of the 2014 International Symposium on Mathematical Theory of Networks and Systems (MTNS 14), pp 1340-1343 (extended abstract review)
# Bill Goodwine, [[Compositional Boundedness of Solutions for Symmetric Nonautonomous Control Systems]], Proceedings of the 2014 Mediterranean Conference on Control and Automation
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2014/icra-1441.pdf Modeling a Multi-Robot System with Fractional-Order Differential Equations], Proceedings of the 2014 IEEE International Conference on Robotics and Automation, Hong Kong, pp 1763-1768
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2013/automatica13.pdf Multi-agent compositional stability exploiting system symmetries], Automatica 49(11): 3158-3166, 2013
# Panos J Antsaklis,Bill Goodwine, Vijay Gupta, Michael J. McCourt, Yue Wang, Po Wu, Meng Xia, Han Yu, and Feng Zhu, [http://controls.ame.nd.edu/~bill/papers/2013/ejc13.pdf Control of cyberphysical systems using passivity and dissipativity based methods], European Journal of Control 19, no. 5 (2013): 379-388
# Bill Goodwine [http://controls.ame.nd.edu/~bill/papers/2013/med-2013a.pdf Compositional stability of approximately symmetric systems: Initial results], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED), pp. 1470-1476 IEEE, 2013
# Jason Nightingale and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2013/med-2013b.pdf An algorithm for stopping a class of underactuated nonlinear mechanical robotic systems], Proceedings of the 21st Mediterranean Conference on Control & Automation (MED) pp. 531-536, 2013
# Alice M. Nightingale, Bill Goodwine, Michael Lemmon and Eric Jumper [http://controls.ame.nd.edu/~bill/papers/2013/aiaa13.pdf Phase-Locked-Loop Adaptive-Optic Controller and Simulated Shear Layer Correction], AIAA journal, 51(11), 2714-2726, 2013
# John Gallagher and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/cdio12.pdf CDIO-Oriented Inverted Pendulum Control Project for Undergraduate Engineering Students], 2012 CDIO International Conference, Brisbane, Australia, 2012
# Michael O'Connor and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2012/med12a.pdf Symmetry-Breaking in Bifurcations of Optimal Solutions for Coordinated Nonholonomic Robotic Control], Proceedings of the 2012 Mediterranean Conference on Control & Automation (MED), pp. 1554-1559, 2012
# Janos Sztipanovits, Xenofon Koutsoukos, Gabor Karsai, Nicholas Kottenstette, Panos Antsaklis, Vijay Gupta, Bill Goodwine, John Baras, and Shige Wang, [http://controls.ame.nd.edu/~bill/papers/2011/procieee11.pdf Toward a science of cyber–physical system integration], Proceedings of the IEEE 100, no. 1 (2012): 29-44
# Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2011/icra11.pdf Fault-Tolerant Multiagent Robotic Formation Control Exploiting System Symmetries], Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, pp. 2872-2877
# Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2011/ifac11.pdf Nonlinear Disturbance Decoupling for a Mobile Robotic Manipulator over Uneven Terrain], Proceedings of the 2011 International Federation of Automatic Control World Congress, Milan, Italy, Vol. 18, No. 1, pp. 6930-6936
# Dayu Lv and Bill Goodwine, "Pancreas Modeling by a Deterministic Optimization Method" 'International Journal of Data Mining and Bioinformatics,' Volume 5, Number 3, Pages 308-320 (2011).
# Goodwine, Bill, and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent coordination exploiting system symmetries], American Control Conference (ACC), 2010, pp. 830-835
# Baoyang Deng, Mihir Sen, and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/acc09.pdf Bifurcations and symmetries of optimal solutions for distributed robotic systems], Proceedings of the 2009 American Control Conference, St. Louis, MO, pp. 4127-4133
#Joel Jimenez-Lozano and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icarcv10.pdf Nonlinear Disturbance Decoupling for a Nonholonomic Mobile Robotic Manipulation Platform], Proceedings of the Eleventh International Conference on Control, Automation, Robotics and Vision (ICARCV 2010), Singapore, pp. 1530-1535
#Neil Petroff and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/iros10.pdf Nonholonomic and Stratified Robotic Manipulation Supplemented with Fuzzy Control: Theory and Experiment], Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, pp. 1202-1208
#Bill Goodwine and Panos Antsaklis, [http://controls.ame.nd.edu/~bill/papers/2010/acc10.pdf Multiagent Coordination Exploiting System Symmetries], Proceedings of the 2010 American Controls Conference, pp. 830-835
#Baoyang Deng, Andreas K. Valenzuela and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2010/icra10a.pdf Bifurcations of Optimal Solutions for Coordinated Robotic Systems: Numerical and Homotopy Methods], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 4475-4480
#Bill Goodwine and Jason Nightingale, [http://controls.ame.nd.edu/~bill/papers/2010/icra10b.pdf The Effect of Dynamic Singularities on Robotic Control and Design], Proceedings of the 2010 IEEE International Conference on Robotics and Automation, (41.6% acceptance rate) Anchorage, AK, pp. 5213-5218
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/bibm09.pdf Pancreas Modeling from IVGTT Data Using a Deterministic Optimal Search], Proceedings of the 2009 IEEE International Conference on Bioinformatics & Biomedicine, (35% acceptance rate) Washington, D.C.
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2009/wafr09.pdf A Stopping Algorithm for Mechanical Systems], Algorithmic Foundations of Robotics VIII, Gregory S. Chirikjian, et al., editors, Eighth International Workshop on the Algorithmic Foundations of Robotics, Guanajuato, Mexico, 2009, pp. 167-180
#Jason Nightingale, Richard Hind and Bill Goodwine, "Geometric analysis of a class of constrained mechanical control systems in the nonzero velocity setting,"Proceedings of the 17th International Federation of Automatic Control (IFAC) World Congress, Seoul, Korea July, 2008.
#Jason Nightingale, Richard Hind and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/icra08.pdf Intrinsic Vector-Valued Symmetric Form for Simple Mechanical Control Systems in the Nonzero Velocity Setting], Proceedings of the 2008 IEEE International Conference on Robotics and Automation, (43.4% acceptance rate) Pasadena, CA, May, 2008
#Dayu Lv and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2008/biodevices08.pdf A New Metabolism Model for Human Skeletal Muscle], Proceedings of the IEEE International Conference on Biomedical Electronics and Devices, January, 2008, Maderia, Portugal
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2007/ijrr07.pdf Motion Planning for Nonlinear Symmetric Distributed Robotic Formation], International Journal of Robotics Research, 2007, 26:10, pp. 1025-1042
#Alice Nightingale, Bill Goodwine, Michael Lemmon, and Eric Jumper, 2007, "Feedforward Adaptive-Optic System Identification Analysis for Mitigating Aero-Optic Disturbances," Proceedings of the AIAA 2007 Plasmadynamics and Lasers Conference.
#Alice Nightingale, Daniel D. Duffin, Michael Lemmon, Bill Goodwine and Eric Jumper, 2005, "Adaptive-Optic Correction of a Regularized Compressible Shear Layer," Proceedings of the 37th AIAA Plasmadynamics and Lasers Conference, San Francisco, CA, June, 2006.
#Alice Nightingale, Bill Goodwine and Eric Jumper, 2005, "Regularizing Shear Layer for Adaptive Optics Control Application," accepted for presentation at the 36th AIAA Plasmadynamics and Lasers Conference.
# Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2004/ra04.pdf Stratified motion planning on nonsmooth domains with robotic applications], IEEE Transactions on Robotics and Automation 20.1 (2004): 128-132
#Yejun Wei, Bill Goodwine and Steven B. Skaar, 2004, "Kinematics of Vision-Based Stratified Robotic Manipulation," Proceedings of the 11th IFToMM World Congress, Tianjin, China. Abstract review.
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, "Flow-based control of temperature in long ducts," 2004, International Journal of Heat and Mass Transfer, 47,pp. 4995-5009.
# M. Brett McMickell and Bill Goodwine, 2003, "Reduction and Controllability of Nonlinear Symmetric Distributed Systems," International Journal of Control, 76:18, pp. 1809-1822, 2003.
#M. Brett McMickell and Bill Goodwine, 2003, [http://controls.ame.nd.edu/~bill/papers/2003/icra03a.pdf Reduced Order Motion Planning for Nonlinear Symmetric Distributed Robotic Systems], Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review
#Sorour Alotaibi, Mihir Sen, Bill Goodwine and K.T. Yang, 2003, "Controllability of Cross-Flow Heat Exchangers," International Journal of Heat and Mass Transfer, 47, pp. 913-924
#M. Brett McMickell and Bill Goodwine, 2003, MICAbot: A Platform for Large Scale Coordinated Distributed Mobile Robot Control, Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan. Full paper review.
#S. Alotaibi, J.W. Goodwine, M. Sen and K.T. Yang, 2003, Controllability of conductive-convective systems, Proceedings of the 6th ASME-JSME Thermal Engineering Joint Conference, Hawaii, Paper No. TED-AJ03-247, pp. 1-6.
#Antonio Cardenas, Bill Goodwine, Steven B. Skaar and Michael Seelinger, Vision-Based Control of a Mobile Base and On-Board Arm, The International Journal of Robotic Research, 22: 9, pp. 677-698, 2003
#Yejun Wei and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/icarcv2002.pdf Vision-Based Non-Smooth Kinematic Stratified Object Manipulation], Proceedings of the 2002 Seventh Annual Conference on Control, Automation, Robotics and Vision, Singapore, 2002
#Yejun Wei, S.B. Skaar and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2002/iros02.pdf Vision-Based Stratified Robotic Manipulation], Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, 2002
#S. Batill, S. Skaar, R. Nelson, B. Goodwine, J. Mason, and M. Sen, 2002, Development of a Curriculum for Mechanical Engineering Based Upon Intelligent Systems and Automation, Session 1526, Proceedings of the 2002 American Society for Engineering Education Annual Conference and Exposition, 2002
#S. Alotaibi, Mihir Sen, B. Goodwine, and K.T. Yang, Numerical Simulation of Thermal Control of Heat Exchangers, Numerical Heat Transfer Journal, Part A: Applications, 41:3, pp. 229-244, 2002
#Bill Goodwine and Joel Burdick, A General Method for Motion Planning for Quasi-Static Legged Robotic Locomotion," IEEE International Journal of Robotics and Automation, 18:2, pp. 209-222, 2002
#M. Brett McMickell and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02b.pdf Reduction and Controllability of Symmetric Distributed Systems with Drift], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3454-3460, 2002. Full paper review.
#Yejun Wei and Bill Goodwine, 2002, [http://controls.ame.nd.edu/~bill/papers/2002/icra02a.pdf Stratified Motion Planning on Non-Smooth Domains with Application to Robotic Legged Locomotion and Manipulation], Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 3546-3552. Full paper review.
#Bill Goodwine and Milos Zefran, 2002, Feedback Stabilization of a Class of Unstable Nonholonomic Systems, Transactions of the ASME, Journal of Dynamics Systems, Measurement, & Control, 124, pp. 221-230.
#M. Brett McMickell and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/2001/iros01.pdf Reduction and Controllability of Symmetric Distributed Systems with Robotic Applications], Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, Hawaii, pp. 1232-1237. Full paper review.
#S. Alotaibi, M. Sen, Bill Goodwine, and K.T. Yang, 2001, Thermal Control of Heat Exchangers, Proceedings of the 35th National Heat Transfer Conference, NHTC01-12517, Anaheim, CA.
#Yejun Wei and Bill Goodwine,, 2001, Theoretical and Experimental Investigation of Stratified Robotic Manipulation, Proceedings of the 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea. Full paper review.
#Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.
#Bill Goodwine and Gabor Stepan, 2000, "Controlling unstable Rolling Phenomena, Journal of Vibration and Control, 6:1, pp. 137-158, January 2000.
# Qun Ma, Antonio Cardenas, Mike Seelinger, Bill Goodwine and Steven Skaar, 2000, "Supervisory Control of a Mobile Robot Using Point-and-Click Mobile Camera-Space Manipulation," Proceedings of the 4th World Multiconference on Systemics, Cybernetics and Informatics SCI 2000 and The 6th International Conference on Information Systems, Analysis and Synthesis ISAS 2000, Orlando, Florida.
# Bill Goodwine and Yejun Wei, 2000, [http://controls.ame.nd.edu/~bill/papers/2000/allerton.pdf Theoretical and Experimental Investigation of Stratified Robotic Finger Gaiting and Manipulation], Proceedings of the 38th Annual Allerton Conference on Communication, Control and Computing, Allerton, Illinois
# Bill Goodwine and Joel Burdick, Motion Planning for Kinematic Stratified Systems with application to Quasi-Static Legged Locomotion and Finger Gaiting, Proceedings of the Workshop Algorithmic Foundations of Robotics.
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/1999/ifac99.pdf Stratified Motion Planning with Application to Robotic Finger Gaiting], Proceedings of the 1999 International Federation of Automatic Control, IFAC'99: 14th World Congress Beijing, China. Full paper review.
# Gabor Stepan and Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/1999/ds99.pdf Analysis and Control of Unstable Rolling Wheel Dynamics], 1999 SIAM Conference on Applications of Dynamical Systems, Showbird, UT, 1999, abstract submission
# B. Goodwine, Michael Seelinger, John-David Yoder, Qun Ma and Steven Skaar, [http://controls.ame.nd.edu/~bill/papers/1999/fsr99.pdf Applications of mobile camera-space manipulation], Proceedings of FSR'99: Field and Service Robotics, pages 102-113, Pittsburg, 1999
# Bill Goodwine, 1999, Stratified Motion Planning with Application to Robotic Finger Gaiting, Proceedings of the 1999 IFToMM 10th World Congress, Oulu, Finland. Abstract review.
# Bill Goodwine and Gabor Stepan, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/misk98.pdf Stabilizing Switching Controllers], Proceedings of the 1998 Conference on Numerical Mathematics and Computational Mechanics, Miskolc, Hungary. Abstract review
# Bill Goodwine, Michael Seelinger, Steven B. Skaar and Qun Ma, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/spie98.pdf Nonholonomic Camera Space Manipulation using Cameras Mounted on a Mobile Base], Proceedings of the 1998 SPIE conference on Sensor Fusion and Decentralized Control in Robotic Systems, Boston, Massachusetts. Abstract review
# Bill Goodwine and Joel Burdick, 1998, [http://controls.ame.nd.edu/~bill/papers/1998/icra98.pdf Gait Controllability for Legged Robots], Proceedings of the 1998 IEEE Conference on Robotics and Automation,Leuven, Belgium. Full paper review.
# Bill Goodwine, [http://controls.ame.nd.edu/~bill/papers/thesis.pdf Control of Stratified Systems with Robotic Applications], Ph.D Thesis, California Institute of Technology, 1997
# Bill Goodwine and Joel Burdick, 1997, [http://controls.ame.nd.edu/~bill/papers/1997/icra97.pdf Trajectory Generation for Legged Robotic Systems], Proceedings of the 1997 IEEE Conference on Robotics and Automation, Albuquerque, New Mexico. Full paper review
# Shuuji Kajita, Bill Goodwine and Joel Burdick, Walking Direction Control of a Biped Robot with Point Feet Using Dynamic Effects in 3-D Space, Proceedings of the 1997 Robotics Society of Japan Conference, Tokyo, Japan. 1997 (in Japanese).
# Bill Goodwine and Joel Burdick, [http://controls.ame.nd.edu/~bill/papers/1996/mtns96.pdf Controllability of Kinematic Control Systems on Stratified Configuration Spaces], Mathematical Theory of Networks and Systems, 1996, St. Louis
# Bill Goodwine and Joel Burdick, 1996, [http://controls.ame.nd.edu/~bill/papers/1996/cdc96.pdf Controllability with Unilateral Control Inputs], Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan. Full paper review, 1996, (Vol. 3, pp. 3394-3399
# Bill Goodwine and Gabor Stepan, [http://controls.ame.nd.edu/~bill/papers/1996/enoc96.pdf Stabilization of the Classical Shimmying Wheel], Proceedings of the 2nd European Nonlinear Oscillations Conference, Prague, Czech Republic, 1996
#Bill Goodwine, 1991, Abortion Parental Notification Statutes: Hodgson v. Minnesota, 110 S. Ct. 2926 (1990) and Ohio v. Akron Center for Reproductive Health, 110 S. Ct. 2972 (1990), Harvard Journal of Law & Public Policy, 14:1, pp. 237-247.

==Books and Chapters in Books==
# Bill Goodwine, [http://www.springer.com/mathematics/dynamical+systems/book/978-1-4419-7918-6 Engineering Differential Equations: Theory and Applications], Springer, 2010.
#* Some [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Movies movies] are available illustrating some of the more interesting solutions, generally for PDEs
#* A list of [http://controls.ame.nd.edu/mediawiki/index.php/Engineering_Differential_Equations:_Theory_and_Applications,_Springer_2010#Errata errata] is also available
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849318047 Robotics and Automation Handbook], Chapter 3, Inverse Kinematics, Thomas R. Kurfess, Editor, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2nd Edition, 2005.
# Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Fundamentals of Control Theory, Mohamed Gad-el-Hak, Editor, 2001.
# Mihir Sen and Bill Goodwine, [http://www.crcpress.com/product/isbn/9780849321061 The MEMS Handbook], Chapter on Soft Computing in Control, Mohamed Gad-el-Hak, Editor, 2001.

==Erdős Number==
# Erdős, P.; Shapiro, H. S.; Shields, A. L. Large and small subspaces of Hilbert space. Michigan Math. J. 12 1965 169--178.
# Shields, Allen L. Some problems in operator theory. Notes by Michael J. Hoffman. Lecture Notes in Math., 693, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977), pp. 157--167, Springer, Berlin, 1978.
# Marsden, Jerrold E.; Hoffman, Michael J. Basic complex analysis. Second edition. W. H. Freeman and Company, New York, 1987. xiv+604 pp. ISBN: 0-7167-1814-6
# Banavara N. Shashikanth, Jerrold E. Marsden, Joel W. Burdick and Scott D. Kelly, The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vorticesPhys. Fluids 14, 1214 (2002).
# Bill Goodwine and Joel Burdick, 2001, "Controllability of Kinematic Control Systems on Stratified Configuration Spaces," IEEE Transactions on Automatic Control, 46:3, pp. 358-368.

=Students=

==PhD Students==
* Kevin Leyden, in progress
* Jason Nightingale, Ph.D. defended 8:00 am, June 4, 2012 [http://controls.ame.nd.edu/~bill/students/jason.pdf thesis]
* Dayu Lv, Ph.D. defended March 17, 2011, [http://controls.ame.nd.edu/~bill/students/dayu.pdf thesis]
* Baoyang Deng, Ph.D., defended March 11, 2011 [http://controls.ame.nd.edu/~bill/students/baoyang.pdf thesis]
* Alice Nightingale, Ph.D. defended November 3, 2010 [http://controls.ame.nd.edu/~bill/students/alice.pdf thesis]
* Neil Petroff, Ph.D. defended, October 6, 2006 [http://controls.ame.nd.edu/~bill/students/neil.pdf thesis]
* M. Brett McMickell, Ph.D. defended 2003
* Yejun Wei, Ph.D. defended 2002

==MS Students==
* Ashley Nettleman, M.S., November 2014 [http://controls.ame.nd.edu/~bill/students/ashley.pdf thesis]
* Nicholas Galati, July 15, 2013
* Michael O'Connor, Fall 2011
* Qun (Marc) Ma, M.S., 2000

==Undergraduate Research Projects==

* Patrick O’Meara, “Control and Dynamics of a Fleet of Automobiles,” spring, summer and fall 2013
* Nick Turner, “Mathematics and Theory of Origami,” summer 2013
* Catherine Bentzen, “Jellyfish Propulsion,” summer 2013
* Blair Rasmus, John Gallagher, Derek Wolf, “Development of Feedback Microcontroller for an Inverted Pendulum System for AME 30315” (all three, Fall 2011, John Gallagher continued through Spring 2012)
* Jeff O’Brien, “Synchronization and Limit Cycle Solutions for Coupled Hybrid Systems” (Fall and Spring, 2011)
* John Gallagher, “Describing Function Analysis with Non-Harmonic Basis Functions” (Spring 2012 – started in January)
* Adam Wojcik,. “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Paul Fleury, “Development and rehabilitation of a stratified robotic manipulation platform,” Fall 2010 and Spring 2011
* Robert Powers, “Energy storage technologies: a sustainable solution to electrical load shedding in rural Bangladesh,” Spring 2010
* “Raymond LeGrand, "Development of a Microprocessor controlled Inverted Pendulum Experiment,” , Summer and Fall 2010
* Steven Brus, “Homotopy Methods for Coordinated Robotic Systems,” Summer 2010
* Andres Valenzuela, “Bifurcation Measures for Nonlinear Boundary Value Problems in Optimal Control of Mobile Robot Formations,” Fall 2008 and Spring 2009. Undergraduate thesis in Spring 2009
* Blake Shilide, “Aero-Optic Shear Layer Control and Simulation,” Spring, 2005
* Tim Ronan, “MICAbot Programming and TinyOS,” Summer, 2003
* Timothy Kacmar, “Development of a Multi-Manipulator Path Planning Collision Avoidance System,” Fall, 2003
* Meaghan Perry-Eaton, “Investigation of Automotive Fuel Cell Energy System Usage and Feasibility,” Fall, 2003
* Peter Balough, “Development of a Mobile Multi-Robot Simulation Environment in Java and Hardware Development for the TagMote,” Summer and Fall, 2003
* Kristin Dormuth, “MICAbot Programming and TinyOS,” Summer, 2003
* John Aman, “MICAbot Programming and TinyOS,” Summer, 2003
* Denis Sullivan, “MICAbot Programming and TinyOS,” Summer and Fall, 2003
* Thomas Apker, “Investigation of the Efficacy of Switching Multi-Controller Systems,” Spring, 2003
* Daniel Luedtke, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Spring, 2003
* Tommy Ferrara, “Development of a Distributed Mobile Robotic Platform,” Summer, 2002 and Fall, 2003.
* Dennis Abdelnour, “Development Programming for a Mobile Robot,” Spring, 2001.
* Eric Shearer, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer 2000.
* Bethany Wilson, “Investigation and Implementation of a Robotic Stratified Manipulation System,” Summer, 2000.
* Leonard Conapinski, “Investigation of the Presence of Chaos in a Hybrid Switching System, ” Fall, 2000.

=Research Summary=

===Cyber Physical Systems===

My research focuses primarily on theoretical nonlinear control with recent emphasis on Cyber Physical Systems. Cyber physical systems are systems with highly integrated physical and computational components (often involving the complication of networked communication). They tend to be very large and complex in scale. While many CPS systems exist in the real world, to date there are few general theoretical results available to guide both the design of such systems and the control of such systems. Most existing CPS systems are designed and controlled based upon accumulated real-world industrial knowledge that tends to be industry- or application-specific. My recent work has focused particularly on so-called ''symmetric systems.'' A symmetric system is comprised of many components with the restriction that the components be very closely related and connected together in a "regular" manner. With such restrictions, it is possible to formulate general models and then consider what types of properties remain invariant as components are added to or removed from the system. A related question is how the system behaves as components fail, which is a question of robustness.

===Stratified Systems===

Many interesting and important control systems evolve on
''stratified'' configuration spaces. Roughly speaking, we
will call a configuration manifold stratified if it contains
submanifolds upon which the system is subjected to additional
constraints or has different equations of state. For such
systems, the equations of motion on each submanifold may change
in a non-smooth, or even discontinuous manner, when the system
moves from one submanifold to another. In such cases,
traditional nonlinear control methodologies are inapplicable
because they generally rely upon differentiation in one form or
another. Yet it is the discontinuous nature of such systems
that is often their most important characteristic because the
system must cycle through different submanifolds to effectively
be controlled. Therefore, it is necessary to incorporate
explicitly into control methodologies the non-smooth or
discontinuous nature of these systems.

Robotic systems, in particular, are of this nature. A legged
robot has discontinuous equations of motion near points in the
configuration space where each of its ``feet'' come into contact
with the ground, and it is precisely the ability of the robot to
lift its feet off of the ground that enables it to move about.
Similarly, a robotic hand grasping an object often cannot
reorient the object without lifting its fingers off of the
object. Despite the obvious utility of such systems, however, a
comprehensive framework in which to consider control issues for
such systems does not exist.

The fundamental approach of this work has been to exploit the
physical geometric structure present in such problems to address
control issues such as nonlinear controllability, trajectory
generation and stabilization. The fundamental philosophy is to
generate ''general'' results, i.e., results
independent of a particular robot's number of legs, fingers or
morphology.

===Control of Mechanical Systems===

Most theoretical control results are based upon very generic dynamical systems formulations, such as
<math>\dot x = A x + B u</math> for linear systems or <math>\dot x =f(x) + g(x)u</math> for a nonlinear system. Of course this leads to the question of whether a more restrictive starting point can lead to valuable results. An important area of research along these lines is so-called control of mechanical systems where the equations of motion are not as general, but are assumed from the beginning to come from some first principle of mechanics. We have focused specifically on control of Lagrangian systems that are underactuated. Specifically, it is possible in such a framework to write general expressions for the relationship of the coupling between the controlled degree of freedoms and uncontrolled degrees of freedom, and given such expressions it is possible to know when there is close coupling between them and total decoupling between them. Furthermore, it is often the case that the coupling between the controlled and uncontrolled degrees of freedom is such that it may be only of one sign, ''i.e.'', no matter what is done with the control inputs, the uncontrolled degrees of freedom may only increase (or decrease) in magnitude. Such results have obvious important implications for control algorithms.

===Other Projects===

Other smaller projects include:
* control of aero-optic systems
* predictive biosimulation for human metabolism
* fuzzy logic-based robust control for stratified systems
* model-predictive control for marine navigation.

=Biographical Sketch=

* MS and PhD degrees in Applied Mechanics from the California Institute of Technology in 1993 and 1998, respectively.
* JD degree from Harvard Law School, 1991, ''cum laude''
* Instructor, Assistant Professor, Associate Professor, Department of Aerospace and Mechanical Engineering, University of Notre Dame, 1998 - present.
* Associate Department Chair, Department of Aerospace and Mechanical Engineering, University of Notre Dame, August 2008 - August 2012.
* Member of the Illinois Bar Association, 1991 - present.
* Registered Patent Attorney, 1998 - 2004 (not maintained).
* NSF CAREER Award Recipient.
* Boeing Welliver Faculty Fellow.
* Dockweiler Award for Excellence in Undergraduate Advising, May 2010.
* BP Foundation Outstanding Teacher of the Year, College of Engineering, Spring, 2008.
* Joyce Award (teaching), Spring, 2008.
* University of Notre Dame Kaneb teaching award, Spring, 2005.
* Department of Aerospace and Mechanical Engineering Ruth and Joel Spira Award for Excellence in Teaching, 2003 - 2004 and 2007 - 2008.
* American Society of Engineering Education Illinois/Indiana Section Outstanding Teaching Award, April, 2003.
* Department of Aerospace and Mechanical Engineering Faculty Award (teaching), 1998 - 1999.

=Courses=

* Fall 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=337 AME 30314: Differential Equations, Vibrations and Control I] (121 Students)
* Spring 2014: [http://controls.ame.nd.edu/courses/viewforum.php?f=323 AME 50652: Intermediate Controls] (7 Students) and AME 50650: Introduction to Nonlinear Analysis (9 Students)
* Fall 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=309 AME 30314, Differential Equations, Vibrations and Control I] (118 Students)
* Spring 2013: [http://controls.ame.nd.edu/courses/viewforum.php?f=304 AME 90951: Geometric Nonlinear Control] (8 students)
* Fall 2012: AME 30314: Differential Equations, Vibrations and Control I (86 Students)
* Spring 2012: [http://controls.ame.nd.edu/courses/viewforum.php?f=289 AME 30315: Differential Equations, Vibrations and Control II] (129 Students)
* Fall 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=274 AME 30314: Differential Equations, Vibrations and Control I] (112 Students)
* Summer 2011: [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Course_Syllabus,_Summer_2011 AME 40590: Intellectual Property for Engineers] [http://controls.ame.nd.edu/mediawiki/index.php/AME_44590_Homework,_Summer_2011 (homeworks)]
* Spring 2011: [http://controls.ame.nd.edu/courses/viewforum.php?f=255 AME 30315: Differential Equations, Vibrations and Control II] (89 Students) and [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Intellectual_Property_for_Engineers AME 40590: Intellectual Property for Engineers] (56 Students) [http://controls.ame.nd.edu/mediawiki/index.php/AME_40590_Homeworks,_Spring_2011 {homeworks)]
* Fall 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=227 AME 30314: Differential Equations, Vibrations and Control I] (81 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=228 AME 20214: Introduction to Engineering Computing] (131 Students)
* Spring 2010: [http://controls.ame.nd.edu/courses/viewforum.php?f=201 AME 30315: Differential Equations, Vibrations and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=202 AME 60652: Advanced Controls (now AME 50562: Intermediate Controls)]
* Fall 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=186 AME 30314: Differential Equations, Vibrations and Control I] (91 students)
* Spring 2009: [http://controls.ame.nd.edu/courses/viewforum.php?f=170 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=140 AME 30314: Differential Equations, Vibrations and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=141 AME 20214: Introduction to Engineering Computing]
* Spring 2008: [http://controls.ame.nd.edu/courses/viewforum.php?f=124 AME 30315: Differential Equations, Vibrations and Control II]
* Fall 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=125 AME 30314: Differential Equations, Vibrations and Control I] (86 Students), [http://controls.ame.nd.edu/courses/viewforum.php?f=127 AME 60652: Advanced Controls] (11 Students) and AME 53591: Engineering Seminar Series.
* Spring 2007: [http://controls.ame.nd.edu/courses/viewforum.php?f=129 AME 30315: Differential Equations, Vibrations and Control II] (94 Students)
* Fall 2006: [http://controls.ame.nd.edu/courses/viewforum.php?f=130 AME 30314: Differential Equations, Vibrations and Control I] (79 Students) and [http://controls.ame.nd.edu/courses/viewforum.php?f=131 AME 60611: Mathematical Methods I] (24 Students)
* Fall 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=132 AME 34314: Differential Equations, Vibrations and Control I (London)] and Intermediate Dynamics.
* Spring 2005: [http://controls.ame.nd.edu/courses/viewforum.php?f=133 AME 302: Modeling and Control II] and [http://controls.ame.nd.edu/courses/viewforum.php?f=134 Geometric Nonlinear Control]
* Fall 2004: [http://controls.ame.nd.edu/courses/viewforum.php?f=135 AME 301: Modeling and Control I] and [http://controls.ame.nd.edu/courses/viewforum.php?f=136 AME 550: Advanced Controls]
* Spring 2004: [http://controls.ame.nd.edu/courses/ame302/S2004 AME 302: Modeling and Control II] (72 students)
* Fall 2003: [http://controls.ame.nd.edu/courses/ame301/F2003/ AME 301: Modeling and Control I] (54 students) and AME 654: Geometric Nonlinear Control (2 students)
* Spring 2003: [http://controls.ame.nd.edu/courses/ame437/S2003/ AME 437: Control Systems Engineering] (68 students)
* Spring 2002: [http://controls.ame.nd.edu/courses/ame437/S2002/ AME 437: Control Systems Engineering] (64 students)
* Fall 2001: [http://controls.ame.nd.edu/courses/ame654/F2001/ AME 654: Geometric Nonlinear Control] (3 students)
* Spring 2001: [http://controls.ame.nd.edu/courses/ame469/S2001/ AME 469: Introduction to Robotics] (33 students)
* Spring 2000: [http://controls.ame.nd.edu/courses/ame469/S2000/ AME 469: Introduction to Robotics] (48 students), [http://controls.ame.nd.edu/courses/ame437/S2000/ AME 437: Control Systems Engineering] (50 students) and AME 598: Engineering Applications of Artificial Intelligence (5 students).
* Fall 1999: [http://controls.ame.nd.edu/courses/ame698/F1999/ AME 698: Geometric Nonlinear Control] (10 students)
* Spring 1999: [http://controls.ame.nd.edu/courses/ame469/S1999/ AME 469: Introduction to Robotics] (33 students)
* Fall 1998: [http://controls.ame.nd.edu/courses/ame469/F1998/ AME 469: Introduction to Robotics] (12 students)
* Spring 1998: [http://controls.ame.nd.edu/courses/ame437/S1998/ AME 437: Control Systems Engineering] (44 students)

===Course Blog===

In order to be able to interactively answer questions online, I've maintained a [http://controls.ame.nd.edu/courses course blog for all courses since 2002].

===AME 30315 Differential Equations, Vibrations and Control II===
*[[AME 30315 Pendulum Project]]

===AME 40590, Intellectual Property for Engineers===
*[[AME 44590 Course Syllabus, Summer 2011]]
*[[AME 44590 Homework, Summer 2011]]
*[[AME 40590 Intellectual Property for Engineers|AME 40590 Course Content]]
*[[AME 40590 Homeworks, Spring 2011]]

===AME 50652, Intermediate Controls===
*[[AME 50652 Pendulum Project]]

=[[Engineering Differential Equations: Theory and Applications, Springer 2010]]=

=[[Engineering China Summer Program]]=

=[[London CPS Workshop]]=

=[[CDIO Regional Meeting]]=

Engineering Differential Equations: Theory and Applications, Springer 2010

2015-08-26T14:53:39Z

Bill: /* Chapter 1 */

This page contains supplementary material for the book, ''Engineering Differential Equations: Theory and Applications'', by Bill Goodwine. 2010, Springer.

=Movies=
Chapter 11 considers solutions to partial differential equations.
==The One-Dimensional Wave Equation==
Section 11.1 considers the one-dimensional wave equation.

Some movies:
*String of length 3 plucked at L=1 (modeling a guitar):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode1.mpg The first (fundamental) mode of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15.mpg The first five modes of the plucked string plotted separately]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15sum.mpg The sum of the first five modes of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode50sum.mpg The sum of the first fifty modes of the plucked string]
*String of length 3 that is impacted near L=1 (modeling a piano):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact10sum.mpg The sum of the first ten modes of the impacted string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact50sum.mpg The sum of the first fifty modes of the impacted string]

==The One-Dimensional Heat Conduction Equation==
Section 11.3 considers the one-dimensional heat conduction equation.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinhomo.mpg The solution to the heat equation with inhomogeneous boundary conditions]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinsulated.mpg The solution to the heat equation with an insulated end]

==The Two-Dimensional Heat Equation==
Movie:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/twoheat.mpg Solution to the heat conduction equation in two dimensions]

==Vibrating Membranes==
Partial differential equations describing vibrating membranes in rectangular and polar coordinates are considered in Section 11.5.

Section 11.5.1 presents the two-dimensional wave equation in rectangular coordinates.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum11.mpg 1-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum21.mpg 2-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum22.mpg 2-2 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrumimpact.mpg Rectangular drum impacted near a corner]

Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum10.mpg 1-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum11.mpg 1-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum12.mpg 1-2 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum13.mpg 1-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum20.mpg 2-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum21.mpg 2-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum43.mpg 4-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drumimpact.mpg Circular drum that is impacted by a drum stick]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum.mpg Another drum impact movie]
*[http://www.youtube.com/watch?v=w8Gxut0odyc#t=4m10s Cool youtube movie of slow motion impact of drum head and cymbal]

=Errata=

==Chapter 1==
*[[p. 58, line -3, Equation 2.4]]: the ''c'' in the denominator should be the specific heat.

==Chapter 2==
*p. 61, second paragraph of Section 2.2, line 2: "and" should be "is".
*[[p. 89, line -7]]: the right hand side of the equation below equation 2.35 should be a function of t, not x.

==Chapter 3==
*[[p. 97, line -3]]: there is an extra closing parenthesis in the equation for the Wronskian.
*[[p. 105, line 12]]: both exponents should be <math>-\omega_n</math>.
*[[p. 117, Figure 3.5]]: the figure plots the solution to <math>\ddot x + \dot x + 10 x = 0</math> and not <math>2 \ddot x + \dot x + 10 x = 0</math> as stated. It really doesn't change the qualitative aspects of the problem, however.

==Chapter 4==
*[[p. 125, line 5]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line 8]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line -4]]: the coefficient of the x term in the differential equation should be squared.
*[[p. 128, Equation 4.8]]: the numerator of the coefficient of the sine term should be the initial velocity.
*[[p. 138, line 6 (large boxed equation)]]: the first zeta in the parentheses in the coefficient of the second exponential on the second line should be negative.
*[[p. 139, Equation 4.14]]: the second term should contain the derivative of x, not x.
*[[p. 142, Figure 4.16]]: the figure is incorrect in that the square root was not used to plot the curves.
*[[p. 156, Exercise 4.22]]: at this point in the book we don't know how to find the homogeneous solutions for these two systems.
*[[p. 158, Exercise 4.26, Figure 4.32]]: the variable x is not the distance along the beam, but rather the displacement at the end.
*[[p. 159, Exercise 4.27, Figure 4.33]]: the angle is incorrectly marked as the angular velocity.

==Chapter 5==
*[[p. 163, line 6]]: the first (n+1) term should be (n+2).
*[[p. 164, Equation 5.5]]: the first coefficient in the second series should be (n+2) not (n+1).
*[[p. 167, lines -4,-3 and -2]]: the expressions for the derivatives of the function are wrong.
* p. 170, line 6: at the end of the line "Table 5.2" should be "Table 5.1."
*[[p. 172, line -5]]: there should be a negative sign on the right hand side of the equation.
*[[p. 174, Equation 5.14]]: the first term in the numerator on the right hand side should be multiplied by 20.
*[[p. 181, line 16]]: the two terms on the right-hand side of the equation are switched, leading to the wrong answer for <math>a_2</math>. This wrong number then propagates to lines -1 and -6 on the same page.
*[[p. 182, line 14]]: in the first series for the second derivative, the exponent should be (n-2) not (n-1).
*[[p. 185, line 2]]: the recursion relation has two mistakes. The left hand side should be for a_{n+2} not {n+1}. Also, the negative sign should not be there.
*[[p. 186, line 6]]: the left hand side of the recursion relation should be for a_{n+2} not {n+1}.
*p. 188, Exercise 5.1, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*p. 189, Exercise 5.2, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*[[p. 190, Exercise 5.13]]: the middle term in the denominator of the second term should be "2 t" not "t2".
*[[p. 191, Exercise 5.16]]: the independent variable in the equation is x, so the derivative terms should be with respect to x.

==Chapter 6==
*[[p. 195, line 1]]: the third term in the vector on the right hand side should have a subscript of 4, not 3.
*[[p. 209, line -8]]: the exponential term should be multiplying the second term as well.
*[[p. 210, line 1]]: same error as on p. 209 carried through.
*[[p. 220, line -9]]: the superscript for the second term in the equation should be m-3.
*[[p. 244, line -11]]: the first component of the vector on the far right should contain t, not tau.
*[[p. 245, line 8]]: the matrix A7 does not have a set of n linearly-independent eigenvectors.
*[[p. 247, line -7]]: A3 should be A2.

==Chapter 7==
*p. 253, line 5: the word "of" is repeated.
*[[p. 265, Equation (7.16)]]: this equation has multiple typos. The last term in parentheses in the last line should be (1-k1-2 k3). Also the second line has misaligned parentheses.

==Chapter 8==
*[[p. 288, last line in Table 8.1]]: the exponent should be "-a t" and not "a t".
*p. 297, Example 8.14: the "3" multiplying the <math>t^2</math> term on the right hand side is dropped half way through the example. Because it scales the whole right hand side, it scales simply scales the solution by 3. Thus the final answer on p. 299 should be multiplied by 3, as should the equation on the top of page 299. Also the two equations in the middle of p. 298 involving X(s) should have the right hand side multiplied by 3.
*p. 326, line -10: "Figure 8.8" should be "Figure 8.37".
*p. 327: the pendulum in Figure 8.36 should indicate a length, ''l'', for the pendulum.

==Chapter 9==
*[[p. 348, line 4]]: the numerator for both expressions of G1 should be 5.
*[[p. 348, line 6]]: the numerator for both expressions of G1 should be 10.
*[[p. 349, caption to Figure 9.16]]: the numerator for G1 should be 4 in the numerator for G2 should be 9.
*p. 354, line 9: the word "row" should be "column".
*p. 368, line 4: "r=10, 1, -1, and 10" should be "r=10, 1, -1, -10".
*p. 368, line -4: "Systems with left half-plane zeros are called..." should be "Systems with right half-plane zeros are called...".
*[[p. 403, line -7]]: the arctan should be a ratio of the imaginary to real components of G(i \omega).

==Chapter 11==
*[[p. 513, line 2]]: the coefficient is alpha^2, not alpha.
*[[p. 515, line 6]]: the "x" should be outside, not inside, the square root.
*[[p. 524, line 1]]: the sine function should not equal n pi, the argument to it should.
*[[p. 525, Equation 11.43]]: the denominator in both exponentials should be <math>L_x</math>.
*[[p. 525, Equation 11.44]]: the first term in the denominator of the coefficient in front of the integral should be <math>L_x</math>, not <math>L</math>.
*[[p. 532, line 12]]: on the right-hand side of the equations, one of the terms should be the steady-state solution.
*[[p. 534, Equation 11.51]]: one of the partial derivatives should be with respect to x.
*[[p. 534, Equation 11.52]]: the frequency in the sine and cosine functions should be multiplied by t.
*p. 536, line 10: "right-hand side of Equation (11.51)" should be "left-hand side of Equation (11.51)".
*[[p. 539, Figure 11.28]]: in the label on the vertical axis, the subscript on z should be "0,n" not "1,n".
*[[p. 542, last boxed set of equations]]: the expressions for the ''c'' and ''d'' coefficients should be in terms of the function ''g'' not the function ''f''. Also, the ''d'' coefficient should have a sine function instead of cosine.
*[[p. 559, line -4]]: the tension and mass per unit length appearing in the frequency term should both be the square root of those terms.
*p. 561, line 1: the second word "subsection" should be "subsections".
*p. 570, Exercise 11.2: add to the problem statement "let <math>m=1, b=0</math> and <math>k = 9\pi^2</math>."
*[[p. 571, line 21]]: for Exercise 11.4, number 4, the initial condition should be for u(x,0) not the partial derivative of u with respect to t.
*[[p. 572, Exercise 11.9]]: in the "denominator" of the operators the partial sign is "squared" when it should be the x and y, respectively.

==Chapter 12==
* p. 580, line 16: the word "so" should be deleted near the end of the line.
* p. 580, line -14: the exact solution is cos(t), not -cos(t).
*[[p. 588, line 2]]: the middle term in the numerator should be evaluated at 2.0, not 1.5.
*[[p. 592, lines 11 and 12]]: the minus sign multiplying the cubed term was dropped. Also, it would be more complete if the expression for f(x(t),t) were substituted into the final expression.
*[[p. 600, line 10]]: the error term on the right-hand side should be at two time steps back, not one.
*[[p. 625, Exercise 12.2, number 6]]: the first derivative term should be a second derivative.

==Chapter 13==
*p. 662, Figure 13.24: the output Y(s) should be X(s) because that is what it is called in the text that refers to the figure.
*[[p. 662, line 8]]: the second equation on the page should have X(s) on the left hand side, not G_p(s).
*[[p. 664, line 1]]: the sine term inside the friction function should be multiplied by M.
*[[p. 654, line 1, Equation (13.23)]]: the second equilibrium point should be x=2, x'=0, not x=0, x'=2.
*[[p. 664, line 4]]: the term multiplying ''a'' on the left hand side of the equation should be the reciprocal of what is printed.
*[[p. 664, line 8]]: the term multiplying ''b'' on the left hand side of the equation should be the reciprocal of what is printed. Also, there should be an ''M'' multiplying the sine function that is the argument to the ''friction()'' function and no ''M'' multiplying the sine function outside the ''friction()'' function.
*[[p. 666, line 5]]: the "0.3" in the equation should be "-0.3".
*[[p. 679, exercise 13.12, number 2]]: "G(s) =" is missing from the left side of the equation.

==Appendix E==
*Various FORTRAN programs have semicolons terminating lines (always in the declaration statements): E.2.0.20, E.2.0.21, E2.0.22, E.2.0.23, E2.0.24, E2.0.25, E.2.0.26. These semicolons should not be there.
* p. 727, program in E.2.0.18, for Example 1.30: the program contains the variable n which does nothing. The declaration, initialization to zero and increment inside the do loop should be removed.
*[[p. 733, line 19]]: the equation to update x(2) should not have an x(1) in it, it should be copy(1). Also, while it will not affect how the program works, x(2) should be copy(2) for consistency.
*p. 737, line 5: The program in E.2.0.31 is for Example 12.17, not Example 12.16.

Thisisatest

2015-08-26T14:49:29Z

Bill: Created page with "<math>\frac{\sqrt{x^3}}{\pi^2}</math>"

Engineering Differential Equations: Theory and Applications, Springer 2010

2015-08-26T14:49:09Z

Bill: /* Chapter 1 */

This page contains supplementary material for the book, ''Engineering Differential Equations: Theory and Applications'', by Bill Goodwine. 2010, Springer.

=Movies=
Chapter 11 considers solutions to partial differential equations.
==The One-Dimensional Wave Equation==
Section 11.1 considers the one-dimensional wave equation.

Some movies:
*String of length 3 plucked at L=1 (modeling a guitar):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode1.mpg The first (fundamental) mode of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15.mpg The first five modes of the plucked string plotted separately]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15sum.mpg The sum of the first five modes of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode50sum.mpg The sum of the first fifty modes of the plucked string]
*String of length 3 that is impacted near L=1 (modeling a piano):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact10sum.mpg The sum of the first ten modes of the impacted string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact50sum.mpg The sum of the first fifty modes of the impacted string]

==The One-Dimensional Heat Conduction Equation==
Section 11.3 considers the one-dimensional heat conduction equation.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinhomo.mpg The solution to the heat equation with inhomogeneous boundary conditions]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinsulated.mpg The solution to the heat equation with an insulated end]

==The Two-Dimensional Heat Equation==
Movie:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/twoheat.mpg Solution to the heat conduction equation in two dimensions]

==Vibrating Membranes==
Partial differential equations describing vibrating membranes in rectangular and polar coordinates are considered in Section 11.5.

Section 11.5.1 presents the two-dimensional wave equation in rectangular coordinates.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum11.mpg 1-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum21.mpg 2-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum22.mpg 2-2 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrumimpact.mpg Rectangular drum impacted near a corner]

Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum10.mpg 1-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum11.mpg 1-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum12.mpg 1-2 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum13.mpg 1-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum20.mpg 2-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum21.mpg 2-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum43.mpg 4-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drumimpact.mpg Circular drum that is impacted by a drum stick]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum.mpg Another drum impact movie]
*[http://www.youtube.com/watch?v=w8Gxut0odyc#t=4m10s Cool youtube movie of slow motion impact of drum head and cymbal]

=Errata=

==Chapter 1==
*[[p. 58, line -3, Equation 2.4]]: the ''c'' in the denominator should be the specific heat.
*[[thisisatest]] asdf

==Chapter 2==
*p. 61, second paragraph of Section 2.2, line 2: "and" should be "is".
*[[p. 89, line -7]]: the right hand side of the equation below equation 2.35 should be a function of t, not x.

==Chapter 3==
*[[p. 97, line -3]]: there is an extra closing parenthesis in the equation for the Wronskian.
*[[p. 105, line 12]]: both exponents should be <math>-\omega_n</math>.
*[[p. 117, Figure 3.5]]: the figure plots the solution to <math>\ddot x + \dot x + 10 x = 0</math> and not <math>2 \ddot x + \dot x + 10 x = 0</math> as stated. It really doesn't change the qualitative aspects of the problem, however.

==Chapter 4==
*[[p. 125, line 5]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line 8]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line -4]]: the coefficient of the x term in the differential equation should be squared.
*[[p. 128, Equation 4.8]]: the numerator of the coefficient of the sine term should be the initial velocity.
*[[p. 138, line 6 (large boxed equation)]]: the first zeta in the parentheses in the coefficient of the second exponential on the second line should be negative.
*[[p. 139, Equation 4.14]]: the second term should contain the derivative of x, not x.
*[[p. 142, Figure 4.16]]: the figure is incorrect in that the square root was not used to plot the curves.
*[[p. 156, Exercise 4.22]]: at this point in the book we don't know how to find the homogeneous solutions for these two systems.
*[[p. 158, Exercise 4.26, Figure 4.32]]: the variable x is not the distance along the beam, but rather the displacement at the end.
*[[p. 159, Exercise 4.27, Figure 4.33]]: the angle is incorrectly marked as the angular velocity.

==Chapter 5==
*[[p. 163, line 6]]: the first (n+1) term should be (n+2).
*[[p. 164, Equation 5.5]]: the first coefficient in the second series should be (n+2) not (n+1).
*[[p. 167, lines -4,-3 and -2]]: the expressions for the derivatives of the function are wrong.
* p. 170, line 6: at the end of the line "Table 5.2" should be "Table 5.1."
*[[p. 172, line -5]]: there should be a negative sign on the right hand side of the equation.
*[[p. 174, Equation 5.14]]: the first term in the numerator on the right hand side should be multiplied by 20.
*[[p. 181, line 16]]: the two terms on the right-hand side of the equation are switched, leading to the wrong answer for <math>a_2</math>. This wrong number then propagates to lines -1 and -6 on the same page.
*[[p. 182, line 14]]: in the first series for the second derivative, the exponent should be (n-2) not (n-1).
*[[p. 185, line 2]]: the recursion relation has two mistakes. The left hand side should be for a_{n+2} not {n+1}. Also, the negative sign should not be there.
*[[p. 186, line 6]]: the left hand side of the recursion relation should be for a_{n+2} not {n+1}.
*p. 188, Exercise 5.1, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*p. 189, Exercise 5.2, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*[[p. 190, Exercise 5.13]]: the middle term in the denominator of the second term should be "2 t" not "t2".
*[[p. 191, Exercise 5.16]]: the independent variable in the equation is x, so the derivative terms should be with respect to x.

==Chapter 6==
*[[p. 195, line 1]]: the third term in the vector on the right hand side should have a subscript of 4, not 3.
*[[p. 209, line -8]]: the exponential term should be multiplying the second term as well.
*[[p. 210, line 1]]: same error as on p. 209 carried through.
*[[p. 220, line -9]]: the superscript for the second term in the equation should be m-3.
*[[p. 244, line -11]]: the first component of the vector on the far right should contain t, not tau.
*[[p. 245, line 8]]: the matrix A7 does not have a set of n linearly-independent eigenvectors.
*[[p. 247, line -7]]: A3 should be A2.

==Chapter 7==
*p. 253, line 5: the word "of" is repeated.
*[[p. 265, Equation (7.16)]]: this equation has multiple typos. The last term in parentheses in the last line should be (1-k1-2 k3). Also the second line has misaligned parentheses.

==Chapter 8==
*[[p. 288, last line in Table 8.1]]: the exponent should be "-a t" and not "a t".
*p. 297, Example 8.14: the "3" multiplying the <math>t^2</math> term on the right hand side is dropped half way through the example. Because it scales the whole right hand side, it scales simply scales the solution by 3. Thus the final answer on p. 299 should be multiplied by 3, as should the equation on the top of page 299. Also the two equations in the middle of p. 298 involving X(s) should have the right hand side multiplied by 3.
*p. 326, line -10: "Figure 8.8" should be "Figure 8.37".
*p. 327: the pendulum in Figure 8.36 should indicate a length, ''l'', for the pendulum.

==Chapter 9==
*[[p. 348, line 4]]: the numerator for both expressions of G1 should be 5.
*[[p. 348, line 6]]: the numerator for both expressions of G1 should be 10.
*[[p. 349, caption to Figure 9.16]]: the numerator for G1 should be 4 in the numerator for G2 should be 9.
*p. 354, line 9: the word "row" should be "column".
*p. 368, line 4: "r=10, 1, -1, and 10" should be "r=10, 1, -1, -10".
*p. 368, line -4: "Systems with left half-plane zeros are called..." should be "Systems with right half-plane zeros are called...".
*[[p. 403, line -7]]: the arctan should be a ratio of the imaginary to real components of G(i \omega).

==Chapter 11==
*[[p. 513, line 2]]: the coefficient is alpha^2, not alpha.
*[[p. 515, line 6]]: the "x" should be outside, not inside, the square root.
*[[p. 524, line 1]]: the sine function should not equal n pi, the argument to it should.
*[[p. 525, Equation 11.43]]: the denominator in both exponentials should be <math>L_x</math>.
*[[p. 525, Equation 11.44]]: the first term in the denominator of the coefficient in front of the integral should be <math>L_x</math>, not <math>L</math>.
*[[p. 532, line 12]]: on the right-hand side of the equations, one of the terms should be the steady-state solution.
*[[p. 534, Equation 11.51]]: one of the partial derivatives should be with respect to x.
*[[p. 534, Equation 11.52]]: the frequency in the sine and cosine functions should be multiplied by t.
*p. 536, line 10: "right-hand side of Equation (11.51)" should be "left-hand side of Equation (11.51)".
*[[p. 539, Figure 11.28]]: in the label on the vertical axis, the subscript on z should be "0,n" not "1,n".
*[[p. 542, last boxed set of equations]]: the expressions for the ''c'' and ''d'' coefficients should be in terms of the function ''g'' not the function ''f''. Also, the ''d'' coefficient should have a sine function instead of cosine.
*[[p. 559, line -4]]: the tension and mass per unit length appearing in the frequency term should both be the square root of those terms.
*p. 561, line 1: the second word "subsection" should be "subsections".
*p. 570, Exercise 11.2: add to the problem statement "let <math>m=1, b=0</math> and <math>k = 9\pi^2</math>."
*[[p. 571, line 21]]: for Exercise 11.4, number 4, the initial condition should be for u(x,0) not the partial derivative of u with respect to t.
*[[p. 572, Exercise 11.9]]: in the "denominator" of the operators the partial sign is "squared" when it should be the x and y, respectively.

==Chapter 12==
* p. 580, line 16: the word "so" should be deleted near the end of the line.
* p. 580, line -14: the exact solution is cos(t), not -cos(t).
*[[p. 588, line 2]]: the middle term in the numerator should be evaluated at 2.0, not 1.5.
*[[p. 592, lines 11 and 12]]: the minus sign multiplying the cubed term was dropped. Also, it would be more complete if the expression for f(x(t),t) were substituted into the final expression.
*[[p. 600, line 10]]: the error term on the right-hand side should be at two time steps back, not one.
*[[p. 625, Exercise 12.2, number 6]]: the first derivative term should be a second derivative.

==Chapter 13==
*p. 662, Figure 13.24: the output Y(s) should be X(s) because that is what it is called in the text that refers to the figure.
*[[p. 662, line 8]]: the second equation on the page should have X(s) on the left hand side, not G_p(s).
*[[p. 664, line 1]]: the sine term inside the friction function should be multiplied by M.
*[[p. 654, line 1, Equation (13.23)]]: the second equilibrium point should be x=2, x'=0, not x=0, x'=2.
*[[p. 664, line 4]]: the term multiplying ''a'' on the left hand side of the equation should be the reciprocal of what is printed.
*[[p. 664, line 8]]: the term multiplying ''b'' on the left hand side of the equation should be the reciprocal of what is printed. Also, there should be an ''M'' multiplying the sine function that is the argument to the ''friction()'' function and no ''M'' multiplying the sine function outside the ''friction()'' function.
*[[p. 666, line 5]]: the "0.3" in the equation should be "-0.3".
*[[p. 679, exercise 13.12, number 2]]: "G(s) =" is missing from the left side of the equation.

==Appendix E==
*Various FORTRAN programs have semicolons terminating lines (always in the declaration statements): E.2.0.20, E.2.0.21, E2.0.22, E.2.0.23, E2.0.24, E2.0.25, E.2.0.26. These semicolons should not be there.
* p. 727, program in E.2.0.18, for Example 1.30: the program contains the variable n which does nothing. The declaration, initialization to zero and increment inside the do loop should be removed.
*[[p. 733, line 19]]: the equation to update x(2) should not have an x(1) in it, it should be copy(1). Also, while it will not affect how the program works, x(2) should be copy(2) for consistency.
*p. 737, line 5: The program in E.2.0.31 is for Example 12.17, not Example 12.16.

Engineering Differential Equations: Theory and Applications, Springer 2010

2015-08-25T21:38:52Z

Bill: /* Chapter 1 */

This page contains supplementary material for the book, ''Engineering Differential Equations: Theory and Applications'', by Bill Goodwine. 2010, Springer.

=Movies=
Chapter 11 considers solutions to partial differential equations.
==The One-Dimensional Wave Equation==
Section 11.1 considers the one-dimensional wave equation.

Some movies:
*String of length 3 plucked at L=1 (modeling a guitar):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode1.mpg The first (fundamental) mode of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15.mpg The first five modes of the plucked string plotted separately]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15sum.mpg The sum of the first five modes of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode50sum.mpg The sum of the first fifty modes of the plucked string]
*String of length 3 that is impacted near L=1 (modeling a piano):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact10sum.mpg The sum of the first ten modes of the impacted string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact50sum.mpg The sum of the first fifty modes of the impacted string]

==The One-Dimensional Heat Conduction Equation==
Section 11.3 considers the one-dimensional heat conduction equation.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinhomo.mpg The solution to the heat equation with inhomogeneous boundary conditions]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinsulated.mpg The solution to the heat equation with an insulated end]

==The Two-Dimensional Heat Equation==
Movie:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/twoheat.mpg Solution to the heat conduction equation in two dimensions]

==Vibrating Membranes==
Partial differential equations describing vibrating membranes in rectangular and polar coordinates are considered in Section 11.5.

Section 11.5.1 presents the two-dimensional wave equation in rectangular coordinates.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum11.mpg 1-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum21.mpg 2-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum22.mpg 2-2 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrumimpact.mpg Rectangular drum impacted near a corner]

Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum10.mpg 1-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum11.mpg 1-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum12.mpg 1-2 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum13.mpg 1-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum20.mpg 2-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum21.mpg 2-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum43.mpg 4-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drumimpact.mpg Circular drum that is impacted by a drum stick]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum.mpg Another drum impact movie]
*[http://www.youtube.com/watch?v=w8Gxut0odyc#t=4m10s Cool youtube movie of slow motion impact of drum head and cymbal]

=Errata=

==Chapter 1==
*[[p. 58, line -3, Equation 2.4]]: the ''c'' in the denominator should be the specific heat.

==Chapter 2==
*p. 61, second paragraph of Section 2.2, line 2: "and" should be "is".
*[[p. 89, line -7]]: the right hand side of the equation below equation 2.35 should be a function of t, not x.

==Chapter 3==
*[[p. 97, line -3]]: there is an extra closing parenthesis in the equation for the Wronskian.
*[[p. 105, line 12]]: both exponents should be <math>-\omega_n</math>.
*[[p. 117, Figure 3.5]]: the figure plots the solution to <math>\ddot x + \dot x + 10 x = 0</math> and not <math>2 \ddot x + \dot x + 10 x = 0</math> as stated. It really doesn't change the qualitative aspects of the problem, however.

==Chapter 4==
*[[p. 125, line 5]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line 8]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line -4]]: the coefficient of the x term in the differential equation should be squared.
*[[p. 128, Equation 4.8]]: the numerator of the coefficient of the sine term should be the initial velocity.
*[[p. 138, line 6 (large boxed equation)]]: the first zeta in the parentheses in the coefficient of the second exponential on the second line should be negative.
*[[p. 139, Equation 4.14]]: the second term should contain the derivative of x, not x.
*[[p. 142, Figure 4.16]]: the figure is incorrect in that the square root was not used to plot the curves.
*[[p. 156, Exercise 4.22]]: at this point in the book we don't know how to find the homogeneous solutions for these two systems.
*[[p. 158, Exercise 4.26, Figure 4.32]]: the variable x is not the distance along the beam, but rather the displacement at the end.
*[[p. 159, Exercise 4.27, Figure 4.33]]: the angle is incorrectly marked as the angular velocity.

==Chapter 5==
*[[p. 163, line 6]]: the first (n+1) term should be (n+2).
*[[p. 164, Equation 5.5]]: the first coefficient in the second series should be (n+2) not (n+1).
*[[p. 167, lines -4,-3 and -2]]: the expressions for the derivatives of the function are wrong.
* p. 170, line 6: at the end of the line "Table 5.2" should be "Table 5.1."
*[[p. 172, line -5]]: there should be a negative sign on the right hand side of the equation.
*[[p. 174, Equation 5.14]]: the first term in the numerator on the right hand side should be multiplied by 20.
*[[p. 181, line 16]]: the two terms on the right-hand side of the equation are switched, leading to the wrong answer for <math>a_2</math>. This wrong number then propagates to lines -1 and -6 on the same page.
*[[p. 182, line 14]]: in the first series for the second derivative, the exponent should be (n-2) not (n-1).
*[[p. 185, line 2]]: the recursion relation has two mistakes. The left hand side should be for a_{n+2} not {n+1}. Also, the negative sign should not be there.
*[[p. 186, line 6]]: the left hand side of the recursion relation should be for a_{n+2} not {n+1}.
*p. 188, Exercise 5.1, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*p. 189, Exercise 5.2, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*[[p. 190, Exercise 5.13]]: the middle term in the denominator of the second term should be "2 t" not "t2".
*[[p. 191, Exercise 5.16]]: the independent variable in the equation is x, so the derivative terms should be with respect to x.

==Chapter 6==
*[[p. 195, line 1]]: the third term in the vector on the right hand side should have a subscript of 4, not 3.
*[[p. 209, line -8]]: the exponential term should be multiplying the second term as well.
*[[p. 210, line 1]]: same error as on p. 209 carried through.
*[[p. 220, line -9]]: the superscript for the second term in the equation should be m-3.
*[[p. 244, line -11]]: the first component of the vector on the far right should contain t, not tau.
*[[p. 245, line 8]]: the matrix A7 does not have a set of n linearly-independent eigenvectors.
*[[p. 247, line -7]]: A3 should be A2.

==Chapter 7==
*p. 253, line 5: the word "of" is repeated.
*[[p. 265, Equation (7.16)]]: this equation has multiple typos. The last term in parentheses in the last line should be (1-k1-2 k3). Also the second line has misaligned parentheses.

==Chapter 8==
*[[p. 288, last line in Table 8.1]]: the exponent should be "-a t" and not "a t".
*p. 297, Example 8.14: the "3" multiplying the <math>t^2</math> term on the right hand side is dropped half way through the example. Because it scales the whole right hand side, it scales simply scales the solution by 3. Thus the final answer on p. 299 should be multiplied by 3, as should the equation on the top of page 299. Also the two equations in the middle of p. 298 involving X(s) should have the right hand side multiplied by 3.
*p. 326, line -10: "Figure 8.8" should be "Figure 8.37".
*p. 327: the pendulum in Figure 8.36 should indicate a length, ''l'', for the pendulum.

==Chapter 9==
*[[p. 348, line 4]]: the numerator for both expressions of G1 should be 5.
*[[p. 348, line 6]]: the numerator for both expressions of G1 should be 10.
*[[p. 349, caption to Figure 9.16]]: the numerator for G1 should be 4 in the numerator for G2 should be 9.
*p. 354, line 9: the word "row" should be "column".
*p. 368, line 4: "r=10, 1, -1, and 10" should be "r=10, 1, -1, -10".
*p. 368, line -4: "Systems with left half-plane zeros are called..." should be "Systems with right half-plane zeros are called...".
*[[p. 403, line -7]]: the arctan should be a ratio of the imaginary to real components of G(i \omega).

==Chapter 11==
*[[p. 513, line 2]]: the coefficient is alpha^2, not alpha.
*[[p. 515, line 6]]: the "x" should be outside, not inside, the square root.
*[[p. 524, line 1]]: the sine function should not equal n pi, the argument to it should.
*[[p. 525, Equation 11.43]]: the denominator in both exponentials should be <math>L_x</math>.
*[[p. 525, Equation 11.44]]: the first term in the denominator of the coefficient in front of the integral should be <math>L_x</math>, not <math>L</math>.
*[[p. 532, line 12]]: on the right-hand side of the equations, one of the terms should be the steady-state solution.
*[[p. 534, Equation 11.51]]: one of the partial derivatives should be with respect to x.
*[[p. 534, Equation 11.52]]: the frequency in the sine and cosine functions should be multiplied by t.
*p. 536, line 10: "right-hand side of Equation (11.51)" should be "left-hand side of Equation (11.51)".
*[[p. 539, Figure 11.28]]: in the label on the vertical axis, the subscript on z should be "0,n" not "1,n".
*[[p. 542, last boxed set of equations]]: the expressions for the ''c'' and ''d'' coefficients should be in terms of the function ''g'' not the function ''f''. Also, the ''d'' coefficient should have a sine function instead of cosine.
*[[p. 559, line -4]]: the tension and mass per unit length appearing in the frequency term should both be the square root of those terms.
*p. 561, line 1: the second word "subsection" should be "subsections".
*p. 570, Exercise 11.2: add to the problem statement "let <math>m=1, b=0</math> and <math>k = 9\pi^2</math>."
*[[p. 571, line 21]]: for Exercise 11.4, number 4, the initial condition should be for u(x,0) not the partial derivative of u with respect to t.
*[[p. 572, Exercise 11.9]]: in the "denominator" of the operators the partial sign is "squared" when it should be the x and y, respectively.

==Chapter 12==
* p. 580, line 16: the word "so" should be deleted near the end of the line.
* p. 580, line -14: the exact solution is cos(t), not -cos(t).
*[[p. 588, line 2]]: the middle term in the numerator should be evaluated at 2.0, not 1.5.
*[[p. 592, lines 11 and 12]]: the minus sign multiplying the cubed term was dropped. Also, it would be more complete if the expression for f(x(t),t) were substituted into the final expression.
*[[p. 600, line 10]]: the error term on the right-hand side should be at two time steps back, not one.
*[[p. 625, Exercise 12.2, number 6]]: the first derivative term should be a second derivative.

==Chapter 13==
*p. 662, Figure 13.24: the output Y(s) should be X(s) because that is what it is called in the text that refers to the figure.
*[[p. 662, line 8]]: the second equation on the page should have X(s) on the left hand side, not G_p(s).
*[[p. 664, line 1]]: the sine term inside the friction function should be multiplied by M.
*[[p. 654, line 1, Equation (13.23)]]: the second equilibrium point should be x=2, x'=0, not x=0, x'=2.
*[[p. 664, line 4]]: the term multiplying ''a'' on the left hand side of the equation should be the reciprocal of what is printed.
*[[p. 664, line 8]]: the term multiplying ''b'' on the left hand side of the equation should be the reciprocal of what is printed. Also, there should be an ''M'' multiplying the sine function that is the argument to the ''friction()'' function and no ''M'' multiplying the sine function outside the ''friction()'' function.
*[[p. 666, line 5]]: the "0.3" in the equation should be "-0.3".
*[[p. 679, exercise 13.12, number 2]]: "G(s) =" is missing from the left side of the equation.

==Appendix E==
*Various FORTRAN programs have semicolons terminating lines (always in the declaration statements): E.2.0.20, E.2.0.21, E2.0.22, E.2.0.23, E2.0.24, E2.0.25, E.2.0.26. These semicolons should not be there.
* p. 727, program in E.2.0.18, for Example 1.30: the program contains the variable n which does nothing. The declaration, initialization to zero and increment inside the do loop should be removed.
*[[p. 733, line 19]]: the equation to update x(2) should not have an x(1) in it, it should be copy(1). Also, while it will not affect how the program works, x(2) should be copy(2) for consistency.
*p. 737, line 5: The program in E.2.0.31 is for Example 12.17, not Example 12.16.

Engineering Differential Equations: Theory and Applications, Springer 2010

2015-08-25T21:33:08Z

Bill: /* Chapter 1 */

This page contains supplementary material for the book, ''Engineering Differential Equations: Theory and Applications'', by Bill Goodwine. 2010, Springer.

=Movies=
Chapter 11 considers solutions to partial differential equations.
==The One-Dimensional Wave Equation==
Section 11.1 considers the one-dimensional wave equation.

Some movies:
*String of length 3 plucked at L=1 (modeling a guitar):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode1.mpg The first (fundamental) mode of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15.mpg The first five modes of the plucked string plotted separately]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15sum.mpg The sum of the first five modes of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode50sum.mpg The sum of the first fifty modes of the plucked string]
*String of length 3 that is impacted near L=1 (modeling a piano):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact10sum.mpg The sum of the first ten modes of the impacted string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact50sum.mpg The sum of the first fifty modes of the impacted string]

==The One-Dimensional Heat Conduction Equation==
Section 11.3 considers the one-dimensional heat conduction equation.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinhomo.mpg The solution to the heat equation with inhomogeneous boundary conditions]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinsulated.mpg The solution to the heat equation with an insulated end]

==The Two-Dimensional Heat Equation==
Movie:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/twoheat.mpg Solution to the heat conduction equation in two dimensions]

==Vibrating Membranes==
Partial differential equations describing vibrating membranes in rectangular and polar coordinates are considered in Section 11.5.

Section 11.5.1 presents the two-dimensional wave equation in rectangular coordinates.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum11.mpg 1-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum21.mpg 2-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum22.mpg 2-2 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrumimpact.mpg Rectangular drum impacted near a corner]

Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum10.mpg 1-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum11.mpg 1-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum12.mpg 1-2 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum13.mpg 1-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum20.mpg 2-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum21.mpg 2-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum43.mpg 4-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drumimpact.mpg Circular drum that is impacted by a drum stick]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum.mpg Another drum impact movie]
*[http://www.youtube.com/watch?v=w8Gxut0odyc#t=4m10s Cool youtube movie of slow motion impact of drum head and cymbal]

=Errata=

==Chapter 1==
*[[p. 58, line -3, Equation 2.4]]: the ''c'' in the denominator should be the specific heat.
*[[testmath]] test
*[[and another]] test
*[[and yet another]] asdfadsf

==Chapter 2==
*p. 61, second paragraph of Section 2.2, line 2: "and" should be "is".
*[[p. 89, line -7]]: the right hand side of the equation below equation 2.35 should be a function of t, not x.

==Chapter 3==
*[[p. 97, line -3]]: there is an extra closing parenthesis in the equation for the Wronskian.
*[[p. 105, line 12]]: both exponents should be <math>-\omega_n</math>.
*[[p. 117, Figure 3.5]]: the figure plots the solution to <math>\ddot x + \dot x + 10 x = 0</math> and not <math>2 \ddot x + \dot x + 10 x = 0</math> as stated. It really doesn't change the qualitative aspects of the problem, however.

==Chapter 4==
*[[p. 125, line 5]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line 8]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line -4]]: the coefficient of the x term in the differential equation should be squared.
*[[p. 128, Equation 4.8]]: the numerator of the coefficient of the sine term should be the initial velocity.
*[[p. 138, line 6 (large boxed equation)]]: the first zeta in the parentheses in the coefficient of the second exponential on the second line should be negative.
*[[p. 139, Equation 4.14]]: the second term should contain the derivative of x, not x.
*[[p. 142, Figure 4.16]]: the figure is incorrect in that the square root was not used to plot the curves.
*[[p. 156, Exercise 4.22]]: at this point in the book we don't know how to find the homogeneous solutions for these two systems.
*[[p. 158, Exercise 4.26, Figure 4.32]]: the variable x is not the distance along the beam, but rather the displacement at the end.
*[[p. 159, Exercise 4.27, Figure 4.33]]: the angle is incorrectly marked as the angular velocity.

==Chapter 5==
*[[p. 163, line 6]]: the first (n+1) term should be (n+2).
*[[p. 164, Equation 5.5]]: the first coefficient in the second series should be (n+2) not (n+1).
*[[p. 167, lines -4,-3 and -2]]: the expressions for the derivatives of the function are wrong.
* p. 170, line 6: at the end of the line "Table 5.2" should be "Table 5.1."
*[[p. 172, line -5]]: there should be a negative sign on the right hand side of the equation.
*[[p. 174, Equation 5.14]]: the first term in the numerator on the right hand side should be multiplied by 20.
*[[p. 181, line 16]]: the two terms on the right-hand side of the equation are switched, leading to the wrong answer for <math>a_2</math>. This wrong number then propagates to lines -1 and -6 on the same page.
*[[p. 182, line 14]]: in the first series for the second derivative, the exponent should be (n-2) not (n-1).
*[[p. 185, line 2]]: the recursion relation has two mistakes. The left hand side should be for a_{n+2} not {n+1}. Also, the negative sign should not be there.
*[[p. 186, line 6]]: the left hand side of the recursion relation should be for a_{n+2} not {n+1}.
*p. 188, Exercise 5.1, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*p. 189, Exercise 5.2, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*[[p. 190, Exercise 5.13]]: the middle term in the denominator of the second term should be "2 t" not "t2".
*[[p. 191, Exercise 5.16]]: the independent variable in the equation is x, so the derivative terms should be with respect to x.

==Chapter 6==
*[[p. 195, line 1]]: the third term in the vector on the right hand side should have a subscript of 4, not 3.
*[[p. 209, line -8]]: the exponential term should be multiplying the second term as well.
*[[p. 210, line 1]]: same error as on p. 209 carried through.
*[[p. 220, line -9]]: the superscript for the second term in the equation should be m-3.
*[[p. 244, line -11]]: the first component of the vector on the far right should contain t, not tau.
*[[p. 245, line 8]]: the matrix A7 does not have a set of n linearly-independent eigenvectors.
*[[p. 247, line -7]]: A3 should be A2.

==Chapter 7==
*p. 253, line 5: the word "of" is repeated.
*[[p. 265, Equation (7.16)]]: this equation has multiple typos. The last term in parentheses in the last line should be (1-k1-2 k3). Also the second line has misaligned parentheses.

==Chapter 8==
*[[p. 288, last line in Table 8.1]]: the exponent should be "-a t" and not "a t".
*p. 297, Example 8.14: the "3" multiplying the <math>t^2</math> term on the right hand side is dropped half way through the example. Because it scales the whole right hand side, it scales simply scales the solution by 3. Thus the final answer on p. 299 should be multiplied by 3, as should the equation on the top of page 299. Also the two equations in the middle of p. 298 involving X(s) should have the right hand side multiplied by 3.
*p. 326, line -10: "Figure 8.8" should be "Figure 8.37".
*p. 327: the pendulum in Figure 8.36 should indicate a length, ''l'', for the pendulum.

==Chapter 9==
*[[p. 348, line 4]]: the numerator for both expressions of G1 should be 5.
*[[p. 348, line 6]]: the numerator for both expressions of G1 should be 10.
*[[p. 349, caption to Figure 9.16]]: the numerator for G1 should be 4 in the numerator for G2 should be 9.
*p. 354, line 9: the word "row" should be "column".
*p. 368, line 4: "r=10, 1, -1, and 10" should be "r=10, 1, -1, -10".
*p. 368, line -4: "Systems with left half-plane zeros are called..." should be "Systems with right half-plane zeros are called...".
*[[p. 403, line -7]]: the arctan should be a ratio of the imaginary to real components of G(i \omega).

==Chapter 11==
*[[p. 513, line 2]]: the coefficient is alpha^2, not alpha.
*[[p. 515, line 6]]: the "x" should be outside, not inside, the square root.
*[[p. 524, line 1]]: the sine function should not equal n pi, the argument to it should.
*[[p. 525, Equation 11.43]]: the denominator in both exponentials should be <math>L_x</math>.
*[[p. 525, Equation 11.44]]: the first term in the denominator of the coefficient in front of the integral should be <math>L_x</math>, not <math>L</math>.
*[[p. 532, line 12]]: on the right-hand side of the equations, one of the terms should be the steady-state solution.
*[[p. 534, Equation 11.51]]: one of the partial derivatives should be with respect to x.
*[[p. 534, Equation 11.52]]: the frequency in the sine and cosine functions should be multiplied by t.
*p. 536, line 10: "right-hand side of Equation (11.51)" should be "left-hand side of Equation (11.51)".
*[[p. 539, Figure 11.28]]: in the label on the vertical axis, the subscript on z should be "0,n" not "1,n".
*[[p. 542, last boxed set of equations]]: the expressions for the ''c'' and ''d'' coefficients should be in terms of the function ''g'' not the function ''f''. Also, the ''d'' coefficient should have a sine function instead of cosine.
*[[p. 559, line -4]]: the tension and mass per unit length appearing in the frequency term should both be the square root of those terms.
*p. 561, line 1: the second word "subsection" should be "subsections".
*p. 570, Exercise 11.2: add to the problem statement "let <math>m=1, b=0</math> and <math>k = 9\pi^2</math>."
*[[p. 571, line 21]]: for Exercise 11.4, number 4, the initial condition should be for u(x,0) not the partial derivative of u with respect to t.
*[[p. 572, Exercise 11.9]]: in the "denominator" of the operators the partial sign is "squared" when it should be the x and y, respectively.

==Chapter 12==
* p. 580, line 16: the word "so" should be deleted near the end of the line.
* p. 580, line -14: the exact solution is cos(t), not -cos(t).
*[[p. 588, line 2]]: the middle term in the numerator should be evaluated at 2.0, not 1.5.
*[[p. 592, lines 11 and 12]]: the minus sign multiplying the cubed term was dropped. Also, it would be more complete if the expression for f(x(t),t) were substituted into the final expression.
*[[p. 600, line 10]]: the error term on the right-hand side should be at two time steps back, not one.
*[[p. 625, Exercise 12.2, number 6]]: the first derivative term should be a second derivative.

==Chapter 13==
*p. 662, Figure 13.24: the output Y(s) should be X(s) because that is what it is called in the text that refers to the figure.
*[[p. 662, line 8]]: the second equation on the page should have X(s) on the left hand side, not G_p(s).
*[[p. 664, line 1]]: the sine term inside the friction function should be multiplied by M.
*[[p. 654, line 1, Equation (13.23)]]: the second equilibrium point should be x=2, x'=0, not x=0, x'=2.
*[[p. 664, line 4]]: the term multiplying ''a'' on the left hand side of the equation should be the reciprocal of what is printed.
*[[p. 664, line 8]]: the term multiplying ''b'' on the left hand side of the equation should be the reciprocal of what is printed. Also, there should be an ''M'' multiplying the sine function that is the argument to the ''friction()'' function and no ''M'' multiplying the sine function outside the ''friction()'' function.
*[[p. 666, line 5]]: the "0.3" in the equation should be "-0.3".
*[[p. 679, exercise 13.12, number 2]]: "G(s) =" is missing from the left side of the equation.

==Appendix E==
*Various FORTRAN programs have semicolons terminating lines (always in the declaration statements): E.2.0.20, E.2.0.21, E2.0.22, E.2.0.23, E2.0.24, E2.0.25, E.2.0.26. These semicolons should not be there.
* p. 727, program in E.2.0.18, for Example 1.30: the program contains the variable n which does nothing. The declaration, initialization to zero and increment inside the do loop should be removed.
*[[p. 733, line 19]]: the equation to update x(2) should not have an x(1) in it, it should be copy(1). Also, while it will not affect how the program works, x(2) should be copy(2) for consistency.
*p. 737, line 5: The program in E.2.0.31 is for Example 12.17, not Example 12.16.

Engineering Differential Equations: Theory and Applications, Springer 2010

2015-08-25T21:27:44Z

Bill: /* Chapter 1 */

This page contains supplementary material for the book, ''Engineering Differential Equations: Theory and Applications'', by Bill Goodwine. 2010, Springer.

=Movies=
Chapter 11 considers solutions to partial differential equations.
==The One-Dimensional Wave Equation==
Section 11.1 considers the one-dimensional wave equation.

Some movies:
*String of length 3 plucked at L=1 (modeling a guitar):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode1.mpg The first (fundamental) mode of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15.mpg The first five modes of the plucked string plotted separately]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15sum.mpg The sum of the first five modes of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode50sum.mpg The sum of the first fifty modes of the plucked string]
*String of length 3 that is impacted near L=1 (modeling a piano):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact10sum.mpg The sum of the first ten modes of the impacted string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact50sum.mpg The sum of the first fifty modes of the impacted string]

==The One-Dimensional Heat Conduction Equation==
Section 11.3 considers the one-dimensional heat conduction equation.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinhomo.mpg The solution to the heat equation with inhomogeneous boundary conditions]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinsulated.mpg The solution to the heat equation with an insulated end]

==The Two-Dimensional Heat Equation==
Movie:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/twoheat.mpg Solution to the heat conduction equation in two dimensions]

==Vibrating Membranes==
Partial differential equations describing vibrating membranes in rectangular and polar coordinates are considered in Section 11.5.

Section 11.5.1 presents the two-dimensional wave equation in rectangular coordinates.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum11.mpg 1-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum21.mpg 2-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum22.mpg 2-2 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrumimpact.mpg Rectangular drum impacted near a corner]

Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum10.mpg 1-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum11.mpg 1-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum12.mpg 1-2 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum13.mpg 1-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum20.mpg 2-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum21.mpg 2-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum43.mpg 4-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drumimpact.mpg Circular drum that is impacted by a drum stick]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum.mpg Another drum impact movie]
*[http://www.youtube.com/watch?v=w8Gxut0odyc#t=4m10s Cool youtube movie of slow motion impact of drum head and cymbal]

=Errata=

==Chapter 1==
*[[p. 58, line -3, Equation 2.4]]: the ''c'' in the denominator should be the specific heat.
*[[testmath]] test
*[[and another]] test

==Chapter 2==
*p. 61, second paragraph of Section 2.2, line 2: "and" should be "is".
*[[p. 89, line -7]]: the right hand side of the equation below equation 2.35 should be a function of t, not x.

==Chapter 3==
*[[p. 97, line -3]]: there is an extra closing parenthesis in the equation for the Wronskian.
*[[p. 105, line 12]]: both exponents should be <math>-\omega_n</math>.
*[[p. 117, Figure 3.5]]: the figure plots the solution to <math>\ddot x + \dot x + 10 x = 0</math> and not <math>2 \ddot x + \dot x + 10 x = 0</math> as stated. It really doesn't change the qualitative aspects of the problem, however.

==Chapter 4==
*[[p. 125, line 5]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line 8]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line -4]]: the coefficient of the x term in the differential equation should be squared.
*[[p. 128, Equation 4.8]]: the numerator of the coefficient of the sine term should be the initial velocity.
*[[p. 138, line 6 (large boxed equation)]]: the first zeta in the parentheses in the coefficient of the second exponential on the second line should be negative.
*[[p. 139, Equation 4.14]]: the second term should contain the derivative of x, not x.
*[[p. 142, Figure 4.16]]: the figure is incorrect in that the square root was not used to plot the curves.
*[[p. 156, Exercise 4.22]]: at this point in the book we don't know how to find the homogeneous solutions for these two systems.
*[[p. 158, Exercise 4.26, Figure 4.32]]: the variable x is not the distance along the beam, but rather the displacement at the end.
*[[p. 159, Exercise 4.27, Figure 4.33]]: the angle is incorrectly marked as the angular velocity.

==Chapter 5==
*[[p. 163, line 6]]: the first (n+1) term should be (n+2).
*[[p. 164, Equation 5.5]]: the first coefficient in the second series should be (n+2) not (n+1).
*[[p. 167, lines -4,-3 and -2]]: the expressions for the derivatives of the function are wrong.
* p. 170, line 6: at the end of the line "Table 5.2" should be "Table 5.1."
*[[p. 172, line -5]]: there should be a negative sign on the right hand side of the equation.
*[[p. 174, Equation 5.14]]: the first term in the numerator on the right hand side should be multiplied by 20.
*[[p. 181, line 16]]: the two terms on the right-hand side of the equation are switched, leading to the wrong answer for <math>a_2</math>. This wrong number then propagates to lines -1 and -6 on the same page.
*[[p. 182, line 14]]: in the first series for the second derivative, the exponent should be (n-2) not (n-1).
*[[p. 185, line 2]]: the recursion relation has two mistakes. The left hand side should be for a_{n+2} not {n+1}. Also, the negative sign should not be there.
*[[p. 186, line 6]]: the left hand side of the recursion relation should be for a_{n+2} not {n+1}.
*p. 188, Exercise 5.1, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*p. 189, Exercise 5.2, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*[[p. 190, Exercise 5.13]]: the middle term in the denominator of the second term should be "2 t" not "t2".
*[[p. 191, Exercise 5.16]]: the independent variable in the equation is x, so the derivative terms should be with respect to x.

==Chapter 6==
*[[p. 195, line 1]]: the third term in the vector on the right hand side should have a subscript of 4, not 3.
*[[p. 209, line -8]]: the exponential term should be multiplying the second term as well.
*[[p. 210, line 1]]: same error as on p. 209 carried through.
*[[p. 220, line -9]]: the superscript for the second term in the equation should be m-3.
*[[p. 244, line -11]]: the first component of the vector on the far right should contain t, not tau.
*[[p. 245, line 8]]: the matrix A7 does not have a set of n linearly-independent eigenvectors.
*[[p. 247, line -7]]: A3 should be A2.

==Chapter 7==
*p. 253, line 5: the word "of" is repeated.
*[[p. 265, Equation (7.16)]]: this equation has multiple typos. The last term in parentheses in the last line should be (1-k1-2 k3). Also the second line has misaligned parentheses.

==Chapter 8==
*[[p. 288, last line in Table 8.1]]: the exponent should be "-a t" and not "a t".
*p. 297, Example 8.14: the "3" multiplying the <math>t^2</math> term on the right hand side is dropped half way through the example. Because it scales the whole right hand side, it scales simply scales the solution by 3. Thus the final answer on p. 299 should be multiplied by 3, as should the equation on the top of page 299. Also the two equations in the middle of p. 298 involving X(s) should have the right hand side multiplied by 3.
*p. 326, line -10: "Figure 8.8" should be "Figure 8.37".
*p. 327: the pendulum in Figure 8.36 should indicate a length, ''l'', for the pendulum.

==Chapter 9==
*[[p. 348, line 4]]: the numerator for both expressions of G1 should be 5.
*[[p. 348, line 6]]: the numerator for both expressions of G1 should be 10.
*[[p. 349, caption to Figure 9.16]]: the numerator for G1 should be 4 in the numerator for G2 should be 9.
*p. 354, line 9: the word "row" should be "column".
*p. 368, line 4: "r=10, 1, -1, and 10" should be "r=10, 1, -1, -10".
*p. 368, line -4: "Systems with left half-plane zeros are called..." should be "Systems with right half-plane zeros are called...".
*[[p. 403, line -7]]: the arctan should be a ratio of the imaginary to real components of G(i \omega).

==Chapter 11==
*[[p. 513, line 2]]: the coefficient is alpha^2, not alpha.
*[[p. 515, line 6]]: the "x" should be outside, not inside, the square root.
*[[p. 524, line 1]]: the sine function should not equal n pi, the argument to it should.
*[[p. 525, Equation 11.43]]: the denominator in both exponentials should be <math>L_x</math>.
*[[p. 525, Equation 11.44]]: the first term in the denominator of the coefficient in front of the integral should be <math>L_x</math>, not <math>L</math>.
*[[p. 532, line 12]]: on the right-hand side of the equations, one of the terms should be the steady-state solution.
*[[p. 534, Equation 11.51]]: one of the partial derivatives should be with respect to x.
*[[p. 534, Equation 11.52]]: the frequency in the sine and cosine functions should be multiplied by t.
*p. 536, line 10: "right-hand side of Equation (11.51)" should be "left-hand side of Equation (11.51)".
*[[p. 539, Figure 11.28]]: in the label on the vertical axis, the subscript on z should be "0,n" not "1,n".
*[[p. 542, last boxed set of equations]]: the expressions for the ''c'' and ''d'' coefficients should be in terms of the function ''g'' not the function ''f''. Also, the ''d'' coefficient should have a sine function instead of cosine.
*[[p. 559, line -4]]: the tension and mass per unit length appearing in the frequency term should both be the square root of those terms.
*p. 561, line 1: the second word "subsection" should be "subsections".
*p. 570, Exercise 11.2: add to the problem statement "let <math>m=1, b=0</math> and <math>k = 9\pi^2</math>."
*[[p. 571, line 21]]: for Exercise 11.4, number 4, the initial condition should be for u(x,0) not the partial derivative of u with respect to t.
*[[p. 572, Exercise 11.9]]: in the "denominator" of the operators the partial sign is "squared" when it should be the x and y, respectively.

==Chapter 12==
* p. 580, line 16: the word "so" should be deleted near the end of the line.
* p. 580, line -14: the exact solution is cos(t), not -cos(t).
*[[p. 588, line 2]]: the middle term in the numerator should be evaluated at 2.0, not 1.5.
*[[p. 592, lines 11 and 12]]: the minus sign multiplying the cubed term was dropped. Also, it would be more complete if the expression for f(x(t),t) were substituted into the final expression.
*[[p. 600, line 10]]: the error term on the right-hand side should be at two time steps back, not one.
*[[p. 625, Exercise 12.2, number 6]]: the first derivative term should be a second derivative.

==Chapter 13==
*p. 662, Figure 13.24: the output Y(s) should be X(s) because that is what it is called in the text that refers to the figure.
*[[p. 662, line 8]]: the second equation on the page should have X(s) on the left hand side, not G_p(s).
*[[p. 664, line 1]]: the sine term inside the friction function should be multiplied by M.
*[[p. 654, line 1, Equation (13.23)]]: the second equilibrium point should be x=2, x'=0, not x=0, x'=2.
*[[p. 664, line 4]]: the term multiplying ''a'' on the left hand side of the equation should be the reciprocal of what is printed.
*[[p. 664, line 8]]: the term multiplying ''b'' on the left hand side of the equation should be the reciprocal of what is printed. Also, there should be an ''M'' multiplying the sine function that is the argument to the ''friction()'' function and no ''M'' multiplying the sine function outside the ''friction()'' function.
*[[p. 666, line 5]]: the "0.3" in the equation should be "-0.3".
*[[p. 679, exercise 13.12, number 2]]: "G(s) =" is missing from the left side of the equation.

==Appendix E==
*Various FORTRAN programs have semicolons terminating lines (always in the declaration statements): E.2.0.20, E.2.0.21, E2.0.22, E.2.0.23, E2.0.24, E2.0.25, E.2.0.26. These semicolons should not be there.
* p. 727, program in E.2.0.18, for Example 1.30: the program contains the variable n which does nothing. The declaration, initialization to zero and increment inside the do loop should be removed.
*[[p. 733, line 19]]: the equation to update x(2) should not have an x(1) in it, it should be copy(1). Also, while it will not affect how the program works, x(2) should be copy(2) for consistency.
*p. 737, line 5: The program in E.2.0.31 is for Example 12.17, not Example 12.16.

Engineering Differential Equations: Theory and Applications, Springer 2010

2015-08-25T21:26:35Z

Bill: /* Chapter 1 */

This page contains supplementary material for the book, ''Engineering Differential Equations: Theory and Applications'', by Bill Goodwine. 2010, Springer.

=Movies=
Chapter 11 considers solutions to partial differential equations.
==The One-Dimensional Wave Equation==
Section 11.1 considers the one-dimensional wave equation.

Some movies:
*String of length 3 plucked at L=1 (modeling a guitar):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode1.mpg The first (fundamental) mode of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15.mpg The first five modes of the plucked string plotted separately]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15sum.mpg The sum of the first five modes of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode50sum.mpg The sum of the first fifty modes of the plucked string]
*String of length 3 that is impacted near L=1 (modeling a piano):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact10sum.mpg The sum of the first ten modes of the impacted string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact50sum.mpg The sum of the first fifty modes of the impacted string]

==The One-Dimensional Heat Conduction Equation==
Section 11.3 considers the one-dimensional heat conduction equation.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinhomo.mpg The solution to the heat equation with inhomogeneous boundary conditions]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinsulated.mpg The solution to the heat equation with an insulated end]

==The Two-Dimensional Heat Equation==
Movie:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/twoheat.mpg Solution to the heat conduction equation in two dimensions]

==Vibrating Membranes==
Partial differential equations describing vibrating membranes in rectangular and polar coordinates are considered in Section 11.5.

Section 11.5.1 presents the two-dimensional wave equation in rectangular coordinates.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum11.mpg 1-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum21.mpg 2-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum22.mpg 2-2 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrumimpact.mpg Rectangular drum impacted near a corner]

Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum10.mpg 1-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum11.mpg 1-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum12.mpg 1-2 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum13.mpg 1-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum20.mpg 2-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum21.mpg 2-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum43.mpg 4-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drumimpact.mpg Circular drum that is impacted by a drum stick]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum.mpg Another drum impact movie]
*[http://www.youtube.com/watch?v=w8Gxut0odyc#t=4m10s Cool youtube movie of slow motion impact of drum head and cymbal]

=Errata=

==Chapter 1==
*[[p. 58, line -3, Equation 2.4]]: the ''c'' in the denominator should be the specific heat.
*[[testmath]] test

==Chapter 2==
*p. 61, second paragraph of Section 2.2, line 2: "and" should be "is".
*[[p. 89, line -7]]: the right hand side of the equation below equation 2.35 should be a function of t, not x.

==Chapter 3==
*[[p. 97, line -3]]: there is an extra closing parenthesis in the equation for the Wronskian.
*[[p. 105, line 12]]: both exponents should be <math>-\omega_n</math>.
*[[p. 117, Figure 3.5]]: the figure plots the solution to <math>\ddot x + \dot x + 10 x = 0</math> and not <math>2 \ddot x + \dot x + 10 x = 0</math> as stated. It really doesn't change the qualitative aspects of the problem, however.

==Chapter 4==
*[[p. 125, line 5]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line 8]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line -4]]: the coefficient of the x term in the differential equation should be squared.
*[[p. 128, Equation 4.8]]: the numerator of the coefficient of the sine term should be the initial velocity.
*[[p. 138, line 6 (large boxed equation)]]: the first zeta in the parentheses in the coefficient of the second exponential on the second line should be negative.
*[[p. 139, Equation 4.14]]: the second term should contain the derivative of x, not x.
*[[p. 142, Figure 4.16]]: the figure is incorrect in that the square root was not used to plot the curves.
*[[p. 156, Exercise 4.22]]: at this point in the book we don't know how to find the homogeneous solutions for these two systems.
*[[p. 158, Exercise 4.26, Figure 4.32]]: the variable x is not the distance along the beam, but rather the displacement at the end.
*[[p. 159, Exercise 4.27, Figure 4.33]]: the angle is incorrectly marked as the angular velocity.

==Chapter 5==
*[[p. 163, line 6]]: the first (n+1) term should be (n+2).
*[[p. 164, Equation 5.5]]: the first coefficient in the second series should be (n+2) not (n+1).
*[[p. 167, lines -4,-3 and -2]]: the expressions for the derivatives of the function are wrong.
* p. 170, line 6: at the end of the line "Table 5.2" should be "Table 5.1."
*[[p. 172, line -5]]: there should be a negative sign on the right hand side of the equation.
*[[p. 174, Equation 5.14]]: the first term in the numerator on the right hand side should be multiplied by 20.
*[[p. 181, line 16]]: the two terms on the right-hand side of the equation are switched, leading to the wrong answer for <math>a_2</math>. This wrong number then propagates to lines -1 and -6 on the same page.
*[[p. 182, line 14]]: in the first series for the second derivative, the exponent should be (n-2) not (n-1).
*[[p. 185, line 2]]: the recursion relation has two mistakes. The left hand side should be for a_{n+2} not {n+1}. Also, the negative sign should not be there.
*[[p. 186, line 6]]: the left hand side of the recursion relation should be for a_{n+2} not {n+1}.
*p. 188, Exercise 5.1, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*p. 189, Exercise 5.2, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*[[p. 190, Exercise 5.13]]: the middle term in the denominator of the second term should be "2 t" not "t2".
*[[p. 191, Exercise 5.16]]: the independent variable in the equation is x, so the derivative terms should be with respect to x.

==Chapter 6==
*[[p. 195, line 1]]: the third term in the vector on the right hand side should have a subscript of 4, not 3.
*[[p. 209, line -8]]: the exponential term should be multiplying the second term as well.
*[[p. 210, line 1]]: same error as on p. 209 carried through.
*[[p. 220, line -9]]: the superscript for the second term in the equation should be m-3.
*[[p. 244, line -11]]: the first component of the vector on the far right should contain t, not tau.
*[[p. 245, line 8]]: the matrix A7 does not have a set of n linearly-independent eigenvectors.
*[[p. 247, line -7]]: A3 should be A2.

==Chapter 7==
*p. 253, line 5: the word "of" is repeated.
*[[p. 265, Equation (7.16)]]: this equation has multiple typos. The last term in parentheses in the last line should be (1-k1-2 k3). Also the second line has misaligned parentheses.

==Chapter 8==
*[[p. 288, last line in Table 8.1]]: the exponent should be "-a t" and not "a t".
*p. 297, Example 8.14: the "3" multiplying the <math>t^2</math> term on the right hand side is dropped half way through the example. Because it scales the whole right hand side, it scales simply scales the solution by 3. Thus the final answer on p. 299 should be multiplied by 3, as should the equation on the top of page 299. Also the two equations in the middle of p. 298 involving X(s) should have the right hand side multiplied by 3.
*p. 326, line -10: "Figure 8.8" should be "Figure 8.37".
*p. 327: the pendulum in Figure 8.36 should indicate a length, ''l'', for the pendulum.

==Chapter 9==
*[[p. 348, line 4]]: the numerator for both expressions of G1 should be 5.
*[[p. 348, line 6]]: the numerator for both expressions of G1 should be 10.
*[[p. 349, caption to Figure 9.16]]: the numerator for G1 should be 4 in the numerator for G2 should be 9.
*p. 354, line 9: the word "row" should be "column".
*p. 368, line 4: "r=10, 1, -1, and 10" should be "r=10, 1, -1, -10".
*p. 368, line -4: "Systems with left half-plane zeros are called..." should be "Systems with right half-plane zeros are called...".
*[[p. 403, line -7]]: the arctan should be a ratio of the imaginary to real components of G(i \omega).

==Chapter 11==
*[[p. 513, line 2]]: the coefficient is alpha^2, not alpha.
*[[p. 515, line 6]]: the "x" should be outside, not inside, the square root.
*[[p. 524, line 1]]: the sine function should not equal n pi, the argument to it should.
*[[p. 525, Equation 11.43]]: the denominator in both exponentials should be <math>L_x</math>.
*[[p. 525, Equation 11.44]]: the first term in the denominator of the coefficient in front of the integral should be <math>L_x</math>, not <math>L</math>.
*[[p. 532, line 12]]: on the right-hand side of the equations, one of the terms should be the steady-state solution.
*[[p. 534, Equation 11.51]]: one of the partial derivatives should be with respect to x.
*[[p. 534, Equation 11.52]]: the frequency in the sine and cosine functions should be multiplied by t.
*p. 536, line 10: "right-hand side of Equation (11.51)" should be "left-hand side of Equation (11.51)".
*[[p. 539, Figure 11.28]]: in the label on the vertical axis, the subscript on z should be "0,n" not "1,n".
*[[p. 542, last boxed set of equations]]: the expressions for the ''c'' and ''d'' coefficients should be in terms of the function ''g'' not the function ''f''. Also, the ''d'' coefficient should have a sine function instead of cosine.
*[[p. 559, line -4]]: the tension and mass per unit length appearing in the frequency term should both be the square root of those terms.
*p. 561, line 1: the second word "subsection" should be "subsections".
*p. 570, Exercise 11.2: add to the problem statement "let <math>m=1, b=0</math> and <math>k = 9\pi^2</math>."
*[[p. 571, line 21]]: for Exercise 11.4, number 4, the initial condition should be for u(x,0) not the partial derivative of u with respect to t.
*[[p. 572, Exercise 11.9]]: in the "denominator" of the operators the partial sign is "squared" when it should be the x and y, respectively.

==Chapter 12==
* p. 580, line 16: the word "so" should be deleted near the end of the line.
* p. 580, line -14: the exact solution is cos(t), not -cos(t).
*[[p. 588, line 2]]: the middle term in the numerator should be evaluated at 2.0, not 1.5.
*[[p. 592, lines 11 and 12]]: the minus sign multiplying the cubed term was dropped. Also, it would be more complete if the expression for f(x(t),t) were substituted into the final expression.
*[[p. 600, line 10]]: the error term on the right-hand side should be at two time steps back, not one.
*[[p. 625, Exercise 12.2, number 6]]: the first derivative term should be a second derivative.

==Chapter 13==
*p. 662, Figure 13.24: the output Y(s) should be X(s) because that is what it is called in the text that refers to the figure.
*[[p. 662, line 8]]: the second equation on the page should have X(s) on the left hand side, not G_p(s).
*[[p. 664, line 1]]: the sine term inside the friction function should be multiplied by M.
*[[p. 654, line 1, Equation (13.23)]]: the second equilibrium point should be x=2, x'=0, not x=0, x'=2.
*[[p. 664, line 4]]: the term multiplying ''a'' on the left hand side of the equation should be the reciprocal of what is printed.
*[[p. 664, line 8]]: the term multiplying ''b'' on the left hand side of the equation should be the reciprocal of what is printed. Also, there should be an ''M'' multiplying the sine function that is the argument to the ''friction()'' function and no ''M'' multiplying the sine function outside the ''friction()'' function.
*[[p. 666, line 5]]: the "0.3" in the equation should be "-0.3".
*[[p. 679, exercise 13.12, number 2]]: "G(s) =" is missing from the left side of the equation.

==Appendix E==
*Various FORTRAN programs have semicolons terminating lines (always in the declaration statements): E.2.0.20, E.2.0.21, E2.0.22, E.2.0.23, E2.0.24, E2.0.25, E.2.0.26. These semicolons should not be there.
* p. 727, program in E.2.0.18, for Example 1.30: the program contains the variable n which does nothing. The declaration, initialization to zero and increment inside the do loop should be removed.
*[[p. 733, line 19]]: the equation to update x(2) should not have an x(1) in it, it should be copy(1). Also, while it will not affect how the program works, x(2) should be copy(2) for consistency.
*p. 737, line 5: The program in E.2.0.31 is for Example 12.17, not Example 12.16.

Engineering Differential Equations: Theory and Applications, Springer 2010

2015-08-25T21:26:21Z

Bill: /* Chapter 1 */

This page contains supplementary material for the book, ''Engineering Differential Equations: Theory and Applications'', by Bill Goodwine. 2010, Springer.

=Movies=
Chapter 11 considers solutions to partial differential equations.
==The One-Dimensional Wave Equation==
Section 11.1 considers the one-dimensional wave equation.

Some movies:
*String of length 3 plucked at L=1 (modeling a guitar):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode1.mpg The first (fundamental) mode of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15.mpg The first five modes of the plucked string plotted separately]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15sum.mpg The sum of the first five modes of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode50sum.mpg The sum of the first fifty modes of the plucked string]
*String of length 3 that is impacted near L=1 (modeling a piano):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact10sum.mpg The sum of the first ten modes of the impacted string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact50sum.mpg The sum of the first fifty modes of the impacted string]

==The One-Dimensional Heat Conduction Equation==
Section 11.3 considers the one-dimensional heat conduction equation.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinhomo.mpg The solution to the heat equation with inhomogeneous boundary conditions]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinsulated.mpg The solution to the heat equation with an insulated end]

==The Two-Dimensional Heat Equation==
Movie:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/twoheat.mpg Solution to the heat conduction equation in two dimensions]

==Vibrating Membranes==
Partial differential equations describing vibrating membranes in rectangular and polar coordinates are considered in Section 11.5.

Section 11.5.1 presents the two-dimensional wave equation in rectangular coordinates.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum11.mpg 1-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum21.mpg 2-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum22.mpg 2-2 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrumimpact.mpg Rectangular drum impacted near a corner]

Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum10.mpg 1-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum11.mpg 1-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum12.mpg 1-2 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum13.mpg 1-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum20.mpg 2-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum21.mpg 2-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum43.mpg 4-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drumimpact.mpg Circular drum that is impacted by a drum stick]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum.mpg Another drum impact movie]
*[http://www.youtube.com/watch?v=w8Gxut0odyc#t=4m10s Cool youtube movie of slow motion impact of drum head and cymbal]

=Errata=

==Chapter 1==
*[[p. 58, line -3, Equation 2.4]]: the ''c'' in the denominator should be the specific heat.

==Chapter 2==
*p. 61, second paragraph of Section 2.2, line 2: "and" should be "is".
*[[p. 89, line -7]]: the right hand side of the equation below equation 2.35 should be a function of t, not x.

==Chapter 3==
*[[p. 97, line -3]]: there is an extra closing parenthesis in the equation for the Wronskian.
*[[p. 105, line 12]]: both exponents should be <math>-\omega_n</math>.
*[[p. 117, Figure 3.5]]: the figure plots the solution to <math>\ddot x + \dot x + 10 x = 0</math> and not <math>2 \ddot x + \dot x + 10 x = 0</math> as stated. It really doesn't change the qualitative aspects of the problem, however.

==Chapter 4==
*[[p. 125, line 5]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line 8]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line -4]]: the coefficient of the x term in the differential equation should be squared.
*[[p. 128, Equation 4.8]]: the numerator of the coefficient of the sine term should be the initial velocity.
*[[p. 138, line 6 (large boxed equation)]]: the first zeta in the parentheses in the coefficient of the second exponential on the second line should be negative.
*[[p. 139, Equation 4.14]]: the second term should contain the derivative of x, not x.
*[[p. 142, Figure 4.16]]: the figure is incorrect in that the square root was not used to plot the curves.
*[[p. 156, Exercise 4.22]]: at this point in the book we don't know how to find the homogeneous solutions for these two systems.
*[[p. 158, Exercise 4.26, Figure 4.32]]: the variable x is not the distance along the beam, but rather the displacement at the end.
*[[p. 159, Exercise 4.27, Figure 4.33]]: the angle is incorrectly marked as the angular velocity.

==Chapter 5==
*[[p. 163, line 6]]: the first (n+1) term should be (n+2).
*[[p. 164, Equation 5.5]]: the first coefficient in the second series should be (n+2) not (n+1).
*[[p. 167, lines -4,-3 and -2]]: the expressions for the derivatives of the function are wrong.
* p. 170, line 6: at the end of the line "Table 5.2" should be "Table 5.1."
*[[p. 172, line -5]]: there should be a negative sign on the right hand side of the equation.
*[[p. 174, Equation 5.14]]: the first term in the numerator on the right hand side should be multiplied by 20.
*[[p. 181, line 16]]: the two terms on the right-hand side of the equation are switched, leading to the wrong answer for <math>a_2</math>. This wrong number then propagates to lines -1 and -6 on the same page.
*[[p. 182, line 14]]: in the first series for the second derivative, the exponent should be (n-2) not (n-1).
*[[p. 185, line 2]]: the recursion relation has two mistakes. The left hand side should be for a_{n+2} not {n+1}. Also, the negative sign should not be there.
*[[p. 186, line 6]]: the left hand side of the recursion relation should be for a_{n+2} not {n+1}.
*p. 188, Exercise 5.1, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*p. 189, Exercise 5.2, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*[[p. 190, Exercise 5.13]]: the middle term in the denominator of the second term should be "2 t" not "t2".
*[[p. 191, Exercise 5.16]]: the independent variable in the equation is x, so the derivative terms should be with respect to x.

==Chapter 6==
*[[p. 195, line 1]]: the third term in the vector on the right hand side should have a subscript of 4, not 3.
*[[p. 209, line -8]]: the exponential term should be multiplying the second term as well.
*[[p. 210, line 1]]: same error as on p. 209 carried through.
*[[p. 220, line -9]]: the superscript for the second term in the equation should be m-3.
*[[p. 244, line -11]]: the first component of the vector on the far right should contain t, not tau.
*[[p. 245, line 8]]: the matrix A7 does not have a set of n linearly-independent eigenvectors.
*[[p. 247, line -7]]: A3 should be A2.

==Chapter 7==
*p. 253, line 5: the word "of" is repeated.
*[[p. 265, Equation (7.16)]]: this equation has multiple typos. The last term in parentheses in the last line should be (1-k1-2 k3). Also the second line has misaligned parentheses.

==Chapter 8==
*[[p. 288, last line in Table 8.1]]: the exponent should be "-a t" and not "a t".
*p. 297, Example 8.14: the "3" multiplying the <math>t^2</math> term on the right hand side is dropped half way through the example. Because it scales the whole right hand side, it scales simply scales the solution by 3. Thus the final answer on p. 299 should be multiplied by 3, as should the equation on the top of page 299. Also the two equations in the middle of p. 298 involving X(s) should have the right hand side multiplied by 3.
*p. 326, line -10: "Figure 8.8" should be "Figure 8.37".
*p. 327: the pendulum in Figure 8.36 should indicate a length, ''l'', for the pendulum.

==Chapter 9==
*[[p. 348, line 4]]: the numerator for both expressions of G1 should be 5.
*[[p. 348, line 6]]: the numerator for both expressions of G1 should be 10.
*[[p. 349, caption to Figure 9.16]]: the numerator for G1 should be 4 in the numerator for G2 should be 9.
*p. 354, line 9: the word "row" should be "column".
*p. 368, line 4: "r=10, 1, -1, and 10" should be "r=10, 1, -1, -10".
*p. 368, line -4: "Systems with left half-plane zeros are called..." should be "Systems with right half-plane zeros are called...".
*[[p. 403, line -7]]: the arctan should be a ratio of the imaginary to real components of G(i \omega).

==Chapter 11==
*[[p. 513, line 2]]: the coefficient is alpha^2, not alpha.
*[[p. 515, line 6]]: the "x" should be outside, not inside, the square root.
*[[p. 524, line 1]]: the sine function should not equal n pi, the argument to it should.
*[[p. 525, Equation 11.43]]: the denominator in both exponentials should be <math>L_x</math>.
*[[p. 525, Equation 11.44]]: the first term in the denominator of the coefficient in front of the integral should be <math>L_x</math>, not <math>L</math>.
*[[p. 532, line 12]]: on the right-hand side of the equations, one of the terms should be the steady-state solution.
*[[p. 534, Equation 11.51]]: one of the partial derivatives should be with respect to x.
*[[p. 534, Equation 11.52]]: the frequency in the sine and cosine functions should be multiplied by t.
*p. 536, line 10: "right-hand side of Equation (11.51)" should be "left-hand side of Equation (11.51)".
*[[p. 539, Figure 11.28]]: in the label on the vertical axis, the subscript on z should be "0,n" not "1,n".
*[[p. 542, last boxed set of equations]]: the expressions for the ''c'' and ''d'' coefficients should be in terms of the function ''g'' not the function ''f''. Also, the ''d'' coefficient should have a sine function instead of cosine.
*[[p. 559, line -4]]: the tension and mass per unit length appearing in the frequency term should both be the square root of those terms.
*p. 561, line 1: the second word "subsection" should be "subsections".
*p. 570, Exercise 11.2: add to the problem statement "let <math>m=1, b=0</math> and <math>k = 9\pi^2</math>."
*[[p. 571, line 21]]: for Exercise 11.4, number 4, the initial condition should be for u(x,0) not the partial derivative of u with respect to t.
*[[p. 572, Exercise 11.9]]: in the "denominator" of the operators the partial sign is "squared" when it should be the x and y, respectively.

==Chapter 12==
* p. 580, line 16: the word "so" should be deleted near the end of the line.
* p. 580, line -14: the exact solution is cos(t), not -cos(t).
*[[p. 588, line 2]]: the middle term in the numerator should be evaluated at 2.0, not 1.5.
*[[p. 592, lines 11 and 12]]: the minus sign multiplying the cubed term was dropped. Also, it would be more complete if the expression for f(x(t),t) were substituted into the final expression.
*[[p. 600, line 10]]: the error term on the right-hand side should be at two time steps back, not one.
*[[p. 625, Exercise 12.2, number 6]]: the first derivative term should be a second derivative.

==Chapter 13==
*p. 662, Figure 13.24: the output Y(s) should be X(s) because that is what it is called in the text that refers to the figure.
*[[p. 662, line 8]]: the second equation on the page should have X(s) on the left hand side, not G_p(s).
*[[p. 664, line 1]]: the sine term inside the friction function should be multiplied by M.
*[[p. 654, line 1, Equation (13.23)]]: the second equilibrium point should be x=2, x'=0, not x=0, x'=2.
*[[p. 664, line 4]]: the term multiplying ''a'' on the left hand side of the equation should be the reciprocal of what is printed.
*[[p. 664, line 8]]: the term multiplying ''b'' on the left hand side of the equation should be the reciprocal of what is printed. Also, there should be an ''M'' multiplying the sine function that is the argument to the ''friction()'' function and no ''M'' multiplying the sine function outside the ''friction()'' function.
*[[p. 666, line 5]]: the "0.3" in the equation should be "-0.3".
*[[p. 679, exercise 13.12, number 2]]: "G(s) =" is missing from the left side of the equation.

==Appendix E==
*Various FORTRAN programs have semicolons terminating lines (always in the declaration statements): E.2.0.20, E.2.0.21, E2.0.22, E.2.0.23, E2.0.24, E2.0.25, E.2.0.26. These semicolons should not be there.
* p. 727, program in E.2.0.18, for Example 1.30: the program contains the variable n which does nothing. The declaration, initialization to zero and increment inside the do loop should be removed.
*[[p. 733, line 19]]: the equation to update x(2) should not have an x(1) in it, it should be copy(1). Also, while it will not affect how the program works, x(2) should be copy(2) for consistency.
*p. 737, line 5: The program in E.2.0.31 is for Example 12.17, not Example 12.16.

Engineering Differential Equations: Theory and Applications, Springer 2010

2015-08-25T21:25:24Z

Bill: /* Chapter 1 */

This page contains supplementary material for the book, ''Engineering Differential Equations: Theory and Applications'', by Bill Goodwine. 2010, Springer.

=Movies=
Chapter 11 considers solutions to partial differential equations.
==The One-Dimensional Wave Equation==
Section 11.1 considers the one-dimensional wave equation.

Some movies:
*String of length 3 plucked at L=1 (modeling a guitar):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode1.mpg The first (fundamental) mode of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15.mpg The first five modes of the plucked string plotted separately]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode15sum.mpg The sum of the first five modes of the plucked string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/pluckedmode50sum.mpg The sum of the first fifty modes of the plucked string]
*String of length 3 that is impacted near L=1 (modeling a piano):
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact10sum.mpg The sum of the first ten modes of the impacted string]
**[http://controls.ame.nd.edu/courses/ame30314/pdes/stringimpact50sum.mpg The sum of the first fifty modes of the impacted string]

==The One-Dimensional Heat Conduction Equation==
Section 11.3 considers the one-dimensional heat conduction equation.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinhomo.mpg The solution to the heat equation with inhomogeneous boundary conditions]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/heatinsulated.mpg The solution to the heat equation with an insulated end]

==The Two-Dimensional Heat Equation==
Movie:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/twoheat.mpg Solution to the heat conduction equation in two dimensions]

==Vibrating Membranes==
Partial differential equations describing vibrating membranes in rectangular and polar coordinates are considered in Section 11.5.

Section 11.5.1 presents the two-dimensional wave equation in rectangular coordinates.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum11.mpg 1-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum21.mpg 2-1 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrum22.mpg 2-2 mode for rectangular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/rectdrumimpact.mpg Rectangular drum impacted near a corner]

Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.

Some movies:
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum10.mpg 1-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum11.mpg 1-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum12.mpg 1-2 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum13.mpg 1-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum20.mpg 2-0 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum21.mpg 2-1 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum43.mpg 4-3 mode for a circular drum]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drumimpact.mpg Circular drum that is impacted by a drum stick]
*[http://controls.ame.nd.edu/courses/ame30314/pdes/drum.mpg Another drum impact movie]
*[http://www.youtube.com/watch?v=w8Gxut0odyc#t=4m10s Cool youtube movie of slow motion impact of drum head and cymbal]

=Errata=

==Chapter 1==
*[[p. 58, line -3, Equation 2.4]]: the ''c'' in the denominator should be the specific heat.
*[[testmath]] asdf

==Chapter 2==
*p. 61, second paragraph of Section 2.2, line 2: "and" should be "is".
*[[p. 89, line -7]]: the right hand side of the equation below equation 2.35 should be a function of t, not x.

==Chapter 3==
*[[p. 97, line -3]]: there is an extra closing parenthesis in the equation for the Wronskian.
*[[p. 105, line 12]]: both exponents should be <math>-\omega_n</math>.
*[[p. 117, Figure 3.5]]: the figure plots the solution to <math>\ddot x + \dot x + 10 x = 0</math> and not <math>2 \ddot x + \dot x + 10 x = 0</math> as stated. It really doesn't change the qualitative aspects of the problem, however.

==Chapter 4==
*[[p. 125, line 5]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line 8]]: one side of the second equation should be multiplied by -1.
*[[p. 125, line -4]]: the coefficient of the x term in the differential equation should be squared.
*[[p. 128, Equation 4.8]]: the numerator of the coefficient of the sine term should be the initial velocity.
*[[p. 138, line 6 (large boxed equation)]]: the first zeta in the parentheses in the coefficient of the second exponential on the second line should be negative.
*[[p. 139, Equation 4.14]]: the second term should contain the derivative of x, not x.
*[[p. 142, Figure 4.16]]: the figure is incorrect in that the square root was not used to plot the curves.
*[[p. 156, Exercise 4.22]]: at this point in the book we don't know how to find the homogeneous solutions for these two systems.
*[[p. 158, Exercise 4.26, Figure 4.32]]: the variable x is not the distance along the beam, but rather the displacement at the end.
*[[p. 159, Exercise 4.27, Figure 4.33]]: the angle is incorrectly marked as the angular velocity.

==Chapter 5==
*[[p. 163, line 6]]: the first (n+1) term should be (n+2).
*[[p. 164, Equation 5.5]]: the first coefficient in the second series should be (n+2) not (n+1).
*[[p. 167, lines -4,-3 and -2]]: the expressions for the derivatives of the function are wrong.
* p. 170, line 6: at the end of the line "Table 5.2" should be "Table 5.1."
*[[p. 172, line -5]]: there should be a negative sign on the right hand side of the equation.
*[[p. 174, Equation 5.14]]: the first term in the numerator on the right hand side should be multiplied by 20.
*[[p. 181, line 16]]: the two terms on the right-hand side of the equation are switched, leading to the wrong answer for <math>a_2</math>. This wrong number then propagates to lines -1 and -6 on the same page.
*[[p. 182, line 14]]: in the first series for the second derivative, the exponent should be (n-2) not (n-1).
*[[p. 185, line 2]]: the recursion relation has two mistakes. The left hand side should be for a_{n+2} not {n+1}. Also, the negative sign should not be there.
*[[p. 186, line 6]]: the left hand side of the recursion relation should be for a_{n+2} not {n+1}.
*p. 188, Exercise 5.1, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*p. 189, Exercise 5.2, part 2: should be "2. Is the point t=0 an ordinary point or singular point?"
*[[p. 190, Exercise 5.13]]: the middle term in the denominator of the second term should be "2 t" not "t2".
*[[p. 191, Exercise 5.16]]: the independent variable in the equation is x, so the derivative terms should be with respect to x.

==Chapter 6==
*[[p. 195, line 1]]: the third term in the vector on the right hand side should have a subscript of 4, not 3.
*[[p. 209, line -8]]: the exponential term should be multiplying the second term as well.
*[[p. 210, line 1]]: same error as on p. 209 carried through.
*[[p. 220, line -9]]: the superscript for the second term in the equation should be m-3.
*[[p. 244, line -11]]: the first component of the vector on the far right should contain t, not tau.
*[[p. 245, line 8]]: the matrix A7 does not have a set of n linearly-independent eigenvectors.
*[[p. 247, line -7]]: A3 should be A2.

==Chapter 7==
*p. 253, line 5: the word "of" is repeated.
*[[p. 265, Equation (7.16)]]: this equation has multiple typos. The last term in parentheses in the last line should be (1-k1-2 k3). Also the second line has misaligned parentheses.

==Chapter 8==
*[[p. 288, last line in Table 8.1]]: the exponent should be "-a t" and not "a t".
*p. 297, Example 8.14: the "3" multiplying the <math>t^2</math> term on the right hand side is dropped half way through the example. Because it scales the whole right hand side, it scales simply scales the solution by 3. Thus the final answer on p. 299 should be multiplied by 3, as should the equation on the top of page 299. Also the two equations in the middle of p. 298 involving X(s) should have the right hand side multiplied by 3.
*p. 326, line -10: "Figure 8.8" should be "Figure 8.37".
*p. 327: the pendulum in Figure 8.36 should indicate a length, ''l'', for the pendulum.

==Chapter 9==
*[[p. 348, line 4]]: the numerator for both expressions of G1 should be 5.
*[[p. 348, line 6]]: the numerator for both expressions of G1 should be 10.
*[[p. 349, caption to Figure 9.16]]: the numerator for G1 should be 4 in the numerator for G2 should be 9.
*p. 354, line 9: the word "row" should be "column".
*p. 368, line 4: "r=10, 1, -1, and 10" should be "r=10, 1, -1, -10".
*p. 368, line -4: "Systems with left half-plane zeros are called..." should be "Systems with right half-plane zeros are called...".
*[[p. 403, line -7]]: the arctan should be a ratio of the imaginary to real components of G(i \omega).

==Chapter 11==
*[[p. 513, line 2]]: the coefficient is alpha^2, not alpha.
*[[p. 515, line 6]]: the "x" should be outside, not inside, the square root.
*[[p. 524, line 1]]: the sine function should not equal n pi, the argument to it should.
*[[p. 525, Equation 11.43]]: the denominator in both exponentials should be <math>L_x</math>.
*[[p. 525, Equation 11.44]]: the first term in the denominator of the coefficient in front of the integral should be <math>L_x</math>, not <math>L</math>.
*[[p. 532, line 12]]: on the right-hand side of the equations, one of the terms should be the steady-state solution.
*[[p. 534, Equation 11.51]]: one of the partial derivatives should be with respect to x.
*[[p. 534, Equation 11.52]]: the frequency in the sine and cosine functions should be multiplied by t.
*p. 536, line 10: "right-hand side of Equation (11.51)" should be "left-hand side of Equation (11.51)".
*[[p. 539, Figure 11.28]]: in the label on the vertical axis, the subscript on z should be "0,n" not "1,n".
*[[p. 542, last boxed set of equations]]: the expressions for the ''c'' and ''d'' coefficients should be in terms of the function ''g'' not the function ''f''. Also, the ''d'' coefficient should have a sine function instead of cosine.
*[[p. 559, line -4]]: the tension and mass per unit length appearing in the frequency term should both be the square root of those terms.
*p. 561, line 1: the second word "subsection" should be "subsections".
*p. 570, Exercise 11.2: add to the problem statement "let <math>m=1, b=0</math> and <math>k = 9\pi^2</math>."
*[[p. 571, line 21]]: for Exercise 11.4, number 4, the initial condition should be for u(x,0) not the partial derivative of u with respect to t.
*[[p. 572, Exercise 11.9]]: in the "denominator" of the operators the partial sign is "squared" when it should be the x and y, respectively.

==Chapter 12==
* p. 580, line 16: the word "so" should be deleted near the end of the line.
* p. 580, line -14: the exact solution is cos(t), not -cos(t).
*[[p. 588, line 2]]: the middle term in the numerator should be evaluated at 2.0, not 1.5.
*[[p. 592, lines 11 and 12]]: the minus sign multiplying the cubed term was dropped. Also, it would be more complete if the expression for f(x(t),t) were substituted into the final expression.
*[[p. 600, line 10]]: the error term on the right-hand side should be at two time steps back, not one.
*[[p. 625, Exercise 12.2, number 6]]: the first derivative term should be a second derivative.

==Chapter 13==
*p. 662, Figure 13.24: the output Y(s) should be X(s) because that is what it is called in the text that refers to the figure.
*[[p. 662, line 8]]: the second equation on the page should have X(s) on the left hand side, not G_p(s).
*[[p. 664, line 1]]: the sine term inside the friction function should be multiplied by M.
*[[p. 654, line 1, Equation (13.23)]]: the second equilibrium point should be x=2, x'=0, not x=0, x'=2.
*[[p. 664, line 4]]: the term multiplying ''a'' on the left hand side of the equation should be the reciprocal of what is printed.
*[[p. 664, line 8]]: the term multiplying ''b'' on the left hand side of the equation should be the reciprocal of what is printed. Also, there should be an ''M'' multiplying the sine function that is the argument to the ''friction()'' function and no ''M'' multiplying the sine function outside the ''friction()'' function.
*[[p. 666, line 5]]: the "0.3" in the equation should be "-0.3".
*[[p. 679, exercise 13.12, number 2]]: "G(s) =" is missing from the left side of the equation.

==Appendix E==
*Various FORTRAN programs have semicolons terminating lines (always in the declaration statements): E.2.0.20, E.2.0.21, E2.0.22, E.2.0.23, E2.0.24, E2.0.25, E.2.0.26. These semicolons should not be there.
* p. 727, program in E.2.0.18, for Example 1.30: the program contains the variable n which does nothing. The declaration, initialization to zero and increment inside the do loop should be removed.
*[[p. 733, line 19]]: the equation to update x(2) should not have an x(1) in it, it should be copy(1). Also, while it will not affect how the program works, x(2) should be copy(2) for consistency.
*p. 737, line 5: The program in E.2.0.31 is for Example 12.17, not Example 12.16.

AME 40590 Intellectual Property for Engineers

2015-04-02T19:53:53Z

Bill: /* ALPHABETICAL LISTING OF CASES */

Cases to add:
* Damages:
** MINTZ V. DIETZ & WATSON, INC. (CAFC, May 2012)
** Monsanto Co. v. McFarling, 488 F.3d 973, 978-79 (Fed. Cir. 2007)
** Georgia-Pacific Corp. v. US Plywood Corp., 318 F. Supp. 1116 (SDNY 1970), modified, 446 F. 2d 295 (2d Cir. 1971)
** The Boeing Company v. The United States, 86 Fed. Cl. 303 (April 2, 2009)
** Mahurkar v. CR Bard, Inc. 79 F. 3d 1572, 1580 (Fed. Cir. 1996), adopting Panduit Corp. v. Stahlin Bros. Fibre Works, Inc.,575 F.2d 1152 (6th Cir. 1978)
** Depuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 567 F.3d 1314 (Fed. Cir. 2009)

* Software patents:
** In re Alappat, 33 F.3d 1526, 1545 (Fed. Cir. 1994).
** CyberSource Corporation v. Retail Decisions, Inc., Slip Op. at 19 (2011)
** Ultramercial, LLC v. Hulu, LLC (Fed. Cir. 2011)

=ALPHABETICAL LISTING OF CASES=

*[[A. & P. Tea Co. v. Supermarket Corp., 340 U.S. 147 (1950)]]
*[[Abbott Laboratories v. Geneva Pharmaceuticals, Inc., 182 F.3d 1315 (1999)]]
*[[Alza Corp. v. Mylan Laboratories, 464 F.3d 1286, (2006)]]
*[[Anderson's Black Rock, Inc. v. Pavement Co., 396 U.S. 57 (1969)]]
*[[Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336 (1961)]]
*[[Arrhythmia Research Technology, Inc. v. Corazonix Corp., 958 F.2d 1053 (1992)]]
*[[Asgrow Seed Co. v. Winterboer, 513 U.S. 179 (1994)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. (2013)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. CAFC (2012)]]
*[[Atlas Powder v. E.I. du Pont de Nemours, 750 F2d 1569 (1984)]]
*[[Bilski v. Kappos, 130 S.Ct. 3218 (2010)]]
*[[Bobbs-Merrill Co. v. Straus, 210 U.S. 339 (1908)]]
*[[Bonito Boats. v. Thunder Craft, 489 U.S. 141 (1989)]]
*[[Bowman v. Monsanto, 133 S.Ct. 1761 (2013)]]
*[[CCS Fitness, Inc. v. Brunswick Corporation, 288 F.3d 1359 (2002)]]
*[[Chester v. Miller, 906 F.2d 1574 (1990)]]
*[[D.L. Auld Co. v. Chroma Graphics Corp., 714 F.2d 1144 (1983)]]
*[[Diamond v. Chakrabarty, 100 S.Ct. 2204 (1980)]]
*[[Diamond v. Diehr, 450 U.S. 175 (1981)]]
*[[Egbert v. Lippmann, 104 U.S. 333 (1881)]]
*[[Electric Storage Battery Co. v. Shimadzu, 307 U.S. 5 (1939)]]
*[[Elizabeth v. American Nicholson Pavement Company, 97 U.S. 126 (1877)]]
*[[Filmtec Corp. v. Allied-Signal Inc., 939 F.2d 1568 (1991)]]
*[[Funk Bros. Seed Co. v. Kalo Inoculant Co. 333 U.S. 127 (1948)]]
*[[Gottschalk v. Benson, 409 U.S. 63 (1972)]]
*[[Gould v. Hellwarth, 472 F2d 1383 (1973)]]
*[[Graham v. John Deere, 383 U.S. 1 (1966)]]
*[[Graver Tank & Mfg. Co. v. Linde Air Products Co. 339 US 605 (1950)]]
*[[H.H. Robertson, Co. v. United Steel Deck, Inc., 820 F.2d 384 (1987)]]
*[[Hotchkiss v. Greenwood, 52 U.S. 11 (1850) ]]
*[[Hybritech v. Monoclonal Antiboties, 802 F.2d 1375 (1986)]]
*[[i4i Ltd. Partnership v. Microsoft Corp., 598 F.3d 831 (2010)]]
*[[In Re Bilski]]
**[[In Re Bilski, Dky concurring opinion]]
**[[In Re Bilski, Newman dissenting opinion]]
**[[In Re Bilski, Mayer dissenting opinion]]
**[[In Re Bilski, Rader dissenting opinion]]
*[[In re Brana, 51 F.3d 1560 (1995)]]
*[[In re Carlson, 983 F.2d 1032 (1992)]]
*[[In re Hall, 781 F.2d 897 (1986)]]
*[[In re Kahn, CAFC 04-1616 (2006)]]
*[[In Re Rouffet, 149 F.3d 1350 (1998)]]
*[[J.E.M. Ag Supply, Inc. v. Pioneer Hi-Bred International, Inc., 534 U.S. 124 (2001)]]
*[[Juicy Whip v. Orange Bang, 185 F.3d 1364 (1999)]]
*[[KSR International Co. v. Teleflex, Inc., 550 U.S. 398 (2007)]]
*[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]
*[[Lorenz v. Colgate-Palmolive-Peet Co., 167 F.2d 423 (1948)]]
*[[Lough v. Brunswick Corp., 86 F.3d 1113 (1996)]]
*[[Lyon v. Bausch & Lomb, 224 F.2d 530 (1955)]]
*[[Metabolit Laboratories, Inc. and Competitive Technologies, Inc. v. Laboratory Corporation of America Holdings, 370 F.3d 1354 (2004)]]
*[[Metallizing Engineering Co., Inc. v. Kenyon Bearing & Auto Parts Co., Inc., 153 F.2d 516 (1946)]]
*[[Microsoft Corp v. At&T Corp., 550 U.S. 437 (2007)]]
*[[Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (1978)]]
*[[Perkin-Elmer Corporation v. Computervision Corporation, 732 F2d 888 (1984)]]
*[[Pfaff vs. Wells Electronics, 525 U.S. 55 (1998)]]
*[[Philips Electric Co. v. Thermal Industries, Inc., 450 F.2d 1164 (1971)]]
*[[Quanta Computer, Inc. v. LG Electronics, Inc., 553 U.S. 617 (2008)]]
*[[Reiner v. I. Leon Co., 285 F.2d 501 (1960)]]
*[[South Corp. v. US 690 F.2d 1368 (1982)]]
*[[State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (1998)]]
*[[Traffix Devices, Inc. vs. Marketing Displays, Inc., 532 U.S. 23 (2001)]]
*[[TurboCare Div. of Demag Delaval Turbomachinery Corp. v. General Elec. Co., 264 F.3d 1111 (2001)]]
*[[UMC Electronics Co. v. U.S., 816 F.2d 647 (1987)]]
*[[US v. Adams, 383 U.S. 39 (1966)]]
*[[U.S. v. Univis Lens Co., 316 U.S. 241 (1942)]]
*[[Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530 (1976)]]
*[[Vas-Cath Inc. v. Mahurkar, 935 F.2d 1555 (1991)]]
*[[Warner-Jenkinson Company v. Hilton Davis Chemical Co., 520 US 17 (1997)]]
**[[Warner-Jenkinson v. Hilton Davis Petitioner Brief]]
**[[Warner-Jenkinson v. Hilton Davis Respondent Brief]]
*[[Winner International Royalty Co. v. Wang, 202 F.3d 1340 (2000)]]
*[[W.L. Gore & Associates, Inc. v. Garlock, Inc., 721 F.2d 1540 (1983)]]

=[[INTRODUCTION]]=
This is a summary. Click on the title for the full chapter: [[INTRODUCTION]]

Outline:
*The main purpose for obtaining a patent is ''economic''.
*It grants the exclusive right to ''make, use or sell'' the invention for a limited period of time.
*The governing law is Title 35 of the United States Code (35 USC).
*The governing regulations are from Title 37 of the Code of Federal Regulations (37 CFR).
*The law is federal, so patent cases are resolved in the federal court system:
**district courts;
**circuit courts;
**the Court of Appeals for the Federal Circuit (CAFC), a special appeals court for patent cases; and,
**the Supreme Court.
*The US Patent and Trademark Office (PTO) processes patent applications.
*Patents last for 20 years from the date the application is filed with the PTO.
*Patents have the attributes of personal property.
*The foundation of the federal government's authority to create a patent system is in the Constitution. The purposes is explicitly economic, "to promote the progress of science and useful arts..."
*Other forms of intellectual property
**copyright;
**trademarks; and,
**trade secrets.

=[[NONOBVIOUSNESS]]=
This is a summary. Click on the title for the full chapter: [[NONOBVIOUSNESS]]

Outline:

*This is perhaps the most difficult factual patent issue. In addition to meeting the novelty requirements of 35 USC 102, 35 USC 103 requires that the claimed invention as a whole must have been nonobvious "at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains."
*There is a lot of historical confusion regarding this standard. Basically, it is a notion of something being meeting some type of sufficient inventive standard or nontriviality.
*To determine this, there are three fundamental lines of inquiry:
**the scope and content of the prior art;
**the differences between the prior art and claims at issue; and,
**the level of ordinary skill in the art.
*Secondary considerations include:
**a long-felt but unsatisfied need met by the invention;
**appreciation by those versed in the art that the need existed;
**substantial attempts to meet this need;
**commercial success of the invention;
**replacement in the industry by the claimed invention;
**acquiescence by the industry;
**''teaching away'' by those skilled in the art;
**unexpectedness of the results; and,
**disbelief or incredulity on the part of industry with respect to the new invention.

=[[INFRINGEMENT]]=
This is a summary. Click on the title for the full chapter: [[INFRINGEMENT]]

=[[THE PATENT DOCUMENT]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT DOCUMENT]]

Outline:
*A patent has several parts:
**specification: describes the invention;
**claims: delineates the ownership rights;
**drawings: not required, but if they are included then any element included in the claims must be shown in the drawings; and,
**other miscellaneous parts.
*Interpreting claims: claims are said to ''read on'' another device.
*The doctrine of equivalence, prevents something from being patented that only has minor alterations from the prior art.
*The date of the invention
**''reduction to practice'';
**''diligence'' requirement.
*The ''file wrapper''.

=[[NOVELTY]]=
This is a summary. Click on the title for the full chapter: [[NOVELTY]]

Outline:
*Specified in 35 USC 102.
*Fundamentally: an invention must be ''new''.
*Section 102 basically defines in a technical way what it means to not be new:
**Events prior to invention
***known or used by others in the US
***patented or in a printed publication in another country
**Events one year before filing the patent application
***patented or in a printed publication anywhere (''in this or a foreign country'')
***in public use or on sale in the US
**Other bars
*The applicant must be the inventor (not the employer)

Outline:
*Literal Infringement
*The Doctrine of Equivalents

=[[UTILITY]]=
This is a summary. Click on the title for the full chapter: [[UTILITY]]

=[[PATENTABLE SUBJECT MATTER]]=
This is a summary. Click on the title for the full chapter: [[PATENTABLE SUBJECT MATTER]]

Can computer programs, algorithms, laws of nature, life forms, plants, ''etc.'' be patented. In particular, are the following patentable:

* Plants
* Algorithms and Computer Programs
* Scientific Facts?

In a recent case
* State Street (1998)
the CAFC substantially broadened the subject matter of section 101 to include such things as methods of doing business, etc.

=[[FOREIGN AND DOMESTIC PRIORITY]]=
This is a summary. Click on the title for the full chapter: [[FOREIGN AND DOMESTIC PRIORITY]]

Outline:
*Priority in general
*Foreign priority
*International applications
*Domestic priority
*Provisional applications

=[[THE PATENT APPLICATION]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT APPLICATION]]

Outline:
*The Disclosure
*The Claims
*Other Sections
*New Matter
*The Examination Process

=[[INVENTOR ELIGIBILITY]]=
This is a summary. Click on the title for the full chapter: [[INVENTOR ELIGIBILITY]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972): full text]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981): (full text)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005): (full text)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]

[[METABOLITE LABORATORIES, INC. and Competitive Technologies, Inc. v. LABORATORY CORPORATION OF AMERICA HOLDINGS (doing business as LabCorp): the CAFC case (full text)]]

=[[ANTICIPATION]]=
This is a summary. Click on the title for the full chapter: [[ANTICIPATION]]

=[[PRIOR ART]]=
This is a summary. Click on the title for the full chapter: [[PRIOR ART]]

[[Pfaff v. Wells Electronics: full text]]

[[Perkin-Elmer Corporation v. Computervision Corporation (full text)]]

[[Perkin-Elmer Corporation v. Computervision Corporation]]

Talk:Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530

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#REDIRECT [[Talk:Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530 (1976)]]

Talk:Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530 (1976)

2015-04-02T19:53:35Z

== Maura ==
At issue in this case is the validity of a United States patent1 that pertains to a weight-lifting apparatus. Originally granted to Harold Zinkin, the patent was owned by Universal Athletic Sales Co. at the time of suit. The patent consists of eight claims, and the district court struck down two of them on
grounds of anticipation and obviousness.2 We must decide whether these rulings were warranted.

For the district court to have granted controlling weight to the testimony of Mr. Lyle constituted error for two reasons. First, because Mr. Lyle's qualifications as an expert are questionable, at least insofar as this litigation is concerned, the trial judge erred in according great weight to his opinions. Second, the district court committed error in failing to discount the value of the testimony, given the interest in the litigation of the law firm with which Mr. Lyle was associated.
A.
Universal first contends that Mr. Lyle's testimony should have been excluded on the ground that he was not an expert with respect to the patent claims at issue here.
This Court previously has delineated the standard which governs the competency of an expert witness in a particular case. As we noted in United
States v. 60.14 Acres of Land,12 an expert witness " 'must have such skill, knowledge and experience in (the) field or calling as to make it appear that
his opinion or inference will probably aid the trier in his search for truth.' "13 Ordinarily, the determination of competency of an expert witness rests
within the discretion of the trial court.14 The Supreme Court has posited that "the trial judge has broad discretion in the matter of the admission or
exclusion of expert evidence, and his action is to be sustained unless manifestly erroneous."15 It follows that this Court will not interfere with the decision of the district judge as to an expert, absent an abuse of discretion.

In considering whether the trial judge should have recognized Mr. Lyle as an expert in this litigation, we must first determine which art is the pertinent one. Universal asserts that the relevant art is weight-training, whereas the defendants and the district court selected mechanical engineering. We doubt whether any mechanical engineer could provide meaningful opinions regarding the devices at issue here. For an engineer to assist the trial judge in his search for truth would require that he have at least some familiarity with body-building machines. At the same time, a mere weight lifter probably would be of marginal assistance to a court in evaluating the design facets of exercise apparatus. Consequently, the art germane to the present case is the design of body-training devices.

As a result, it is doubtful whether he was suited to serve as an expert here.

Simply stated, a patent may be deemed invalid if it is "obvious." 35 U.S.C. § 103 provides, in part: "A patent may not be obtained . . . if the differences between the subject matter sought to be patented and the prior art are such that the subject matter as a whole would have been obvious at the time the invention was made to a person having ordinary skill in the art to which the subject matter pertains."
As observed in Trio Process Corporation v. L. Goldstein's Sons, Inc.,33 the most authoritative construction of section 103 appears in Graham v. John Deere Co.34 There the Supreme Court established three mandatory criteria with which to frame judicial determinations as to obviousness: "The scope
and content of the prior art . . .; differences between prior art and the claims at issue . . .; and the level of ordinary skill in the pertinent art . . . ."35 The Supreme Court also set forth several permissive, or "secondary," considerations: "commercial success, long felt but unsolved needs, failure of
others, etc., might be utilized to give light to the circumstances surrounding the origin of the subject matter sought to be patented."36

With respect to the third mandatory criteria under Graham, that is, the level of ordinary skill in the pertinent art, the district court acknowledged that "The record on this point is somewhat deficient."40 Even so, the trial judge declared that "any competent mechanical engineer . . . could readily create a
machine substantially the same as that of plaintiffs."41 As discussed above, we believe that the pertinent art is neither mechanical engineering nor weight-lifting, but rather the design of body-exercising apparatus. Not only did the district court fail to select the proper art, but it is questionable whether the evidence submitted by the defendants speaks to the level of ordinary skill in the design of weight-lifting devices.

This Court need not consider the permissive, or secondary, criteria mandated in Graham for determinations of obviousness. For we are convinced that the defendants failed to provide adequate evidence to justify invalidation of the Zinkin claims under section 103. Even if the permissive tests were
applied, the commercial success of the Zinkin machine42 would reinforce our conclusion, as would the "failure of others" to eliminate the safety hazards and manpower requirements of the traditional chest press exercise.43 Thus, we cannot say that the Zinkin claims are so obvious as to render them invalid.44
B.

Besides holding the Zinkin claims void for obviousness, the district court concluded that they were anticipated by prior art. 35 U.S.C. § 102 provides, in pertinent part: "A person shall be entitled to a patent unless (a) the invention was . . . patented or described in a printed publication in this or a foreign country, before the invention thereof by the applicant for patent. . . ." The defendants had contended, and the trial judge agreed, that both the Simmons patent and the Loprinzi photograph anticipated the Zinkin claims so as to render them nugatory under the statute. Since there is insufficient evidence to rebut the heavy presumption of patent validity, we do not sustain this conclusion of the district court.
In construing section 102, the trial judge apparently viewed the Loprinzi photograph as a "printed publication" which described the Zinkin invention. While neither this Court nor apparently any other tribunal has yet determined whether a photograph in itself constitutes a "printed publication," we
believe that a photograph may so qualify for purposes of section 102.45 In so stating, we reaffirm our pragmatic pronouncement in Philips Electronic and Pharmaceutical Industries Corp. v. Thermal and Electronics Industries, Inc.,46 that "to restrict our interpretation of Section 102(a)'s 'printed' publication
requirement solely to the traditional printing press would ignore the realities of the scientific and technological period in which we live . . . ."47 With a photograph, one conversant in a pertinent art could make or construct a purported invention without resorting either to the patent or to his own inventive skills. Under certain circumstances, then, a photograph may so anticipate a patent as to render it invalid.
The question remains, however, whether the photograph of Loprinzi's device anticipated those claims of the Zinkin patent that the defendants challenge. We hold that it does not. In Philips we specified the circumstances under which a prior publication could anticipate a patent: "For a prior publication to be sufficient to defeat a patent it must exhibit a substantial representation of the invention in such full, clear, and exact terms that one
skilled in the art may make, construct and practice the invention without having to depend on either the patent or on his own inventive skills."48
In the discussion of obviousness in Part III-A, we commented that it would be difficult, if not impossible, to discern the content of the Loprinzi photograph. That observation is applicable here, for it would not be possible for a trial court to ascertain whether the photograph anticipates the Zinkin invention. The photographic representation of the Loprinzi "super-duper pressing apparatus" hardly is "full, clear, and exact." It is questionable whether one skilled in the design of weight-lifting apparatus could produce the Zinkin device, based on an examination of the Loprinzi photograph. Accordingly, we believe that the magazine photograph is insufficient to render the patent invalid on the ground of anticipation.
Nor can we hold that the Simmons patent anticipated the Zinkin weight-lifting machine. It is unclear whether the Simmons invention encompasses all or substantially all of the elements of the apparatus under scrutiny in this case. The evidence submitted does not reveal whether one skilled in the design of body-exercising devices, or even in mechanical engineering, could develop the Zinkin weight-lifting apparatus based on the Simmons patent or on his own skills. We conclude, therefore, that the defendants in the present case have failed to demonstrate invalidity of the challenged claims under section 102.
IV.
While the validity of the Zinkin patent is not completely free from doubt, we do not accept the decision reached by the district court. The district court erred in according substantial weight to the testimony of Mr. Lyle. Without such unjustified reliance on that testimony, the trial judge could not properly interpret the prior art. Because the evidence produced by the defendants simply is not sufficient to rebut the presumption of validity accorded patents, we must reverse the rulings of the district court as to obviousness and anticipation, and sustain claims numbered 3 and 4 of the Zinkin patent.
The judgment of the district court will be vacated and the cause remanded for proceedings consistent with this opinion.

Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530

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#REDIRECT [[Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530 (1976)]]

Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530 (1976)

2015-04-02T19:53:35Z

United States Court of Appeals,
Third Circuit.

UNIVERSAL ATHLETIC SALES CO., a corporation, Appellant,

v.

AMERICAN GYM, RECREATIONAL & ATHLETIC EQUIPMENT CORPORATION, INC., et al.

No. 76-1023.

Argued Sept. 9, 1976.

Decided Nov. 19, 1976.

As Amended Dec. 30, 1976.

Appeal was taken by owner of patent from a judgment of the United States District Court for the Western District of Pennsylvania, William W. Knox, J., 397 F.Supp. 1063, striking down two of eight claims in patent pertaining to a weight-lifting apparatus. The Court of Appeals, Adams, Circuit Judge, held that since attorney in law firm that represented several defendants in action may have possessed skill and knowledge greater than an average layman with respect to weight-lifting apparatus that was subject of action, district court did not abuse its discretion in recognizing attorney as an expert, but since attorney's qualifications as an expert were questionable due, in part, to fact that his patent work primarily pertained to electrical as opposed to mechanical engineering, attorney's limited experience with class of devices presented in action should have substantially circumscribed weight accorded his testimony and, hence, district court should not have attached controlling weight to his opinions; further, once testimony of associate was discounted, remaining evidence was not adequate to rebut presumptive validity of claims 2 and 3 of patent No. 2,932,509 pertaining to a weight-lifting apparatus, or to sustain district court's rulings as to obviousness and anticipation of prior art. It was further held that practice of an attorney testifying as an expert witness for a client of his law firm is not to be approved.

Vacated and remanded.

Robert D. Yeager, Robert DeMajistre, Pittsburgh, Pa., Lewis M. Dalgarn, Los Angeles, Cal., for appellant; Nilsson, Robbins, Dalgarn & Berliner, Los Angeles, Cal., of counsel.

Thomas H. Murray, Pittsburgh, Pa., Hymen Diamond, Monroeville, Pa., for appellees.

Floyd B. Carothers, Pittsburgh, Pa., for appellee, Donald E. Pinchock.

Before ADAMS, ROSENN and GARTH, Circuit Judges.

OPINION OF THE COURT

ADAMS, Circuit Judge.
At issue in this case is the validity of a United States patent<ref>United States Letters Patent No. 2,932,509 for “Body Exercising Apparatus,” issued on April 12, 1960.</ref> that pertains to a weight-lifting apparatus. Originally granted to Harold Zinkin, the patent was owned by Universal Athletic Sales Co. at the time of suit. The patent consists of eight claims, and the district court struck down two of them on grounds of anticipation and obviousness.<ref>The original opinion of the district court is reported at 397 F.Supp. 1063 (W.D.Pa.1975). That opinion subsequently was amended, and the amended judgment is set forth at 397 F.Supp. at 1074.</ref> We must decide whether these rulings were warranted.

Two issues underlie the basic question of patent validity now before the Court. The first concerns the controlling weight accorded by the trial judge to the testimony of defendants' principal expert witness, an associate in the law firm representing two of the defendants. Assuming that such testimony deserved little or no weight, as plaintiff maintains, we must then decide the second issue, whether there was nonetheless evidence sufficient to support the decision of the district court.

I.

Modern technology has, of course, pervaded almost every province of human endeavor. The Zinkin patent demonstrates the verity of this postulate, for its deals with a somewhat unusual activity weight-lifting. Specifically, the patent relates to the chest-press exercise, one of the cornerstones of the bodily arts. As athletes and physical fitness enthusiasts well know, the chest press enables the zealous practitioner to develop the musculature of his upper torso. Like many modern advances, the Zinkin patent attempts to retain the advantages of old methods, while conferring added benefits with the new.

In the traditional chest press, the exerciser lies on a bench and raises a free barbell from his chest to a position in which his arms are fully extended. He raises and lowers the barbell for as long as he desires or is able. The exercise requires the continuing assistance of another person, the “spotter.” Not only must the spotter hand the barbell to the exerciser at the inception of the routine, but he must also attempt to retrieve the bar should it begin to totter. Occasionally, the spotter is unable to catch the barbell so that it falls upon the exerciser, causing injury that can be quite serious.

The patent in this appeal discloses an apparatus which permits an exerciser to simulate, safely and effectively, the chest press exercise.<ref>The claims of the Zinkin patent that are contested by the defendants contain the following descriptions:“3. A body exercising apparatus comprising an elongated substantially horizontal table having a predetermined head end and a foot end, an elongated bar extended from the head end of the table in substantial alignment therewith and having an end adjacent to the table and an opposite end, means pivotally mounting the extended end of the bar for pivotal movement about a substantially horizontal axis transversely of the table and in spaced relation to the head end thereof whereby elevational movement of the bar causes the end thereof adjacent to the table to describe an arc with its concave side disposed toward the table, a pair of handles aligned transversely of the table, means rigidly mounting the handles on the bar for integral pivotal movement therewith, stop means engageable with the bar limiting downward travel of the handles to positions in upwardly spaced relation to the table, and means connected to the bar resistive to upward pivotal movement thereof.”“4. A body exercising apparatus comprising an elongated substantially horizontal table adapted to support a person in supine position thereon having a predetermined head end and foot end, a framework adjacent to the head end of the table, an elongated bar pivotally mounted in the framework in substantial alignment with the table for movement about a substantially horizontal axis transversely of the table in spaced relation to the head end thereof and said bar being extended toward the table, a pair of handles rigidly mounted on the bar and disposed on opposite sides of the head end of the table, said bar terminating short of the table and leaving the area above the head end thereof free from obstruction, adjustable weight means borne by the bar, and a stop mounted in the framework engageable with the bar limiting downward pivotal movement thereof to a position with the handles disposed at an elevation above the table.”</ref> To use the patented apparatus, the exerciser lies upon a table in a supine position and pushes against handles in an upward movement. These handles shift in an arcuate fashion, analogous to the movement of the bar in the chest press exercise. They extend from a box-like structure which supports and contains the lifting mechanism. The design of the apparatus is such that the handles, the attached bar and the weights cannot strike the exerciser even should he falter. In addition, the Zinkin machine may be utilized without the assistance of a spotter. The patented apparatus thus eliminates the safety hazards posed by the conventional chest press and obviates its manpower requirements as well.<ref>The problems inherent in the simple chest press exercise had spurred several previous attempts at improvement. See Brief of Appellants, at 10-14. The “cradle” device, for example, utilized a rack which held the barbell at the beginning and end of the exercise. This primitive apparatus, however, did not eliminate the need for a spotter during the course of the exercise. Moreover, the cradle device was unstable and often flipped over, injuring the exerciser, his spotter or others. Subsequent improvements included the “power rack” and the “verti-slide.” While these advances remedied the dangers posed by the chest press, their protective features often proved disruptive to the exercise routine. Consequently, prior to the Zinkin patent, many devotees of the chest press continued to use the free barbell in spite of its perils, inconvenience and added expense. The district court did not consider these primitive improvements as “prior art” with respect to the Zinkin apparatus, nor do any of the defendants.</ref>

This action was initiated by Universal against the defendants as part of a complex litigation involving, inter alia, questions of patent infringement, unfair competition, copyright infringement and antitrust violations. When Universal alleged patent infringement in its complaint, the defendants pleaded invalidity of the patent itself. The district court severed the patent infringement and unfair competition issues for trial,<ref>For a report on the related proceedings, see the original district court opinion, 397 F.Supp. at 1065 and n.1.</ref> and the patent issue, alone, is before us on appeal. After a nonjury trial, the district court initially adjudged the Zinkin patent entirely invalid. However, an amended order vacated the earlier judgment, leaving as invalid patent claims numbered 3 and 4.

Defendants had developed a body-exercising apparatus very similar to that covered by the Zinkin patent. Indeed, the district court found that “the defendants' chest press apparatus would infringe the Zinkin patent if the Zinkin patent were not . . .” invalid.<ref>397 F.Supp. at 1070-71.</ref> In their briefs, defendants list several differences between their own device and that of Zinkin. Nevertheless, the defendants do not vigorously contest the determination of infringement by the trial judge. Instead, they rely solely upon his ruling of invalidity, and attempt to buttress his analysis in this respect. At trial, as in the appeal now before us, the primary focus was on whether the Zinkin patent was “anticipated” or made “obvious” by the prior art.

Two references were relied upon by the district court in holding the Zinkin claims invalid: a patent issued to C. A. Simmons in 1871<ref>Patent No. 117,339, dated July 25, 1871, for a “Lifting Machine.”</ref> and a magazine photograph, dated 1950, of a lifting machine designed by Sam Loprinzi.<ref>The photograph appeared in Strength and Health Magazine, May-June 1950, at 50.</ref> Disclosing a lifting machine for “developing the muscular system,” the Simmons device consists of weighted levers which the exerciser apparently lifts and lowers as part of the exercise. The Loprinzi machine is described in the photograph caption as a “super-duper pressing apparatus,” but the magazine caption itself provides no information as to the features of the device or how it was to be used. Defendants' principal expert witness attempted to explain its features based solely on his examination of the photograph.

That expert was Firman Lyle, an associate lawyer in the law firm that represented several of the defendants.<ref>See Appendix at 280 (Trial Transcript at 383).</ref> Controlling weight was given by the district court to his testimony as to obviousness and anticipation: “The court chooses to adopt the view of defendant's expert Firman Lyle.”<ref>397 F.Supp. at 1070.</ref> Relying on the Simmons patent, the Loprinzi photograph, and Mr. Lyle's testimony as to these references, the trial court concluded that the two central claims of the Zinkin patent are void, since they were anticipated and made obvious by prior art.

For reasons to be discussed in this opinion, we have decided that the judgment of the district court must be vacated.<ref>This Court has jurisdiction pursuant to 28 U.S.C. s 1292(a)(1), for the district court below, in effect, denied an injunction against further infringement. It may be that we also possess jurisdiction pursuant to 28 U.S.C. s 1292(a)(4), which authorizes an appeal from a district court judgment in a patent infringement action that is final except for an accounting. But see 9 J. Moore's Federal Practice P 110.19(4) (1975). Because we believe that these provisions constitute sufficient grounds for jurisdiction, we did not certify this case for appeal under 28 U.S.C. s 1292(b), as desired by the district court. See 397 F.Supp. at 1074. Absent these sources of jurisdiction, however, we would have issued the requisite s 1292(b) certificate because this case raises substantial issues, the resolution of which should materially enhance resolution of this protracted litigation.</ref>

II.

For the district court to have granted controlling weight to the testimony of Mr. Lyle constituted error for two reasons. First, because Mr. Lyle's qualifications as an expert are questionable, at least insofar as this litigation is concerned, the trial judge erred in according great weight to his opinions. Second, the district court committed error in failing to discount the value of the testimony, given the interest in the litigation of the law firm with which Mr. Lyle was associated.

A.

Universal first contends that Mr. Lyle's testimony should have been excluded on the ground that he was not an expert with respect to the patent claims at issue here.

This Court previously has delineated the standard which governs the competency of an expert witness in a particular case. As we noted in United States v. 60.14 Acres of Land,<ref>362 F.2d 660 (3d Cir. 1966).</ref> an expert witness “ ‘must have such skill, knowledge and experience in (the) field or calling as to make it appear that his opinion or inference will probably aid the trier in his search for truth.’ ”<ref>Id. at 667 quoting Jenkins v. United States, 113 U.S.App.D.C. 300, 307 F.2d 637, 643 (1962), in turn quoting McCormick, Evidence s 13 (1954).</ref> Ordinarily, the determination of competency of an expert witness rests within the discretion of the trial court.<ref>See, e. g., Salem v. United States Lines Co., 370 U.S. 31, 35, 82 S.Ct. 1119, 8 L.Ed.2d 313, reh. denied 370 U.S. 965, 82 S.Ct. 1578, 8 L.Ed.2d 834 (1962); United States v. 60.14 Acres of Land, 362 F.2d 660, 663 (3d Cir. 1966); Arnold v. Loose, 352 F.2d 959 (3d Cir. 1965).</ref> The Supreme Court has posited that “the trial judge has broad discretion in the matter of the admission or exclusion of expert evidence, and his action is to be sustained unless manifestly erroneous.”<ref>Salem v. United States Lines Co., 370 U.S. 31, 35, 82 S.Ct. 1119, 1122, 8 L.Ed.2d 313 (1962).</ref> It follows that this Court will not interfere with the decision of the district judge as to an expert, absent an abuse of discretion.

In considering whether the trial judge should have recognized Mr. Lyle as an expert in this litigation, we must first determine which art is the pertinent one. Universal asserts that the relevant art is weight-training, whereas the defendants and the district court selected mechanical engineering. We doubt whether any mechanical engineer could provide meaningful opinions regarding the devices at issue here. For an engineer to assist the trial judge in his search for truth would require that he have at least some familiarity with body-building machines. At the same time, a mere weight lifter probably would be of marginal assistance to a court in evaluating the design facets of exercise apparatus. Consequently, the art germane to the present case is the design of body-training devices.

Having selected the relevant art, we proceed to consider whether Mr. Lyle possessed the qualifications to be an expert in this case. It is apparent that he had little familiarity with the design of weight-lifting machines prior to the present litigation. The record reveals that Mr. Lyle did not undertake, even in connection with this law suit, any extensive study of technical references with respect to body-exercising apparatus. Rather, his examination was confined to the elements of prior art selected by defendants' counsel, i. e., the Simmons patent and the Loprinzi photograph. As a result, it is doubtful whether he was suited to serve as an expert here.

Even assuming that the disciplines designated by the parties were the apposite ones, Mr. Lyle's standing as an expert in this litigation still may be called into question. He had no expertise whatsoever in weight training, as he repeatedly conceded during the course of his testimony.<ref>See, e. g., Appendix at 327, 394-95 (Trial Transcript at 458, 211, 632).</ref> It is also questionable whether Mr. Lyle possessed any skill or knowledge in the field of mechanical engineering. A recipient of a bachelor's degree in electrical engineering, he had served for seven years as an examiner in the United States Patent Office and for thirty-five years as a patent attorney for Westinghouse. Although he did handle patent matters relating to turbines, motors and generators, which have mechanical features, his patent work primarily pertained to electrical engineering. Experience may vest one with the qualifications of an expert,<ref>See, e. g., United States v. 60.14 Acres of Land, 362 F.2d 660, 667 (3d Cir. 1966).</ref> but Mr. Lyle had only a limited background even in the province of mechanical engineering.

However, since Mr. Lyle may possess skill and knowledge greater than the average layman with respect to mechanical apparatus, we cannot find that the district court clearly abused its discretion in recognizing him as an expert. Nevertheless, coupled with the arguable deficiencies in his qualifications as an expert witness, Mr. Lyle's limited experience with the class of devices present in this litigation should have substantially circumscribed the weight accorded his testimony. The trial court thus erred in attaching controlling weight to the opinions of defendants' expert.

B.

Universal also challenges the expert testimony of Mr. Lyle, because of the conflict between his association with defense counsel and his role as an expert witness. Over the objection of Universal, the district court permitted Mr. Lyle to testify as an expert.<ref>See Appendix at 273-79 (Trial Transcript at 376-382).</ref>

Ordinarily it is inappropriate for an attorney, or a lawyer in his firm, to testify on behalf of a client. Rules DR 5-101 and 102 of the Code of Professional Responsibility<ref>The Code of Professional Responsibility was promulgated by the American Bar Association in 1969, and it became effective in 1970. The Pennsylvania Supreme Court explicitly adopted the Code in 1974 for members of the Pennsylvania bar, among whose ranks are Mr. Lyle and defendants' attorneys. See Pennsylvania Rules of Court 1975, at 175-241. However, it is apparent that the Code was applicable in Pennsylvania prior to 1974. See In re Estate of Lohm, 440 Pa. 268, 278-79, 269 A.2d 451, 457 (1970); Rules of Court, 331 Pa. xxxvi (1938). By contrast, neither the District Court for the Western District of Pennsylvania, which tried the present case, nor this Court has expressly adopted the Code.</ref> provide that a lawyer shall refuse employment or withdraw as counsel if the “lawyer learns or it is obvious that he or a lawyer in his firm ought to be called as a witness on behalf of his client. . . .” Under such circumstances, the attorney, or his firm, must decide whether to serve either as advocate or as a witness in a particular case. Recognizing that “the role of an advocate and of a witness are inconsistent . . . ,”<ref>EC 5-9.</ref> the Code would appear to preclude the testimony of Mr. Lyle here. As the disciplinary rules logically apply to expert as well as lay witnesses, the law firm should have withdrawn once it decided that its associate would testify, or else the firm should have found another expert.<ref>The defendants contend that DR 5-101 and 102 do not reach the testimony of Mr. Lyle. An exception to these rules allows a lawyer-witness to continue the representation of his client: “As to any matter, if (withdrawal) would work a substantial hardship on the client because of the distinctive value of the lawyer or his firm as counsel in a particular case.” DR 5-101(B)(4). Defense counsel asserted at trial that this exception permitted the firm to continue its representation of the defendants, even if Mr. Lyle testified as an expert. The law firm contended, and the district court agreed, that withdrawal would cause “substantial hardship” for their clients, as the firm had spent great time and resources in preparing for the case.Because the action was tried below without a jury, the trial judge could have adjourned the proceedings, without prejudice to the parties or a waste of court resources, until defendants selected another expert or, if they still desired the testimony of Mr. Lyle, another law firm. There is nothing in the record which indicates that the law firm with which Mr. Lyle was associated has such distinctive value in this litigation as to call DR 5-101(B)(4) into play.Nevertheless, we do recognize that DR 5-101 and 102 are somewhat ambiguous as to whether these disciplinary rules apply literally to Mr. Lyle and his law firm. DR 5-101 and 102 require the withdrawal of an attorney from the conduct of a trial if he or another lawyer in the firm “ought ” to be called as a witness on behalf of his client. Such language suggests that these sections of the Code were concerned only with the lawyer-witness who has crucial information in his possession which must be divulged. Under this test, Mr. Lyle hardly may be characterized as a witness who “ought” to testify on behalf of his firm's client. Defense counsel could have called any number of other experts to the stand. There is no suggestion in the record, nor could there be, that Mr. Lyle alone possessed the expertise necessary to assist the trier of fact. Because the defendants' expert was not an indispensable witness, arguably his testimony at trial did not breach the mandate of the Code.</ref>

Even though the Code inveighs against the participation of a witness in a position comparable to that of Mr. Lyle, it does not necessarily follow that any alleged professional misconduct on his part would in itself render his testimony, once it was adduced, a nullity. This is so because the Code does not delineate rules of evidence but only sets forth strictures on attorney conduct. Moreover, it is well settled that a lawyer is competent to testify on behalf of his client.<ref>See, e. g., City Bank of Honolulu v. Rivera Davila, 438 F.2d 1367, 1369 (1st Cir. 1971); United States v. Harry Barfield Company, 359 F.2d 120, 124 (5th Cir. 1966); United Parts Mfg. Co. v. Lee Motor Products, Inc., 266 F.2d 20, 24 (6th Cir. 1959); Lau Ah Yew v. Dulles, 257 F.2d 744, 746 (9th Cir. 1958). While three of these cases were decided before the promulgation of the Code of Professional Responsibility, Canon 19 of the predecessor Canons of Ethics was roughly identical to DR 5-101 and 102. Consequently, the principles enunciated in the pre-Code cases would appear to retain vitality.Naturally, the statement in the text does not apply where the client invokes the attorney-client privilege, a long-standing rule of evidence. A client may refuse to disclose, and prevent his lawyer from disclosing, confidential communications between the attorney and his client. See 8 Wigmore on Evidence, ss 2290-2329. (McNaughton rev. 1961). Generally, invocation of the privilege results in the exclusion of the attorney's testimony. The attorney-client privilege even embraces a lawyer not presently in the employ of the client, so long as he was the client's lawyer at the time of the privileged communication. See Wigmore, supra, s 2323. In the case at bar, the attorney-client privilege obviously was not claimed, and so Mr. Lyle's testimony is not incompetent.</ref> Of course, such testimony may subject the attorney to separate disciplinary action. Thus, while we do not approve of the practice of an attorney testifying as an expert witness for a client of his law firm, certainly in the absence of some necessity for such testimony, we cannot say that the district court committed error solely by not extirpating that testimony. In so concluding, we are in accord with the courts of appeals in several other circuits.<ref>See cases cited in note 22 supra.It would be appropriate to consider incorporating within the body of evidentiary rules the current disciplinary norm proscribing the testimony of a lawyer for his client. The recently promulgated Federal Rules of Evidence, however, do not render such testimony incompetent. Nor is there any judicial precedent, insofar as we are aware, to support announcement of such a rule at this time.</ref>

In the case at hand, however, the district court did err when it relied so heavily, on the testimony of Mr. Lyle. In Lau Ah Yew v. Dulles,<ref>257 F.2d 744 (9th Cir. 1958).</ref> the Ninth Circuit, after criticizing the practice of an attorney testifying as a lay witness for his client, declared the testimony competent. But the court noted that the relationship of such a witness to his client detrimentally affected the weight to be accorded his testimony and therefore “discounted” its value.<ref>See id. at 746-47.</ref> Such an approach, which would appear to be equally applicable to attorneys who serve as experts for their clients, also reflects our view. We believe that, while a district court may in limited circumstances receive the testimony of a lawyer-witness, the value of such testimony must be discounted because of the interest of the lawyer or his firm in the outcome of the litigation.

Here, there is little indication that the district judge, as the sole trier of fact, scrutinized the expert testimony of Mr. Lyle with the proper circumspection.<ref>When he refused to disqualify Mr. Lyle as an expert witness, the trial judge did state: “We will permit the witness to testify, but as to what effect this has upon his credibility, that will be up to the court . . . .” Appendix at 278-79 (Trial Transcript at 381-82). Nevertheless, there is no subsequent suggestion in the record that the district court evaluated Mr. Lyle's testimony with the requisite special care.</ref> It is one thing for a trial court to give the testimony of an interested witness some weight in reaching a decision. But it is quite another to permit the presumption of patent validity to be rebutted by primary reliance on the testimony of that witness. Even if, in the context of this case, it was not error to permit Mr. Lyle to testify, we conclude that the district court erred when it placed controlling weight, as to patent validity, on the opinions of a lawyer associated with defense counsel.<ref>In so holding, we express doubt that the heavy presumption of patent validity can be overcome by the testimony of an attorney on behalf of his client. For a discussion of the presumption, see Part III infra.</ref>

III.

Because the district court gave undue weight to the testimony of Mr. Lyle, we must consider whether the remaining evidence in the record is sufficient to sustain the ruling that the patent claims are invalid.

It is a fundamental canon governing judicial consideration in this field that a presumption of validity attaches to patents issued by the United States Patent Office.<ref>35 U.S.C. s 282 provides, in pertinent part: “A patent shall be presumed valid. . . . The burden of establishing invalidity of a patent or any claim thereof shall rest on the party asserting it.”Where the Patent Office specifically has considered references of prior art invoked by a defendant to invalidate a patent, the presumption of validity often is further reinforced. See, e. g., Ellipse Corp. v. Ford Motor Co., 452 F.2d 163, 170 n.6 (7th Cir. 1971), cert. denied, 406 U.S. 948, 92 S.Ct. 2041, 32 L.Ed.2d 337 (1972); Woodstream Corporation v. Herter's, Inc., 446 F.2d 1143, 1156 (8th Cir. 1971); Tapco Products Co. v. Van Mark Products Corp., 446 F.2d 420, 426 (6th Cir.), cert. denied, 404 U.S. 986, 92 S.Ct. 451, 30 L.Ed.2d 370 (1971); cf. Philips Electronic and Pharmaceutical Industries Corp. v. Thermal and Electronics Industries, Inc., 450 F.2d 1164 (3d Cir. 1971). In this case, the Patent Office specifically considered the Simmons patent, as Mr. Lyle noted in his testimony. See Appendix at 368 (Trial Transcript at 564). The defendants' expert also stated that the examiner had made a “good search.” The precision exhibited by the Patent Office strengthens the presumption of validity accorded the Zinkin claims.</ref> Not only has a unanimous Supreme Court noted that “patentees are heavily favored as a class of litigants by the patent statute,”<ref>Blonder-Tongue Laboratories v. University of Illinois Foundation, 402 U.S. 313, 335, 91 S.Ct. 1434, 1446, 28 L.Ed.2d 788 (1971).</ref> but this court has stated on several occasions that the burden of proving patent invalidity is a heavy one.<ref>E. g., Trio Process Corporation v. L. Goldstein's Sons, Inc., 461 F.2d 66, 70 (3d Cir.), cert. denied 409 U.S. 997, 93 S.Ct. 319, 34 L.Ed.2d 262 (1972); Eagle Iron Works v. McLanahan Corporation, 429 F.2d 1375, 1382 (3d Cir. 1970); Schmidinger v. Welsh, 383 F.2d 455, 462 n.10 (3d Cir. 1967), cert. denied, 390 U.S. 946, 88 S.Ct. 1031, 19 L.Ed.2d 1134 (1968).</ref> Moreover, such invalidity must be demonstrated by “clear and convincing proof.”<ref>Trio Process Corporation v. L. Goldstein's Sons, Inc., 461 F.2d 66, 70 (3d Cir. 1972). Cf. Woodstream Corporation v. Herter's Inc., 446 F.2d 1143, 1149 n.4 (8 Cir. 1971).</ref> In the case at bar, the evidence as to invalidity, once the testimony of Mr. Lyle is discounted, consists of only two items the Simmons patent and the magazine photograph of Loprinzi's “super-duper pressing apparatus.” This evidence in itself is not adequate to rebut the presumptive validity of the Zinkin patent, or to sustain the lower court's rulings as to obviousness and anticipation.

A.

We now turn to the ruling of the district court on the issue of obviousness. Although the trial judge invoked the proper authorities and standards in his consideration of this question, we believe that he erred in applying them to the Zinkin claims.

Inasmuch as this Court has adumbrated the precepts of obviousness on previous occasions,<ref>See, e. g., Trio Process Corporation v. L. Goldstein's Sons, Inc., 461 F.2d 66, 70-73 (3d Cir. 1972); Philips Electronic and Pharmaceutical Industries Corp. v. Thermal and Electronics Industries, Inc., 450 F.2d 1164, 1172-75 (3d Cir. 1971); Eagle Iron Works v. McLanahan Corporation, 429 F.2d 1375, 1377-79 (3d Cir. 1970).</ref> we need not do so here. Instead, we enunciate only the analytical framework necessary for this case. Simply stated, a patent may be deemed invalid if it is “obvious.” 35 U.S.C. s 103 provides, in part: “A patent may not be obtained . . . if the differences between the subject matter sought to be patented and the prior art are such that the subject matter as a whole would have been obvious at the time the invention was made to a person having ordinary skill in the art to which the subject matter pertains.”

As observed in Trio Process Corporation v. L. Goldstein's Sons, Inc.,<ref>461 F.2d at 70.</ref> the most authoritative construction of section 103 appears in Graham v. John Deere Co.<ref>383 U.S. 1, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966). See also United States v. Adams, 383 U.S. 39, 86 S.Ct. 708, 15 L.Ed.2d 572 (1966).</ref> There the Supreme Court established three mandatory criteria with which to frame judicial determinations as to obviousness: “The scope and content of the prior art . . .; differences between prior art and the claims at issue . . .; and the level of ordinary skill in the pertinent art . . . .”<ref>383 U.S. at 17, 86 S.Ct. at 694. Subsequently, the Supreme Court, in referring to these tests, “admonished that ‘strict observance’ of those requirements is necessary.” Anderson's Black Rock, Inc. v. Pavement Salvage Co., 396 U.S. 57, 62, 90 S.Ct. 305, 308, 24 L.Ed.2d 258 (1969).</ref> The Supreme Court also set forth several permissive, or “secondary,” considerations: “commercial success, long felt but unsolved needs, failure of others, etc., might be utilized to give light to the circumstances surrounding the origin of the subject matter sought to be patented.”<ref>383 U.S. at 17-18, 86 S.Ct. at 694.</ref> This past term the Supreme Court continued to apply these criteria, thereby indicating the enduring vitality of Graham.<ref>See Sakraida v. Ag Pro, Inc., 425 U.S. 273, 96 S.Ct. 1532, 47 L.Ed.2d 784 (1976); Dann v. Johnston, 425 U.S. 219, 96 S.Ct. 1393, 47 L.Ed.2d 692 (1976).</ref> While the district court, in the present case, specifically considered the three mandatory tests, it erred in its evaluations under these requirements, largely because of the dearth of evidence submitted by the defendants.

In analyzing the “scope and content” of the prior art, the trial judge indicated that the only relevant references offered by the defendants were the Simmons patent and the Loprinzi photograph. He properly disregarded exercising machines designed subsequent to the Zinkin patent. Although his opinion does not explicitly discuss the scope of the prior art, the fact that there were only two references suggests that the prior art is quite limited.

The trial judge did attempt to examine the content of the Simmons patent and the Loprinzi photograph. It is evident that he relied considerably upon the testimony of Mr. Lyle in analyzing the latter. As Mr. Lyle's testimony must be discounted, the district court would be hard pressed to evaluate the photograph. Even with Mr. Lyle's assistance, the trial judge appeared to be troubled about the features of the Loprinzi device. Indeed, his opinion reflects uncertainty concerning that apparatus.<ref>See 397 F.Supp. at 1069. The trial judge, in discussing the Loprinzi apparatus, stated: “From looking at the picture, it is not clear in what direction the levers can be moved, but the caption ‘super-duper pressing apparatus' would clearly indicate to one familiar with weight-training that the movement is vertical. It also appears that each lever moved independently of the other, but that, too, is not certain from the picture and caption.”</ref> While the Simmons patent may have been more easily examined, since the defendants did produce detailed patent specifications relating to it, there were unanswered questions regarding its content as well. For example, it is unclear whether the described apparatus could be used for the chest-press exercise. In the absence of expert testimony, other than that of Mr. Lyle, the trial judge could not properly appraise the prior art, narrow in scope as it was. Although there may be instances where a trial court may be able to review prior art references without expert assistance, the devices in this litigation do not lend themselves to such evaluation.<ref>Ordinarily, the trial judge decides whether he needs expert assistance to understand or evaluate a reference relied on as prior art. Experts are not absolutely required, and a district court may disregard the testimony of experts if that testimony appears unreasonable. See Deller's Walker on Patents s 231 (2d ed. 1965) and cases cited therein. Nevertheless, in cases involving complicated inventions, the better rule is that the judge should rely on expert testimony. In Nyyssonen v. Bendix, 342 F.2d 531 (1st Cir. 1965), for example, the First Circuit stated: “a patent speaks to its art and what it says can be told in complicated cases like this only by one skilled in the art.” Id. at 537. Not only are the devices in this litigation somewhat intricate, but the evidence pertaining to them is unclear. We believe that the trial judge should have required the testimony of one skilled in the design of weight-lifting machines before invalidating the Zinkin claims. Even if defendants had produced such an expert, it still is questionable whether the factual proof submitted in this case was sufficient to void the patent.</ref>

The district court also found that the differences between the prior art and the claims at issue were such that the invention is obvious. Nevertheless, because the defendants did not convincingly demonstrate the content of the prior art, we believe that it would be difficult for any court to evaluate differences between that prior art and the challenged claims. Even if it would be possible to do so, there is little evidence to support the conclusion that any variances between defendants' references and the Zinkin claims are “insignificant.”

We recognize that there may be some important differences between the prior art and the Zinkin claims. It is questionable, for example, whether either the Simmons patent or the Loprinzi apparatus obviates the spotter requirement of the chest-press exercise, as does the Zinkin device. The caption of the Loprinzi photograph depicts Sam Loprinzi “coaching a pupil in the use of (the) super-duper pressing apparatus.” Arguably, Mr. Loprinzi is acting as a spotter as well as a coach in the picture, just as Harold Zinkin performed both roles in his gymnasium before designing his machine. Moreover, it is unclear whether the Simmons and Loprinzi devices circumvent, as does the Zinkin apparatus, the safety hazards posed by the chest press. Technically, there are various differences in design between the prior art and the challenged claims, involving, inter alia, the types of handles, the “stops,” the requirement of a single bar and the positioning of numerous elements. While there is some doubt whether the variances between the Zinkin claims and the references are so substantial as to defeat the allegation of obviousness, we conclude that the evidence is insufficient to sustain the conclusion of the trial judge that all differences were such as to render the patented device obvious.

With respect to the third mandatory criteria under Graham, that is, the level of ordinary skill in the pertinent art, the district court acknowledged that “The record on this point is somewhat deficient.”<ref>397 F.Supp. at 1070.</ref> Even so, the trial judge declared that “any competent mechanical engineer . . . could readily create a machine substantially the same as that of plaintiffs.”<ref>Id.</ref> As discussed above, we believe that the pertinent art is neither mechanical engineering nor weight-lifting, but rather the design of body-exercising apparatus. Not only did the district court fail to select the proper art, but it is questionable whether the evidence submitted by the defendants speaks to the level of ordinary skill in the design of weight-lifting devices.

Assuming that mechanical engineering is the relevant art, we are skeptical whether Mr. Lyle, upon whose testimony the district court substantially relied, could provide meaningful opinions thereon, given his inexperience in mechanical engineering. The trial judge suggested that the record as to the level of ordinary skill in the pertinent art was “deficient.” Having so indicated, he should have refused to invalidate the challenged patent claims as obvious.

This Court need not consider the permissive, or secondary, criteria mandated in Graham for determinations of obviousness. For we are convinced that the defendants failed to provide adequate evidence to justify invalidation of the Zinkin claims under section 103. Even if the permissive tests were applied, the commercial success of the Zinkin machine<ref>397 F.Supp. at 1066. While the district court expressly recognized the commercial success of the Zinkin chest press machine, it did not utilize this fact in its analysis of obviousness.</ref> would reinforce our conclusion, as would the “failure of others” to eliminate the safety hazards and manpower requirements of the traditional chest press exercise.<ref>See note 4 supra.</ref> Thus, we cannot say that the Zinkin claims are so obvious as to render them invalid.<ref>Such a holding is not at all inconsistent with Philips Electronic and Pharmaceutical Industries Corp. v. Thermal and Electronics Industries, Inc., 450 F.2d 1164 (1971). There this Court declared that a trial judge's findings as to the Graham criteria are to be evaluated under the “clearly erroneous” standard of Fed.R.Civ.Pro. 52(a). In the case at bar, the requisite findings would appear to be clearly erroneous, as there is insufficient evidence to support them. Thus the district court's conclusion as to invalidity cannot stand.</ref>

B.

Besides holding the Zinkin claims void for obviousness, the district court concluded that they were anticipated by prior art. 35 U.S.C. s 102 provides, in pertinent part: “A person shall be entitled to a patent unless (a) the invention was . . . patented or described in a printed publication in this or a foreign country, before the invention thereof by the applicant for patent. . . .” The defendants had contended, and the trial judge agreed, that both the Simmons patent and the Loprinzi photograph anticipated the Zinkin claims so as to render them nugatory under the statute. Since there is insufficient evidence to rebut the heavy presumption of patent validity, we do not sustain this conclusion of the district court.

In construing section 102, the trial judge apparently viewed the Loprinzi photograph as a “printed publication” which described the Zinkin invention. While neither this Court nor apparently any other tribunal has yet determined whether a photograph in itself constitutes a “printed publication,” we believe that a photograph may so qualify for purposes of section 102.<ref>Several courts have held that a drawing unaccompanied by verbal description may constitute a printed publication within the meaning of section 102. See, e. g., Des Rosiers v. Ford Motor Co., 143 F.2d 907, 911-12 (1st Cir. 1944); In re Bager, 47 F.2d 951, 953 (C.C.P.A.1931). A photograph may disclose an invention as well as, if not better than a drawing and, consequently, is a “printed publication” for purposes of the statute.</ref> In so stating, we reaffirm our pragmatic pronouncement in Philips Electronic and Pharmaceutical Industries Corp. v. Thermal and Electronics Industries, Inc.,<ref>450 F.2d 1164 (3d Cir. 1971).</ref> that “to restrict our interpretation of Section 102(a)‘s ‘printed’ publication requirement solely to the traditional printing press would ignore the realities of the scientific and technological period in which we live . . . .”<ref>Id. at 1170.</ref> With a photograph, one conversant in a pertinent art could make or construct a purported invention without resorting either to the patent or to his own inventive skills. Under certain circumstances, then, a photograph may so anticipate a patent as to render it invalid.

The question remains, however, whether the photograph of Loprinzi's device anticipated those claims of the Zinkin patent that the defendants challenge. We hold that it does not. In Philips we specified the circumstances under which a prior publication could anticipate a patent: “For a prior publication to be sufficient to defeat a patent it must exhibit a substantial representation of the invention in such full, clear, and exact terms that one skilled in the art may make, construct and practice the invention without having to depend on either the patent or on his own inventive skills.”<ref>Id. at 1169. For similar statements of the “anticipation” standard, see Eames v. Andrews, 122 U.S. 40, 66, 7 S.Ct. 1073, 30 L.Ed. 1064 (1886); Seymour v. Osborne, 78 U.S. (11 Wall.) 516, 555, 20 L.Ed. 33 (1870); Rich Products Corporation v. Mitchell Foods, 357 F.2d 176, 180 (2d Cir.), cert. denied 385 U.S. 821, 87 S.Ct. 46, 17 L.Ed.2d 58 (1966); Application of LeGrice, 301 F.2d 929, 936, 49 CCPA 1124 (1962); Deller's Walker on Patents s 60 (2d ed. 1964).</ref>

In the discussion of obviousness in Part III-A, we commented that it would be difficult, if not impossible, to discern the content of the Loprinzi photograph. That observation is applicable here, for it would not be possible for a trial court to ascertain whether the photograph anticipates the Zinkin invention. The photographic representation of the Loprinzi “super-duper pressing apparatus” hardly is “full, clear, and exact.” It is questionable whether one skilled in the design of weight-lifting apparatus could produce the Zinkin device, based on an examination of the Loprinzi photograph. Accordingly, we believe that the magazine photograph is insufficient to render the patent invalid on the ground of anticipation.

Nor can we hold that the Simmons patent anticipated the Zinkin weight-lifting machine. It is unclear whether the Simmons invention encompasses all or substantially all of the elements of the apparatus under scrutiny in this case. The evidence submitted does not reveal whether one skilled in the design of body-exercising devices, or even in mechanical engineering, could develop the Zinkin weight-lifting apparatus based on the Simmons patent or on his own skills. We conclude, therefore, that the defendants in the present case have failed to demonstrate invalidity of the challenged claims under section 102.

IV.

While the validity of the Zinkin patent is not completely free from doubt, we do not accept the decision reached by the district court. The district court erred in according substantial weight to the testimony of Mr. Lyle. Without such unjustified reliance on that testimony, the trial judge could not properly interpret the prior art. Because the evidence produced by the defendants simply is not sufficient to rebut the presumption of validity accorded patents, we must reverse the rulings of the district court as to obviousness and anticipation, and sustain claims numbered 3 and 4 of the Zinkin patent.

The judgment of the district court will be vacated and the cause remanded for proceedings consistent with this opinion.

C.A.Pa. 1976.
Universal Athletic Sales Co. v. American Gym, Recreational & Athletic Equipment Corp., Inc.
546 F.2d 530, 192 U.S.P.Q. 193

===FOOTNOTEs===
<references/>

AME 40590 Intellectual Property for Engineers

2015-04-02T19:51:46Z

Bill: /* ALPHABETICAL LISTING OF CASES */

Cases to add:
* Damages:
** MINTZ V. DIETZ & WATSON, INC. (CAFC, May 2012)
** Monsanto Co. v. McFarling, 488 F.3d 973, 978-79 (Fed. Cir. 2007)
** Georgia-Pacific Corp. v. US Plywood Corp., 318 F. Supp. 1116 (SDNY 1970), modified, 446 F. 2d 295 (2d Cir. 1971)
** The Boeing Company v. The United States, 86 Fed. Cl. 303 (April 2, 2009)
** Mahurkar v. CR Bard, Inc. 79 F. 3d 1572, 1580 (Fed. Cir. 1996), adopting Panduit Corp. v. Stahlin Bros. Fibre Works, Inc.,575 F.2d 1152 (6th Cir. 1978)
** Depuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 567 F.3d 1314 (Fed. Cir. 2009)

* Software patents:
** In re Alappat, 33 F.3d 1526, 1545 (Fed. Cir. 1994).
** CyberSource Corporation v. Retail Decisions, Inc., Slip Op. at 19 (2011)
** Ultramercial, LLC v. Hulu, LLC (Fed. Cir. 2011)

=ALPHABETICAL LISTING OF CASES=

*[[A. & P. Tea Co. v. Supermarket Corp., 340 U.S. 147 (1950)]]
*[[Abbott Laboratories v. Geneva Pharmaceuticals, Inc., 182 F.3d 1315 (1999)]]
*[[Alza Corp. v. Mylan Laboratories, 464 F.3d 1286, (2006)]]
*[[Anderson's Black Rock, Inc. v. Pavement Co., 396 U.S. 57 (1969)]]
*[[Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336 (1961)]]
*[[Arrhythmia Research Technology, Inc. v. Corazonix Corp., 958 F.2d 1053 (1992)]]
*[[Asgrow Seed Co. v. Winterboer, 513 U.S. 179 (1994)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. (2013)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. CAFC (2012)]]
*[[Atlas Powder v. E.I. du Pont de Nemours, 750 F2d 1569 (1984)]]
*[[Bilski v. Kappos, 130 S.Ct. 3218 (2010)]]
*[[Bobbs-Merrill Co. v. Straus, 210 U.S. 339 (1908)]]
*[[Bonito Boats. v. Thunder Craft, 489 U.S. 141 (1989)]]
*[[Bowman v. Monsanto, 133 S.Ct. 1761 (2013)]]
*[[CCS Fitness, Inc. v. Brunswick Corporation, 288 F.3d 1359 (2002)]]
*[[Chester v. Miller, 906 F.2d 1574 (1990)]]
*[[D.L. Auld Co. v. Chroma Graphics Corp., 714 F.2d 1144 (1983)]]
*[[Diamond v. Chakrabarty, 100 S.Ct. 2204 (1980)]]
*[[Diamond v. Diehr, 450 U.S. 175 (1981)]]
*[[Egbert v. Lippmann, 104 U.S. 333 (1881)]]
*[[Electric Storage Battery Co. v. Shimadzu, 307 U.S. 5 (1939)]]
*[[Elizabeth v. American Nicholson Pavement Company, 97 U.S. 126 (1877)]]
*[[Filmtec Corp. v. Allied-Signal Inc., 939 F.2d 1568 (1991)]]
*[[Funk Bros. Seed Co. v. Kalo Inoculant Co. 333 U.S. 127 (1948)]]
*[[Gottschalk v. Benson, 409 U.S. 63 (1972)]]
*[[Gould v. Hellwarth, 472 F2d 1383 (1973)]]
*[[Graham v. John Deere, 383 U.S. 1 (1966)]]
*[[Graver Tank & Mfg. Co. v. Linde Air Products Co. 339 US 605 (1950)]]
*[[H.H. Robertson, Co. v. United Steel Deck, Inc., 820 F.2d 384 (1987)]]
*[[Hotchkiss v. Greenwood, 52 U.S. 11 (1850) ]]
*[[Hybritech v. Monoclonal Antiboties, 802 F.2d 1375 (1986)]]
*[[i4i Ltd. Partnership v. Microsoft Corp., 598 F.3d 831 (2010)]]
*[[In Re Bilski]]
**[[In Re Bilski, Dky concurring opinion]]
**[[In Re Bilski, Newman dissenting opinion]]
**[[In Re Bilski, Mayer dissenting opinion]]
**[[In Re Bilski, Rader dissenting opinion]]
*[[In re Brana, 51 F.3d 1560 (1995)]]
*[[In re Carlson, 983 F.2d 1032 (1992)]]
*[[In re Hall, 781 F.2d 897 (1986)]]
*[[In re Kahn, CAFC 04-1616 (2006)]]
*[[In Re Rouffet, 149 F.3d 1350 (1998)]]
*[[J.E.M. Ag Supply, Inc. v. Pioneer Hi-Bred International, Inc., 534 U.S. 124 (2001)]]
*[[Juicy Whip v. Orange Bang, 185 F.3d 1364 (1999)]]
*[[KSR International Co. v. Teleflex, Inc., 550 U.S. 398 (2007)]]
*[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]
*[[Lorenz v. Colgate-Palmolive-Peet Co., 167 F.2d 423 (1948)]]
*[[Lough v. Brunswick Corp., 86 F.3d 1113 (1996)]]
*[[Lyon v. Bausch & Lomb, 224 F.2d 530 (1955)]]
*[[Metabolit Laboratories, Inc. and Competitive Technologies, Inc. v. Laboratory Corporation of America Holdings, 370 F.3d 1354 (2004)]]
*[[Metallizing Engineering Co., Inc. v. Kenyon Bearing & Auto Parts Co., Inc., 153 F.2d 516 (1946)]]
*[[Microsoft Corp v. At&T Corp., 550 U.S. 437 (2007)]]
*[[Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (1978)]]
*[[Perkin-Elmer Corporation v. Computervision Corporation, 732 F2d 888 (1984)]]
*[[Pfaff vs. Wells Electronics, 525 U.S. 55 (1998)]]
*[[Philips Electric Co. v. Thermal Industries, Inc., 450 F.2d 1164 (1971)]]
*[[Quanta Computer, Inc. v. LG Electronics, Inc., 553 U.S. 617 (2008)]]
*[[Reiner v. I. Leon Co., 285 F.2d 501 (1960)]]
*[[South Corp. v. US 690 F.2d 1368 (1982)]]
*[[State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (1998)]]
*[[Traffix Devices, Inc. vs. Marketing Displays, Inc., 532 U.S. 23 (2001)]]
*[[TurboCare Div. of Demag Delaval Turbomachinery Corp. v. General Elec. Co., 264 F.3d 1111 (2001)]]
*[[UMC Electronics Co. v. U.S., 816 F.2d 647 (1987)]]
*[[US v. Adams, 383 U.S. 39 (1966)]]
*[[U.S. v. Univis Lens Co., 316 U.S. 241 (1942)]]
*[[Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530]]
*[[Vas-Cath Inc. v. Mahurkar, 935 F.2d 1555 (1991)]]
*[[Warner-Jenkinson Company v. Hilton Davis Chemical Co., 520 US 17 (1997)]]
**[[Warner-Jenkinson v. Hilton Davis Petitioner Brief]]
**[[Warner-Jenkinson v. Hilton Davis Respondent Brief]]
*[[Winner International Royalty Co. v. Wang, 202 F.3d 1340 (2000)]]
*[[W.L. Gore & Associates, Inc. v. Garlock, Inc., 721 F.2d 1540 (1983)]]

=[[INTRODUCTION]]=
This is a summary. Click on the title for the full chapter: [[INTRODUCTION]]

Outline:
*The main purpose for obtaining a patent is ''economic''.
*It grants the exclusive right to ''make, use or sell'' the invention for a limited period of time.
*The governing law is Title 35 of the United States Code (35 USC).
*The governing regulations are from Title 37 of the Code of Federal Regulations (37 CFR).
*The law is federal, so patent cases are resolved in the federal court system:
**district courts;
**circuit courts;
**the Court of Appeals for the Federal Circuit (CAFC), a special appeals court for patent cases; and,
**the Supreme Court.
*The US Patent and Trademark Office (PTO) processes patent applications.
*Patents last for 20 years from the date the application is filed with the PTO.
*Patents have the attributes of personal property.
*The foundation of the federal government's authority to create a patent system is in the Constitution. The purposes is explicitly economic, "to promote the progress of science and useful arts..."
*Other forms of intellectual property
**copyright;
**trademarks; and,
**trade secrets.

=[[NONOBVIOUSNESS]]=
This is a summary. Click on the title for the full chapter: [[NONOBVIOUSNESS]]

Outline:

*This is perhaps the most difficult factual patent issue. In addition to meeting the novelty requirements of 35 USC 102, 35 USC 103 requires that the claimed invention as a whole must have been nonobvious "at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains."
*There is a lot of historical confusion regarding this standard. Basically, it is a notion of something being meeting some type of sufficient inventive standard or nontriviality.
*To determine this, there are three fundamental lines of inquiry:
**the scope and content of the prior art;
**the differences between the prior art and claims at issue; and,
**the level of ordinary skill in the art.
*Secondary considerations include:
**a long-felt but unsatisfied need met by the invention;
**appreciation by those versed in the art that the need existed;
**substantial attempts to meet this need;
**commercial success of the invention;
**replacement in the industry by the claimed invention;
**acquiescence by the industry;
**''teaching away'' by those skilled in the art;
**unexpectedness of the results; and,
**disbelief or incredulity on the part of industry with respect to the new invention.

=[[INFRINGEMENT]]=
This is a summary. Click on the title for the full chapter: [[INFRINGEMENT]]

=[[THE PATENT DOCUMENT]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT DOCUMENT]]

Outline:
*A patent has several parts:
**specification: describes the invention;
**claims: delineates the ownership rights;
**drawings: not required, but if they are included then any element included in the claims must be shown in the drawings; and,
**other miscellaneous parts.
*Interpreting claims: claims are said to ''read on'' another device.
*The doctrine of equivalence, prevents something from being patented that only has minor alterations from the prior art.
*The date of the invention
**''reduction to practice'';
**''diligence'' requirement.
*The ''file wrapper''.

=[[NOVELTY]]=
This is a summary. Click on the title for the full chapter: [[NOVELTY]]

Outline:
*Specified in 35 USC 102.
*Fundamentally: an invention must be ''new''.
*Section 102 basically defines in a technical way what it means to not be new:
**Events prior to invention
***known or used by others in the US
***patented or in a printed publication in another country
**Events one year before filing the patent application
***patented or in a printed publication anywhere (''in this or a foreign country'')
***in public use or on sale in the US
**Other bars
*The applicant must be the inventor (not the employer)

Outline:
*Literal Infringement
*The Doctrine of Equivalents

=[[UTILITY]]=
This is a summary. Click on the title for the full chapter: [[UTILITY]]

=[[PATENTABLE SUBJECT MATTER]]=
This is a summary. Click on the title for the full chapter: [[PATENTABLE SUBJECT MATTER]]

Can computer programs, algorithms, laws of nature, life forms, plants, ''etc.'' be patented. In particular, are the following patentable:

* Plants
* Algorithms and Computer Programs
* Scientific Facts?

In a recent case
* State Street (1998)
the CAFC substantially broadened the subject matter of section 101 to include such things as methods of doing business, etc.

=[[FOREIGN AND DOMESTIC PRIORITY]]=
This is a summary. Click on the title for the full chapter: [[FOREIGN AND DOMESTIC PRIORITY]]

Outline:
*Priority in general
*Foreign priority
*International applications
*Domestic priority
*Provisional applications

=[[THE PATENT APPLICATION]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT APPLICATION]]

Outline:
*The Disclosure
*The Claims
*Other Sections
*New Matter
*The Examination Process

=[[INVENTOR ELIGIBILITY]]=
This is a summary. Click on the title for the full chapter: [[INVENTOR ELIGIBILITY]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972): full text]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981): (full text)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005): (full text)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]

[[METABOLITE LABORATORIES, INC. and Competitive Technologies, Inc. v. LABORATORY CORPORATION OF AMERICA HOLDINGS (doing business as LabCorp): the CAFC case (full text)]]

=[[ANTICIPATION]]=
This is a summary. Click on the title for the full chapter: [[ANTICIPATION]]

=[[PRIOR ART]]=
This is a summary. Click on the title for the full chapter: [[PRIOR ART]]

[[Pfaff v. Wells Electronics: full text]]

[[Perkin-Elmer Corporation v. Computervision Corporation (full text)]]

[[Perkin-Elmer Corporation v. Computervision Corporation]]

Talk:Traffix Devices, Inc. vs. Marketing Displays, Inc.

2015-04-02T19:51:28Z

Bill: Bill moved page Talk:Traffix Devices, Inc. vs. Marketing Displays, Inc. to Talk:Traffix Devices, Inc. vs. Marketing Displays, Inc., 532 U.S. 23 (2001)

#REDIRECT [[Talk:Traffix Devices, Inc. vs. Marketing Displays, Inc., 532 U.S. 23 (2001)]]

Talk:Traffix Devices, Inc. vs. Marketing Displays, Inc., 532 U.S. 23 (2001)

2015-04-02T19:51:28Z

Bill: Bill moved page Talk:Traffix Devices, Inc. vs. Marketing Displays, Inc. to Talk:Traffix Devices, Inc. vs. Marketing Displays, Inc., 532 U.S. 23 (2001)

Manufacturer of “WindMaster” outdoor sign stands brought trademark and trade dress infringement action against competitor that used “WindBuster” mark for its traffic sign stands. The United States District Court for the Eastern District of Michigan, 967 F.Supp. 953, enjoined competitor's use of infringing trademark and dismissed counterclaim, but, 971 F.Supp. 262, granted summary judgment for competitor on trade dress claim. Competitor appealed, and manufacturer cross-appealed. The Court of Appeals for the Sixth Circuit, 200 F.3d 929, affirmed in part, reversed in part, and remanded. Competitor petitioned for certiorari which was granted. The Supreme Court, Justice Kennedy, held that existence of expired utility patents claiming dual-spring design mechanism for keeping outdoor signs upright in adverse wind conditions created strong evidentiary inference of design's functionality, and failure of manufacturer to overcome that inference by showing that design was merely ornamental, incidental, or arbitrary precluded trade dress protection for the design.

The design or packaging of a product may acquire a distinctiveness which serves to identify the product with its manufacturer or source; and a design or package which acquires this secondary meaning, assuming other requisites are met, is a“ trade dress” which may not be used by a competitor in a manner likely to cause confusion as to the origin, sponsorship, or approval of the goods.
Held: Because MDI's dual-spring design is a functional feature for which there is no trade dress protection, MDI's claim is barred. Pp. 1259-1263.

Trade dress protection must subsist with the recognition that in many instances there is no prohibition against copying goods and products. In general, unless an intellectual property right such as a patent or copyright protects an item, it will be subject to copying. As the Court has explained, copying is not always discouraged or disfavored by the laws which preserve our competitive economy. Bonito Boats, Inc. v. Thunder Craft Boats, Inc., 489 U.S. 141, 160, 109 S.Ct. 971, 103 L.Ed.2d 118 (1989). Allowing competitors to copy will have salutary effects in many instances. “Reverse engineering of chemical and mechanical articles in the public domain often leads to significant advances in technology.” Ibid.
Because the dual-spring design is functional, it is unnecessary for competitors to explore designs to hide the springs, say, by using a box or framework to cover them, as suggested by the Court of Appeals. Ibid. The dual-spring design assures the user the device will work. If buyers are assured the product serves its purpose by seeing the operative mechanism that in itself serves an important market need. It would be at cross-purposes to those objectives, and something of a paradox, were we to require the manufacturer to conceal the very item the user seeks.

In a case where a manufacturer seeks to protect arbitrary, incidental, or ornamental aspects of features of a product found in the patent claims, such as arbitrary curves in the legs or an ornamental pattern painted on the springs, a different result might obtain. There the manufacturer could perhaps prove that those aspects do not serve a purpose within the terms of the utility patent. The inquiry into whether such features, asserted to be trade dress, are functional by reason of their inclusion in the claims of an expired utility patent could be aided by going beyond the claims and examining the patent and its prosecution history to see if the feature in question is shown as a useful part of the invention. No such claim is made here, however. MDI in essence seeks protection for the dual-spring design alone. The asserted trade dress consists simply of the dual-spring design, four legs, a base, an upright, and a sign. MDI has pointed to nothing arbitrary about the components of its device or the way they are assembled. The Lanham Act does not exist to reward manufacturers for their innovation in creating a particular device; that is the purpose of the patent law and its period of exclusivity. The Lanham Act, furthermore, does not protect trade dress in a functional design simply *35 because an investment has been made to encourage the public to associate a particular functional**1263 feature with a single manufacturer or seller. The Court of Appeals erred in viewing MDI as possessing the right to exclude competitors from using a design identical to MDI's and to require those competitors to adopt a different design simply to avoid copying it. MDI cannot gain the exclusive right to produce sign stands using the dual-spring design by asserting that consumers associate it with the look of the invention itself. Whether a utility patent has expired or there has been no utility patent at all, a product design which has a particular appearance may be functional because it is “essential to the use or purpose of the article” or “affects the cost or quality of the article.” Inwood, 456 U.S., at 850, n. 10, 102 S.Ct. 2182.

Traffix Devices, Inc. vs. Marketing Displays, Inc.

2015-04-02T19:51:28Z

Bill: Bill moved page Traffix Devices, Inc. vs. Marketing Displays, Inc. to Traffix Devices, Inc. vs. Marketing Displays, Inc., 532 U.S. 23 (2001)

#REDIRECT [[Traffix Devices, Inc. vs. Marketing Displays, Inc., 532 U.S. 23 (2001)]]

Traffix Devices, Inc. vs. Marketing Displays, Inc., 532 U.S. 23 (2001)

2015-04-02T19:51:28Z

Bill: Bill moved page Traffix Devices, Inc. vs. Marketing Displays, Inc. to Traffix Devices, Inc. vs. Marketing Displays, Inc., 532 U.S. 23 (2001)

Supreme Court of the United States
TRAFFIX DEVICES, INC., Petitioner,
v.
MARKETING DISPLAYS, INC.

No. 99-1571.
Argued Nov. 29, 2000.
Decided March 20, 2001.
200 F.3d 929, reversed and remanded.

KENNEDY, J., delivered the opinion for a unanimous Court.

John G. Roberts, Washington, DC, for petitioner.

Lawrence G. Wallace, Washington, DC, for United States as amicus curiae, by special leave of the Court.

John A. Artz, Southfield, MI, for respondent.

Justice KENNEDY delivered the opinion of the Court.

Temporary road signs with warnings like “Road Work Ahead” or “Left Shoulder Closed” must withstand strong gusts of wind. An inventor named Robert Sarkisian obtained two utility patents for a mechanism built upon two springs (the dual-spring design) to keep these and other outdoor signs upright despite adverse wind conditions. The holder of the now-expired Sarkisian patents, respondent Marketing Displays, Inc. (MDI), established a successful business in the manufacture and sale of sign stands incorporating the patented feature. MDI's stands for road signs were recognizable to buyers and users (it says) because the dual-spring design was visible near the base of the sign.

This litigation followed after the patents expired and a competitor, TrafFix Devices, Inc., sold sign stands with a visible spring mechanism that looked like MDI's. MDI and TrafFix products looked alike because they were. When TrafFix started in business, it sent an MDI product abroad to have it reverse engineered, that is to say copied. Complicating matters, TrafFix marketed its sign stands under a name similar to MDI's. MDI used the name “WindMaster,” while TrafFix, its new competitor, used “WindBuster.”

MDI brought suit under the Trademark Act of 1946 (Lanham Act), 60 Stat. 427, as amended, 15 U.S.C. § 1051 et seq. , against TrafFix for trademark infringement (based on the similar names), trade dress infringement (based on the copied dual-spring design), and unfair competition. TrafFix counterclaimed on antitrust theories. After the United States District Court for the Eastern District of Michigan considered cross-motions for summary judgment, MDI prevailed on its trademark claim for the confusing similarity of names and was held not liable on the antitrust counterclaim; and those two rulings, affirmed by the Court of Appeals, are not before us.

I

We are concerned with the trade dress question. The District Court ruled against MDI on its trade dress claim. 971 F.Supp. 262 (E.D.Mich.1997). After determining that the one element of MDI's trade dress at issue was the dual-spring design, id., at 265, it held that “no reasonable trier of fact could determine that MDI has established secondary meaning” in its alleged trade dress, id., at 269. In other words, consumers did not associate the look of the dual-spring design with MDI. As a second, independent reason to grant summary judgment in favor of TrafFix, the District Court determined the dual-spring design was functional. On this rationale secondary meaning is irrelevant because there can be no trade dress protection in any event. In ruling on the functional aspect of the design, the District Court noted that Sixth Circuit precedent indicated that the burden was on MDI to prove that its trade dress was nonfunctional, and not on TrafFix to show that it was functional (a rule since adopted by Congress, see 15 U.S.C. § 1125(a)(3) (1994 ed., Supp. V)), and then went on to consider MDI's arguments that the dual-spring design was subject to trade dress protection. Finding none of MDI's contentions persuasive, the District Court concluded MDI had not “proffered sufficient evidence which would enable a reasonable trier of fact to find that MDI's vertical dual-spring design is non-functional.” 971 F.Supp., at 276. Summary judgment was entered against MDI on its trade dress claims.

The Court of Appeals for the Sixth Circuit reversed the trade dress ruling. 200 F.3d 929 (1999). The Court of Appeals held the District Court had erred in ruling MDI failed to show a genuine issue of material fact regarding whether it had secondary meaning in its alleged trade dress, id., at 938, and had erred further in determining that MDI could not prevail in any event because the alleged trade dress was in fact a functional product configuration, id., at 940. The Court of Appeals suggested the District Court committed legal error by looking only to the dual-spring design when evaluating MDI's trade dress. Basic to its reasoning was the Court of Appeals' observation that it took “little imagination to conceive of a hidden dual-spring mechanism or a tri or quad-spring mechanism that might avoid infringing [MDI's] trade dress.” Ibid. The Court of Appeals explained that “[i]f TrafFix or another competitor chooses to use [MDI's] dual-spring design, then it will have to find some other way to set its sign apart to avoid infringing [MDI's] trade dress.” Ibid. It was not sufficient, according to the Court of Appeals, that allowing exclusive use of a particular feature such as the dual-spring design in the guise of trade dress would “hinde[r] competition somewhat.” Rather, “[e]xclusive use of a feature must ‘put competitors at a significant non-reputation-related disadvantage’ before trade dress protection is denied on functionality grounds.” Ibid. (quoting Qualitex Co. v. Jacobson Products Co., 514 U.S. 159, 165, 115 S.Ct. 1300, 131 L.Ed.2d 248 (1995)). In its criticism of the District Court's ruling on the trade dress question, the Court of Appeals took note of a split among Courts of Appeals in various other Circuits on the issue whether the existence of an expired utility patent forecloses the possibility of the patentee's claiming trade dress protection in the product's design. 200 F.3d, at 939. Compare Sunbeam Products, Inc. v. West Bend Co., 123 F.3d 246 (C.A.5 1997) (holding that trade dress protection is not foreclosed), Thomas & Betts Corp. v. Panduit Corp., 138 F.3d 277 (C.A.7 1998) (same), and Midwest Industries, Inc. v. Karavan Trailers, Inc., 175 F.3d 1356 (C.A.Fed.1999) (same), with Vornado Air Circulation Systems, Inc. v. Duracraft Corp., 58 F.3d 1498, 1500 (C.A.10 1995) (“Where a product configuration is a significant inventive component of an invention covered by a utility patent ... it cannot receive trade dress protection”). To resolve the conflict, we granted certiorari. 530 U.S. 1260, 120 S.Ct. 2715, 147 L.Ed.2d 981 (2000).

II

It is well established that trade dress can be protected under federal law. The design or packaging of a product may acquire a distinctiveness which serves to identify the product with its manufacturer or source; and a design or package which acquires this secondary meaning, assuming other requisites are met, is a trade dress which may not be used in a manner likely to cause confusion as to the origin, sponsorship, or approval of the goods. In these respects protection for trade dress exists to promote competition. As we explained just last Term, see Wal-Mart Stores, Inc. v. Samara Brothers, Inc., 529 U.S. 205, 120 S.Ct. 1339, 146 L.Ed.2d 182 (2000), various Courts of Appeals have allowed claims of trade dress infringement relying on the general provision of the Lanham Act which provides a cause of action to one who is injured when a person uses “any word, term name, symbol, or device, or any combination thereof ... which is likely to cause confusion ... as to the origin, sponsorship, or approval of his or her goods.” 15 U.S.C. § 1125(a)(1)(A). Congress confirmed this statutory protection for trade dress by amending the Lanham Act to recognize the concept. Title 15 U.S.C. § 1125(a)(3) (1994 ed., Supp. V) provides: “In a civil action for trade dress infringement under this chapter for trade dress not registered on the principal register, the person who asserts trade dress protection has the burden of proving that the matter sought to be protected is not functional.” This burden of proof gives force to the well-established rule that trade dress protection may not be claimed for product features that are functional. Qualitex, supra, at 164-165, 115 S.Ct. 1300; Two Pesos, Inc. v. Taco Cabana, Inc., 505 U.S. 763, 775, 112 S.Ct. 2753, 120 L.Ed.2d 615 (1992). And in Wal-Mart, supra, we were careful to caution against misuse or overextension of trade dress. We noted that “product design almost invariably serves purposes other than source identification.” Id., at 213, 120 S.Ct. 1339.

Trade dress protection must subsist with the recognition that in many instances there is no prohibition against copying goods and products. In general, unless an intellectual property right such as a patent or copyright protects an item, it will be subject to copying. As the Court has explained, copying is not always discouraged or disfavored by the laws which preserve our competitive economy. Bonito Boats, Inc. v. Thunder Craft Boats, Inc., 489 U.S. 141, 160, 109 S.Ct. 971, 103 L.Ed.2d 118 (1989). Allowing competitors to copy will have salutary effects in many instances. “Reverse engineering of chemical and mechanical articles in the public domain often leads to significant advances in technology.” Ibid.

The principal question in this case is the effect of an expired patent on a claim of trade dress infringement. A prior patent, we conclude, has vital significance in resolving the trade dress claim. A utility patent is strong evidence that the features therein claimed are functional. If trade dress protection is sought for those features the strong evidence of functionality based on the previous patent adds great weight to the statutory presumption that features are deemed functional until proved otherwise by the party seeking trade dress protection. Where the expired patent claimed the features in question, one who seeks to establish trade dress protection must carry the heavy burden of showing that the feature is not functional, for instance by showing that it is merely an ornamental, incidental, or arbitrary aspect of the device.

In the case before us, the central advance claimed in the expired utility patents (the Sarkisian patents) is the dual-spring design; and the dual-spring design is the essential feature of the trade dress MDI now seeks to establish and to protect. The rule we have explained bars the trade dress claim, for MDI did not, and cannot, carry the burden of overcoming the strong evidentiary inference of functionality based on the disclosure of the dual-spring design in the claims of the expired patents.

The dual springs shown in the Sarkisian patents were well apart (at either end of a frame for holding a rectangular sign when one full side is the base) while the dual springs at issue here are close together (in a frame designed to hold a sign by one of its corners). As the District Court recognized, this makes little difference. The point is that the springs are necessary to the operation of the device. The fact that the springs in this very different-looking device fall within the claims of the patents is illustrated by MDI's own position in earlier litigation. In the late 1970's, MDI engaged in a long-running intellectual property battle with a company known as Winn-Proof. Although the precise claims of the Sarkisian patents cover sign stands with springs “spaced apart,” U.S. Patent No. 3,646,696, col. 4; U.S. Patent No. 3,662,482, col. 4, the Winn-Proof sign stands (with springs much like the sign stands at issue here) were found to infringe the patents by the United States District Court for the District of Oregon, and the Court of Appeals for the Ninth Circuit affirmed the judgment. Sarkisian v. Winn-Proof Corp., 697 F.2d 1313 (1983). Although the Winn-Proof traffic sign stand (with dual springs close together) did not appear, then, to infringe the literal terms of the patent claims (which called for “spaced apart” springs), the Winn-Proof sign stand was found to infringe the patents under the doctrine of equivalents, which allows a finding of patent infringement even when the accused product does not fall within the literal terms of the claims. Id., at 1321-1322; see generally Warner-Jenkinson Co. v. Hilton Davis Chemical Co., 520 U.S. 17, 117 S.Ct. 1040, 137 L.Ed.2d 146 (1997). In light of this past ruling-a ruling procured at MDI's own insistence-it must be concluded the products here at issue would have been covered by the claims of the expired patents.

The rationale for the rule that the disclosure of a feature in the claims of a utility patent constitutes strong evidence of functionality is well illustrated in this case. The dual-spring design serves the important purpose of keeping the sign upright even in heavy wind conditions; and, as confirmed by the statements in the expired patents, it does so in a unique and useful manner. As the specification of one of the patents recites, prior art “devices, in practice, will topple under the force of a strong wind.” U.S. Patent No. 3,662,482, col. 1. The dual-spring design allows sign stands to resist toppling in strong winds. Using a dual-spring design rather than a single spring achieves important operational advantages. For example, the specifications of the patents note that the “use of a pair of springs ... as opposed to the use of a single spring to support the frame structure prevents canting or twisting of the sign around a vertical axis,” and that, if not prevented, twisting “may cause damage to the spring structure and may result in tipping of the device.” U.S. Patent No. 3,646,696, col. 3. In the course of patent prosecution, it was said that “[t]he use of a pair of spring connections as opposed to a single spring connection ... forms an important part of this combination” because it “forc[es] the sign frame to tip along the longitudinal axis of the elongated ground-engaging members.” App. 218. The dual-spring design affects the cost of the device as well; it was acknowledged that the device “could use three springs but this would unnecessarily increase the cost of the device.” Id., at 217. These statements made in the patent applications and in the course of procuring the patents demonstrate the functionality of the design. MDI does not assert that any of these representations are mistaken or inaccurate, and this is further strong evidence of the functionality of the dual-spring design.

III

In finding for MDI on the trade dress issue the Court of Appeals gave insufficient recognition to the importance of the expired utility patents, and their evidentiary significance, in establishing the functionality of the device. The error likely was caused by its misinterpretation of trade dress principles in other respects. As we have noted, even if there has been no previous utility patent the party asserting trade dress has the burden to establish the nonfunctionality of alleged trade dress features. MDI could not meet this burden. Discussing trademarks, we have said “ ‘[i]n general terms, a product feature is functional,’ and cannot serve as a trademark, ‘if it is essential to the use or purpose of the article or if it affects the cost or quality of the article.’ ” Qualitex, 514 U.S., at 165, 115 S.Ct. 1300 (quoting Inwood Laboratories, Inc. v. Ives Laboratories, Inc., 456 U.S. 844, 850, n. 10, 102 S.Ct. 2182, 72 L.Ed.2d 606 (1982)). Expanding upon the meaning of this phrase, we have observed that a functional feature is one the “exclusive use of [which] would put competitors at a significant non-reputation-related disadvantage.” 514 U.S., at 165, 115 S.Ct. 1300. The Court of Appeals in the instant case seemed to interpret this language to mean that a necessary test for functionality is “whether the particular product configuration is a competitive necessity.” 200 F.3d, at 940. See also Vornado, 58 F.3d, at 1507 (“Functionality, by contrast, has been defined both by our circuit, and more recently by the Supreme Court, in terms of competitive need”). This was incorrect as a comprehensive definition. As explained in Qualitex, supra, and Inwood, supra, a feature is also functional when it is essential to the use or purpose of the device or when it affects the cost or quality of the device. The Qualitex decision did not purport to displace this traditional rule. Instead, it quoted the rule as Inwood had set it forth. It is proper to inquire into a “significant non-reputation-related disadvantage” in cases of esthetic functionality, the question involved in Qualitex. Where the design is functional under the Inwood formulation there is no need to proceed further to consider if there is a competitive necessity for the feature. In Qualitex, by contrast, esthetic functionality was the central question, there having been no indication that the green-gold color of the laundry press pad had any bearing on the use or purpose of the product or its cost or quality.

The Court has allowed trade dress protection to certain product features that are inherently distinctive. Two Pesos, 505 U.S., at 774, 112 S.Ct. 2753. In Two Pesos, however, the Court at the outset made the explicit analytic assumption that the trade dress features in question (decorations and other features to evoke a Mexican theme in a restaurant) were not functional. Id., at 767, n. 6, 112 S.Ct. 2753. The trade dress in those cases did not bar competitors from copying functional product design features. In the instant case, beyond serving the purpose of informing consumers that the sign stands are made by MDI (assuming it does so), the dual-spring design provides a unique and useful mechanism to resist the force of the wind. Functionality having been established, whether MDI's dual-spring design has acquired secondary meaning need not be considered.

There is no need, furthermore, to engage, as did the Court of Appeals, in speculation about other design possibilities, such as using three or four springs which might serve the same purpose. 200 F.3d, at 940. Here, the functionality of the spring design means that competitors need not explore whether other spring juxtapositions might be used. The dual-spring design is not an arbitrary flourish in the configuration of MDI's product; it is the reason the device works. Other designs need not be attempted.

Because the dual-spring design is functional, it is unnecessary for competitors to explore designs to hide the springs, say, by using a box or framework to cover them, as suggested by the Court of Appeals. Ibid. The dual-spring design assures the user the device will work. If buyers are assured the product serves its purpose by seeing the operative mechanism that in itself serves an important market need. It would be at cross-purposes to those objectives, and something of a paradox, were we to require the manufacturer to conceal the very item the user seeks.

In a case where a manufacturer seeks to protect arbitrary, incidental, or ornamental aspects of features of a product found in the patent claims, such as arbitrary curves in the legs or an ornamental pattern painted on the springs, a different result might obtain. There the manufacturer could perhaps prove that those aspects do not serve a purpose within the terms of the utility patent. The inquiry into whether such features, asserted to be trade dress, are functional by reason of their inclusion in the claims of an expired utility patent could be aided by going beyond the claims and examining the patent and its prosecution history to see if the feature in question is shown as a useful part of the invention. No such claim is made here, however. MDI in essence seeks protection for the dual-spring design alone. The asserted trade dress consists simply of the dual-spring design, four legs, a base, an upright, and a sign. MDI has pointed to nothing arbitrary about the components of its device or the way they are assembled. The Lanham Act does not exist to reward manufacturers for their innovation in creating a particular device; that is the purpose of the patent law and its period of exclusivity. The Lanham Act, furthermore, does not protect trade dress in a functional design simply because an investment has been made to encourage the public to associate a particular functional feature with a single manufacturer or seller. The Court of Appeals erred in viewing MDI as possessing the right to exclude competitors from using a design identical to MDI's and to require those competitors to adopt a different design simply to avoid copying it. MDI cannot gain the exclusive right to produce sign stands using the dual-spring design by asserting that consumers associate it with the look of the invention itself. Whether a utility patent has expired or there has been no utility patent at all, a product design which has a particular appearance may be functional because it is “essential to the use or purpose of the article” or “affects the cost or quality of the article.” Inwood, 456 U.S., at 850, n. 10, 102 S.Ct. 2182.

TrafFix and some of its amici argue that the Patent Clause of the Constitution, Art. I, § 8, cl. 8, of its own force, prohibits the holder of an expired utility patent from claiming trade dress protection. Brief for Petitioner 33-36; Brief for Panduit Corp. as Amicus Curiae 3; Brief for Malla Pollack as Amicus Curiae 2. We need not resolve this question. If, despite the rule that functional features may not be the subject of trade dress protection, a case arises in which trade dress becomes the practical equivalent of an expired utility patent, that will be time enough to consider the matter. The judgment of the Court of Appeals is reversed, and the case is remanded for further proceedings consistent with this opinion.

It is so ordered.

U.S.,2001.
Traffix Devices, Inc. v. Marketing Displays, Inc.
532 U.S. 23, 121 S.Ct. 1255, 149 L.Ed.2d 164, 69 USLW 4172, 58 U.S.P.Q.2d 1001, 01 Cal. Daily Op. Serv. 2223, 2001 Daily Journal D.A.R. 2796, 14 Fla. L. Weekly Fed. S 135, 2001 DJCAR 1496

AME 40590 Intellectual Property for Engineers

2015-04-02T19:50:42Z

Bill: /* ALPHABETICAL LISTING OF CASES */

Cases to add:
* Damages:
** MINTZ V. DIETZ & WATSON, INC. (CAFC, May 2012)
** Monsanto Co. v. McFarling, 488 F.3d 973, 978-79 (Fed. Cir. 2007)
** Georgia-Pacific Corp. v. US Plywood Corp., 318 F. Supp. 1116 (SDNY 1970), modified, 446 F. 2d 295 (2d Cir. 1971)
** The Boeing Company v. The United States, 86 Fed. Cl. 303 (April 2, 2009)
** Mahurkar v. CR Bard, Inc. 79 F. 3d 1572, 1580 (Fed. Cir. 1996), adopting Panduit Corp. v. Stahlin Bros. Fibre Works, Inc.,575 F.2d 1152 (6th Cir. 1978)
** Depuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 567 F.3d 1314 (Fed. Cir. 2009)

* Software patents:
** In re Alappat, 33 F.3d 1526, 1545 (Fed. Cir. 1994).
** CyberSource Corporation v. Retail Decisions, Inc., Slip Op. at 19 (2011)
** Ultramercial, LLC v. Hulu, LLC (Fed. Cir. 2011)

=ALPHABETICAL LISTING OF CASES=

*[[A. & P. Tea Co. v. Supermarket Corp., 340 U.S. 147 (1950)]]
*[[Abbott Laboratories v. Geneva Pharmaceuticals, Inc., 182 F.3d 1315 (1999)]]
*[[Alza Corp. v. Mylan Laboratories, 464 F.3d 1286, (2006)]]
*[[Anderson's Black Rock, Inc. v. Pavement Co., 396 U.S. 57 (1969)]]
*[[Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336 (1961)]]
*[[Arrhythmia Research Technology, Inc. v. Corazonix Corp., 958 F.2d 1053 (1992)]]
*[[Asgrow Seed Co. v. Winterboer, 513 U.S. 179 (1994)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. (2013)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. CAFC (2012)]]
*[[Atlas Powder v. E.I. du Pont de Nemours, 750 F2d 1569 (1984)]]
*[[Bilski v. Kappos, 130 S.Ct. 3218 (2010)]]
*[[Bobbs-Merrill Co. v. Straus, 210 U.S. 339 (1908)]]
*[[Bonito Boats. v. Thunder Craft, 489 U.S. 141 (1989)]]
*[[Bowman v. Monsanto, 133 S.Ct. 1761 (2013)]]
*[[CCS Fitness, Inc. v. Brunswick Corporation, 288 F.3d 1359 (2002)]]
*[[Chester v. Miller, 906 F.2d 1574 (1990)]]
*[[D.L. Auld Co. v. Chroma Graphics Corp., 714 F.2d 1144 (1983)]]
*[[Diamond v. Chakrabarty, 100 S.Ct. 2204 (1980)]]
*[[Diamond v. Diehr, 450 U.S. 175 (1981)]]
*[[Egbert v. Lippmann, 104 U.S. 333 (1881)]]
*[[Electric Storage Battery Co. v. Shimadzu, 307 U.S. 5 (1939)]]
*[[Elizabeth v. American Nicholson Pavement Company, 97 U.S. 126 (1877)]]
*[[Filmtec Corp. v. Allied-Signal Inc., 939 F.2d 1568 (1991)]]
*[[Funk Bros. Seed Co. v. Kalo Inoculant Co. 333 U.S. 127 (1948)]]
*[[Gottschalk v. Benson, 409 U.S. 63 (1972)]]
*[[Gould v. Hellwarth, 472 F2d 1383 (1973)]]
*[[Graham v. John Deere, 383 U.S. 1 (1966)]]
*[[Graver Tank & Mfg. Co. v. Linde Air Products Co. 339 US 605 (1950)]]
*[[H.H. Robertson, Co. v. United Steel Deck, Inc., 820 F.2d 384 (1987)]]
*[[Hotchkiss v. Greenwood, 52 U.S. 11 (1850) ]]
*[[Hybritech v. Monoclonal Antiboties, 802 F.2d 1375 (1986)]]
*[[i4i Ltd. Partnership v. Microsoft Corp., 598 F.3d 831 (2010)]]
*[[In Re Bilski]]
**[[In Re Bilski, Dky concurring opinion]]
**[[In Re Bilski, Newman dissenting opinion]]
**[[In Re Bilski, Mayer dissenting opinion]]
**[[In Re Bilski, Rader dissenting opinion]]
*[[In re Brana, 51 F.3d 1560 (1995)]]
*[[In re Carlson, 983 F.2d 1032 (1992)]]
*[[In re Hall, 781 F.2d 897 (1986)]]
*[[In re Kahn, CAFC 04-1616 (2006)]]
*[[In Re Rouffet, 149 F.3d 1350 (1998)]]
*[[J.E.M. Ag Supply, Inc. v. Pioneer Hi-Bred International, Inc., 534 U.S. 124 (2001)]]
*[[Juicy Whip v. Orange Bang, 185 F.3d 1364 (1999)]]
*[[KSR International Co. v. Teleflex, Inc., 550 U.S. 398 (2007)]]
*[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]
*[[Lorenz v. Colgate-Palmolive-Peet Co., 167 F.2d 423 (1948)]]
*[[Lough v. Brunswick Corp., 86 F.3d 1113 (1996)]]
*[[Lyon v. Bausch & Lomb, 224 F.2d 530 (1955)]]
*[[Metabolit Laboratories, Inc. and Competitive Technologies, Inc. v. Laboratory Corporation of America Holdings, 370 F.3d 1354 (2004)]]
*[[Metallizing Engineering Co., Inc. v. Kenyon Bearing & Auto Parts Co., Inc., 153 F.2d 516 (1946)]]
*[[Microsoft Corp v. At&T Corp., 550 U.S. 437 (2007)]]
*[[Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (1978)]]
*[[Perkin-Elmer Corporation v. Computervision Corporation, 732 F2d 888 (1984)]]
*[[Pfaff vs. Wells Electronics, 525 U.S. 55 (1998)]]
*[[Philips Electric Co. v. Thermal Industries, Inc., 450 F.2d 1164 (1971)]]
*[[Quanta Computer, Inc. v. LG Electronics, Inc., 553 U.S. 617 (2008)]]
*[[Reiner v. I. Leon Co., 285 F.2d 501 (1960)]]
*[[South Corp. v. US 690 F.2d 1368 (1982)]]
*[[State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (1998)]]
*[[Traffix Devices, Inc. vs. Marketing Displays, Inc.]]
*[[TurboCare Div. of Demag Delaval Turbomachinery Corp. v. General Elec. Co., 264 F.3d 1111 (2001)]]
*[[UMC Electronics Co. v. U.S., 816 F.2d 647 (1987)]]
*[[US v. Adams, 383 U.S. 39 (1966)]]
*[[U.S. v. Univis Lens Co., 316 U.S. 241 (1942)]]
*[[Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530]]
*[[Vas-Cath Inc. v. Mahurkar, 935 F.2d 1555 (1991)]]
*[[Warner-Jenkinson Company v. Hilton Davis Chemical Co., 520 US 17 (1997)]]
**[[Warner-Jenkinson v. Hilton Davis Petitioner Brief]]
**[[Warner-Jenkinson v. Hilton Davis Respondent Brief]]
*[[Winner International Royalty Co. v. Wang, 202 F.3d 1340 (2000)]]
*[[W.L. Gore & Associates, Inc. v. Garlock, Inc., 721 F.2d 1540 (1983)]]

=[[INTRODUCTION]]=
This is a summary. Click on the title for the full chapter: [[INTRODUCTION]]

Outline:
*The main purpose for obtaining a patent is ''economic''.
*It grants the exclusive right to ''make, use or sell'' the invention for a limited period of time.
*The governing law is Title 35 of the United States Code (35 USC).
*The governing regulations are from Title 37 of the Code of Federal Regulations (37 CFR).
*The law is federal, so patent cases are resolved in the federal court system:
**district courts;
**circuit courts;
**the Court of Appeals for the Federal Circuit (CAFC), a special appeals court for patent cases; and,
**the Supreme Court.
*The US Patent and Trademark Office (PTO) processes patent applications.
*Patents last for 20 years from the date the application is filed with the PTO.
*Patents have the attributes of personal property.
*The foundation of the federal government's authority to create a patent system is in the Constitution. The purposes is explicitly economic, "to promote the progress of science and useful arts..."
*Other forms of intellectual property
**copyright;
**trademarks; and,
**trade secrets.

=[[NONOBVIOUSNESS]]=
This is a summary. Click on the title for the full chapter: [[NONOBVIOUSNESS]]

Outline:

*This is perhaps the most difficult factual patent issue. In addition to meeting the novelty requirements of 35 USC 102, 35 USC 103 requires that the claimed invention as a whole must have been nonobvious "at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains."
*There is a lot of historical confusion regarding this standard. Basically, it is a notion of something being meeting some type of sufficient inventive standard or nontriviality.
*To determine this, there are three fundamental lines of inquiry:
**the scope and content of the prior art;
**the differences between the prior art and claims at issue; and,
**the level of ordinary skill in the art.
*Secondary considerations include:
**a long-felt but unsatisfied need met by the invention;
**appreciation by those versed in the art that the need existed;
**substantial attempts to meet this need;
**commercial success of the invention;
**replacement in the industry by the claimed invention;
**acquiescence by the industry;
**''teaching away'' by those skilled in the art;
**unexpectedness of the results; and,
**disbelief or incredulity on the part of industry with respect to the new invention.

=[[INFRINGEMENT]]=
This is a summary. Click on the title for the full chapter: [[INFRINGEMENT]]

=[[THE PATENT DOCUMENT]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT DOCUMENT]]

Outline:
*A patent has several parts:
**specification: describes the invention;
**claims: delineates the ownership rights;
**drawings: not required, but if they are included then any element included in the claims must be shown in the drawings; and,
**other miscellaneous parts.
*Interpreting claims: claims are said to ''read on'' another device.
*The doctrine of equivalence, prevents something from being patented that only has minor alterations from the prior art.
*The date of the invention
**''reduction to practice'';
**''diligence'' requirement.
*The ''file wrapper''.

=[[NOVELTY]]=
This is a summary. Click on the title for the full chapter: [[NOVELTY]]

Outline:
*Specified in 35 USC 102.
*Fundamentally: an invention must be ''new''.
*Section 102 basically defines in a technical way what it means to not be new:
**Events prior to invention
***known or used by others in the US
***patented or in a printed publication in another country
**Events one year before filing the patent application
***patented or in a printed publication anywhere (''in this or a foreign country'')
***in public use or on sale in the US
**Other bars
*The applicant must be the inventor (not the employer)

Outline:
*Literal Infringement
*The Doctrine of Equivalents

=[[UTILITY]]=
This is a summary. Click on the title for the full chapter: [[UTILITY]]

=[[PATENTABLE SUBJECT MATTER]]=
This is a summary. Click on the title for the full chapter: [[PATENTABLE SUBJECT MATTER]]

Can computer programs, algorithms, laws of nature, life forms, plants, ''etc.'' be patented. In particular, are the following patentable:

* Plants
* Algorithms and Computer Programs
* Scientific Facts?

In a recent case
* State Street (1998)
the CAFC substantially broadened the subject matter of section 101 to include such things as methods of doing business, etc.

=[[FOREIGN AND DOMESTIC PRIORITY]]=
This is a summary. Click on the title for the full chapter: [[FOREIGN AND DOMESTIC PRIORITY]]

Outline:
*Priority in general
*Foreign priority
*International applications
*Domestic priority
*Provisional applications

=[[THE PATENT APPLICATION]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT APPLICATION]]

Outline:
*The Disclosure
*The Claims
*Other Sections
*New Matter
*The Examination Process

=[[INVENTOR ELIGIBILITY]]=
This is a summary. Click on the title for the full chapter: [[INVENTOR ELIGIBILITY]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972): full text]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981): (full text)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005): (full text)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]

[[METABOLITE LABORATORIES, INC. and Competitive Technologies, Inc. v. LABORATORY CORPORATION OF AMERICA HOLDINGS (doing business as LabCorp): the CAFC case (full text)]]

=[[ANTICIPATION]]=
This is a summary. Click on the title for the full chapter: [[ANTICIPATION]]

=[[PRIOR ART]]=
This is a summary. Click on the title for the full chapter: [[PRIOR ART]]

[[Pfaff v. Wells Electronics: full text]]

[[Perkin-Elmer Corporation v. Computervision Corporation (full text)]]

[[Perkin-Elmer Corporation v. Computervision Corporation]]

South Corp. v. US

2015-04-02T19:49:52Z

Bill: Bill moved page South Corp. v. US to South Corp. v. U.S., 690 F.2d 1368 (1982)

#REDIRECT [[South Corp. v. U.S., 690 F.2d 1368 (1982)]]

South Corp. v. U.S., 690 F.2d 1368 (1982)

2015-04-02T19:49:52Z

Bill: Bill moved page South Corp. v. US to South Corp. v. U.S., 690 F.2d 1368 (1982)

The court sits ''in banc'' to consider what case law, if any, may appropriately serve as established precedent. We hold that the holdings of our predecessor courts, the United States Court of Claims and the United States Court of Customs and Patent Appeals, announced by those courts before the close of business September 30, 1982, shall be binding as precedent in this court.

AME 40590 Intellectual Property for Engineers

2015-04-02T19:40:33Z

Bill: /* ALPHABETICAL LISTING OF CASES */

Cases to add:
* Damages:
** MINTZ V. DIETZ & WATSON, INC. (CAFC, May 2012)
** Monsanto Co. v. McFarling, 488 F.3d 973, 978-79 (Fed. Cir. 2007)
** Georgia-Pacific Corp. v. US Plywood Corp., 318 F. Supp. 1116 (SDNY 1970), modified, 446 F. 2d 295 (2d Cir. 1971)
** The Boeing Company v. The United States, 86 Fed. Cl. 303 (April 2, 2009)
** Mahurkar v. CR Bard, Inc. 79 F. 3d 1572, 1580 (Fed. Cir. 1996), adopting Panduit Corp. v. Stahlin Bros. Fibre Works, Inc.,575 F.2d 1152 (6th Cir. 1978)
** Depuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 567 F.3d 1314 (Fed. Cir. 2009)

* Software patents:
** In re Alappat, 33 F.3d 1526, 1545 (Fed. Cir. 1994).
** CyberSource Corporation v. Retail Decisions, Inc., Slip Op. at 19 (2011)
** Ultramercial, LLC v. Hulu, LLC (Fed. Cir. 2011)

=ALPHABETICAL LISTING OF CASES=

*[[A. & P. Tea Co. v. Supermarket Corp., 340 U.S. 147 (1950)]]
*[[Abbott Laboratories v. Geneva Pharmaceuticals, Inc., 182 F.3d 1315 (1999)]]
*[[Alza Corp. v. Mylan Laboratories, 464 F.3d 1286, (2006)]]
*[[Anderson's Black Rock, Inc. v. Pavement Co., 396 U.S. 57 (1969)]]
*[[Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336 (1961)]]
*[[Arrhythmia Research Technology, Inc. v. Corazonix Corp., 958 F.2d 1053 (1992)]]
*[[Asgrow Seed Co. v. Winterboer, 513 U.S. 179 (1994)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. (2013)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. CAFC (2012)]]
*[[Atlas Powder v. E.I. du Pont de Nemours, 750 F2d 1569 (1984)]]
*[[Bilski v. Kappos, 130 S.Ct. 3218 (2010)]]
*[[Bobbs-Merrill Co. v. Straus, 210 U.S. 339 (1908)]]
*[[Bonito Boats. v. Thunder Craft, 489 U.S. 141 (1989)]]
*[[Bowman v. Monsanto, 133 S.Ct. 1761 (2013)]]
*[[CCS Fitness, Inc. v. Brunswick Corporation, 288 F.3d 1359 (2002)]]
*[[Chester v. Miller, 906 F.2d 1574 (1990)]]
*[[D.L. Auld Co. v. Chroma Graphics Corp., 714 F.2d 1144 (1983)]]
*[[Diamond v. Chakrabarty, 100 S.Ct. 2204 (1980)]]
*[[Diamond v. Diehr, 450 U.S. 175 (1981)]]
*[[Egbert v. Lippmann, 104 U.S. 333 (1881)]]
*[[Electric Storage Battery Co. v. Shimadzu, 307 U.S. 5 (1939)]]
*[[Elizabeth v. American Nicholson Pavement Company, 97 U.S. 126 (1877)]]
*[[Filmtec Corp. v. Allied-Signal Inc., 939 F.2d 1568 (1991)]]
*[[Funk Bros. Seed Co. v. Kalo Inoculant Co. 333 U.S. 127 (1948)]]
*[[Gottschalk v. Benson, 409 U.S. 63 (1972)]]
*[[Gould v. Hellwarth, 472 F2d 1383 (1973)]]
*[[Graham v. John Deere, 383 U.S. 1 (1966)]]
*[[Graver Tank & Mfg. Co. v. Linde Air Products Co. 339 US 605 (1950)]]
*[[H.H. Robertson, Co. v. United Steel Deck, Inc., 820 F.2d 384 (1987)]]
*[[Hotchkiss v. Greenwood, 52 U.S. 11 (1850) ]]
*[[Hybritech v. Monoclonal Antiboties, 802 F.2d 1375 (1986)]]
*[[i4i Ltd. Partnership v. Microsoft Corp., 598 F.3d 831 (2010)]]
*[[In Re Bilski]]
**[[In Re Bilski, Dky concurring opinion]]
**[[In Re Bilski, Newman dissenting opinion]]
**[[In Re Bilski, Mayer dissenting opinion]]
**[[In Re Bilski, Rader dissenting opinion]]
*[[In re Brana, 51 F.3d 1560 (1995)]]
*[[In re Carlson, 983 F.2d 1032 (1992)]]
*[[In re Hall, 781 F.2d 897 (1986)]]
*[[In re Kahn, CAFC 04-1616 (2006)]]
*[[In Re Rouffet, 149 F.3d 1350 (1998)]]
*[[J.E.M. Ag Supply, Inc. v. Pioneer Hi-Bred International, Inc., 534 U.S. 124 (2001)]]
*[[Juicy Whip v. Orange Bang, 185 F.3d 1364 (1999)]]
*[[KSR International Co. v. Teleflex, Inc., 550 U.S. 398 (2007)]]
*[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]
*[[Lorenz v. Colgate-Palmolive-Peet Co., 167 F.2d 423 (1948)]]
*[[Lough v. Brunswick Corp., 86 F.3d 1113 (1996)]]
*[[Lyon v. Bausch & Lomb, 224 F.2d 530 (1955)]]
*[[Metabolit Laboratories, Inc. and Competitive Technologies, Inc. v. Laboratory Corporation of America Holdings, 370 F.3d 1354 (2004)]]
*[[Metallizing Engineering Co., Inc. v. Kenyon Bearing & Auto Parts Co., Inc., 153 F.2d 516 (1946)]]
*[[Microsoft Corp v. At&T Corp., 550 U.S. 437 (2007)]]
*[[Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (1978)]]
*[[Perkin-Elmer Corporation v. Computervision Corporation, 732 F2d 888 (1984)]]
*[[Pfaff vs. Wells Electronics, 525 U.S. 55 (1998)]]
*[[Philips Electric Co. v. Thermal Industries, Inc., 450 F.2d 1164 (1971)]]
*[[Quanta Computer, Inc. v. LG Electronics, Inc., 553 U.S. 617 (2008)]]
*[[Reiner v. I. Leon Co., 285 F.2d 501 (1960)]]
*[[South Corp. v. US]]
*[[South Corp. v. US 690 F.2d 1368 (1982)]]
*[[State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (1998)]]
*[[Traffix Devices, Inc. vs. Marketing Displays, Inc.]]
*[[TurboCare Div. of Demag Delaval Turbomachinery Corp. v. General Elec. Co., 264 F.3d 1111 (2001)]]
*[[UMC Electronics Co. v. U.S., 816 F.2d 647 (1987)]]
*[[US v. Adams, 383 U.S. 39 (1966)]]
*[[U.S. v. Univis Lens Co., 316 U.S. 241 (1942)]]
*[[Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530]]
*[[Vas-Cath Inc. v. Mahurkar, 935 F.2d 1555 (1991)]]
*[[Warner-Jenkinson Company v. Hilton Davis Chemical Co., 520 US 17 (1997)]]
**[[Warner-Jenkinson v. Hilton Davis Petitioner Brief]]
**[[Warner-Jenkinson v. Hilton Davis Respondent Brief]]
*[[Winner International Royalty Co. v. Wang, 202 F.3d 1340 (2000)]]
*[[W.L. Gore & Associates, Inc. v. Garlock, Inc., 721 F.2d 1540 (1983)]]

=[[INTRODUCTION]]=
This is a summary. Click on the title for the full chapter: [[INTRODUCTION]]

Outline:
*The main purpose for obtaining a patent is ''economic''.
*It grants the exclusive right to ''make, use or sell'' the invention for a limited period of time.
*The governing law is Title 35 of the United States Code (35 USC).
*The governing regulations are from Title 37 of the Code of Federal Regulations (37 CFR).
*The law is federal, so patent cases are resolved in the federal court system:
**district courts;
**circuit courts;
**the Court of Appeals for the Federal Circuit (CAFC), a special appeals court for patent cases; and,
**the Supreme Court.
*The US Patent and Trademark Office (PTO) processes patent applications.
*Patents last for 20 years from the date the application is filed with the PTO.
*Patents have the attributes of personal property.
*The foundation of the federal government's authority to create a patent system is in the Constitution. The purposes is explicitly economic, "to promote the progress of science and useful arts..."
*Other forms of intellectual property
**copyright;
**trademarks; and,
**trade secrets.

=[[NONOBVIOUSNESS]]=
This is a summary. Click on the title for the full chapter: [[NONOBVIOUSNESS]]

Outline:

*This is perhaps the most difficult factual patent issue. In addition to meeting the novelty requirements of 35 USC 102, 35 USC 103 requires that the claimed invention as a whole must have been nonobvious "at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains."
*There is a lot of historical confusion regarding this standard. Basically, it is a notion of something being meeting some type of sufficient inventive standard or nontriviality.
*To determine this, there are three fundamental lines of inquiry:
**the scope and content of the prior art;
**the differences between the prior art and claims at issue; and,
**the level of ordinary skill in the art.
*Secondary considerations include:
**a long-felt but unsatisfied need met by the invention;
**appreciation by those versed in the art that the need existed;
**substantial attempts to meet this need;
**commercial success of the invention;
**replacement in the industry by the claimed invention;
**acquiescence by the industry;
**''teaching away'' by those skilled in the art;
**unexpectedness of the results; and,
**disbelief or incredulity on the part of industry with respect to the new invention.

=[[INFRINGEMENT]]=
This is a summary. Click on the title for the full chapter: [[INFRINGEMENT]]

=[[THE PATENT DOCUMENT]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT DOCUMENT]]

Outline:
*A patent has several parts:
**specification: describes the invention;
**claims: delineates the ownership rights;
**drawings: not required, but if they are included then any element included in the claims must be shown in the drawings; and,
**other miscellaneous parts.
*Interpreting claims: claims are said to ''read on'' another device.
*The doctrine of equivalence, prevents something from being patented that only has minor alterations from the prior art.
*The date of the invention
**''reduction to practice'';
**''diligence'' requirement.
*The ''file wrapper''.

=[[NOVELTY]]=
This is a summary. Click on the title for the full chapter: [[NOVELTY]]

Outline:
*Specified in 35 USC 102.
*Fundamentally: an invention must be ''new''.
*Section 102 basically defines in a technical way what it means to not be new:
**Events prior to invention
***known or used by others in the US
***patented or in a printed publication in another country
**Events one year before filing the patent application
***patented or in a printed publication anywhere (''in this or a foreign country'')
***in public use or on sale in the US
**Other bars
*The applicant must be the inventor (not the employer)

Outline:
*Literal Infringement
*The Doctrine of Equivalents

=[[UTILITY]]=
This is a summary. Click on the title for the full chapter: [[UTILITY]]

=[[PATENTABLE SUBJECT MATTER]]=
This is a summary. Click on the title for the full chapter: [[PATENTABLE SUBJECT MATTER]]

Can computer programs, algorithms, laws of nature, life forms, plants, ''etc.'' be patented. In particular, are the following patentable:

* Plants
* Algorithms and Computer Programs
* Scientific Facts?

In a recent case
* State Street (1998)
the CAFC substantially broadened the subject matter of section 101 to include such things as methods of doing business, etc.

=[[FOREIGN AND DOMESTIC PRIORITY]]=
This is a summary. Click on the title for the full chapter: [[FOREIGN AND DOMESTIC PRIORITY]]

Outline:
*Priority in general
*Foreign priority
*International applications
*Domestic priority
*Provisional applications

=[[THE PATENT APPLICATION]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT APPLICATION]]

Outline:
*The Disclosure
*The Claims
*Other Sections
*New Matter
*The Examination Process

=[[INVENTOR ELIGIBILITY]]=
This is a summary. Click on the title for the full chapter: [[INVENTOR ELIGIBILITY]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972): full text]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981): (full text)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005): (full text)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]

[[METABOLITE LABORATORIES, INC. and Competitive Technologies, Inc. v. LABORATORY CORPORATION OF AMERICA HOLDINGS (doing business as LabCorp): the CAFC case (full text)]]

=[[ANTICIPATION]]=
This is a summary. Click on the title for the full chapter: [[ANTICIPATION]]

=[[PRIOR ART]]=
This is a summary. Click on the title for the full chapter: [[PRIOR ART]]

[[Pfaff v. Wells Electronics: full text]]

[[Perkin-Elmer Corporation v. Computervision Corporation (full text)]]

[[Perkin-Elmer Corporation v. Computervision Corporation]]

Talk:Microsoft Corp v. At&T Corp.

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This case concerns the applicability of § 271(f) to computer software first sent from the United States to a foreign manufacturer on a master disk, or by electronic transmission, then copied by the foreign recipient for installation on computers made and sold abroad.

AT & T holds a patent on an apparatus for digitally encoding and compressing recorded speech. Microsoft's Windows operating system, it is conceded, has the potential to infringe AT & T's patent, because Windows incorporates software code *442 that, when installed, enables a computer to process speech in the manner claimed by that patent. It bears emphasis, however, that uninstalled Windows software does not infringe AT & T's patent any more than a computer standing alone does; instead, the patent is infringed only when a computer is loaded with Windows and is thereby rendered capable of performing as the patented speech processor. The question before us: Does Microsoft's liability extend to computers made in another country when loaded with Windows software copied**1751 abroad from a master disk or electronic transmission dispatched by Microsoft from the United States? Our answer is “No.”

The master disk or electronic transmission Microsoft sends from the United States is never installed on any of the foreign-made computers in question. Instead, copies made abroad are used for installation. Because Microsoft does not export from the United States the copies actually installed, it does not “suppl[y] ... from the United States” “components” of the relevant computers, and therefore is not liable under § 271(f) as currently written.

Plausible arguments can be made for and against extending § 271(f) to the conduct charged in this case as infringing AT & T's patent. Recognizing that § 271(f) is an exception to the general rule that our patent law does not apply extraterritorially, we resist giving the language in which Congress cast § 271(f) an expansive interpretation. Our decision leaves to Congress' informed judgment any adjustment of § 271(f) it deems necessary or proper.

III A This case poses two questions: First, when, or in what form, does software qualify as a “component” under § 271(f)? Second,**1754 were “components” of the foreign-made computers involved in this case “supplie[d]” by Microsoft “from the United States”? FN7

FN8. Microsoft and the United States stress that to count as a component, the copy of software must be expressed as “object code.” “Software in the form in which it is written and understood by humans is called ‘source code.’ To be functional, however, software must be converted (or ‘compiled’) into its machine-usable version,” a sequence of binary number instructions typed “object code.” Brief for United States as Amicus Curiae 4, n. 1; 71 USPQ 2d 1118, 1119, n. 5, 2004 WL 406640 (S.D.N.Y.2004) (recounting Microsoft's description of the software development process). It is stipulated that object code was on the master disks and electronic transmissions Microsoft dispatched from the United States.

FN9. On this view of “component,” the copies of Windows on the master disks and electronic transmissions that Microsoft sent from the United States could not themselves serve as a basis for liability, because those copies were not installed on the foreign manufacturers' computers. See § 271(f)(1) (encompassing only those components “combin[ed] ... outside of the United States in a manner that would infringe the patent if such combination occurred within the United States”).

The distinctions advanced by AT & T do not persuade us to characterize software, uncoupled from a medium, as a combinable component. Blueprints too, or any design information for that matter, can be independently developed, bought, *451 and sold. If the point of AT & T's argument is that we do not see blueprints lining stores' shelves, the same observation may be made about software in the abstract: What retailers **1756 sell, and consumers buy, are copies of software. Likewise, before software can be contained in and continuously performed by a computer, before it can be updated or deleted, an actual, physical copy of the software must be delivered by CD-ROM or some other means capable of interfacing with the computer.FN12

Because it is so easy to encode software's instructions onto a medium that can be read by a computer, AT & T intimates, that extra step should not play a decisive role under § 271(f). But the extra step is what renders the software a usable, combinable part of a computer; easy or not, the copy-producing step is essential. Moreover, many tools may be used easily and inexpensively to generate the parts of a device. A machine for making sprockets might be used by a manufacturer to produce tens of thousands of sprockets an hour. That does not make the machine a “component” of the tens of thousands of devices in which the sprockets are incorporated, at least not under any ordinary understanding of the term “component.” Congress, of course, might have included within § 271(f)'s compass, for example, not only combinable “components” of a patented invention, but also “information, instructions, or tools from which those components readily may be generated.” It did not. In sum, a *452 copy of Windows, not Windows in the abstract, qualifies as a “component” under § 271(f).FN13

Section 271(f) prohibits the supply of components “from the United States ... in such manner as to actively induce the combination of such components.” § 271(f)(1) (emphasis added). Under this formulation, the very components supplied from the United States, and not copies thereof, trigger § 271(f) liability when combined abroad to form the patented invention at issue. Here, as we have repeatedly noted, see supra, at 1750 - 1751, 1752 - 1753, the copies of Windows actually installed on the foreign computers were not themselves supplied from the United States.FN14 Indeed, those copies did not exist until they were generated by third parties outside the United States.FN15 Copying software abroad, all might agree, *454 is indeed easy and inexpensive. But the same could be said of other items: “Keys or machine parts might be copied from a master; chemical or biological substances might be created by reproduction; and paper products might be made by electronic copying and printing.” Brief for United States as Amicus Curiae 24. See also supra, at 1755 - 1756 (rejecting argument similarly based on ease of copying in construing “component”). Section 271(f) contains no instruction to gauge when duplication is easy and cheap enough to deem a copy in fact made abroad nevertheless “supplie[d] ... from the United States.” The absence of anything addressing copying in the statutory text weighs against a judicial determination that replication abroad of a master dispatched from the United States “supplies” the foreign-made copies from the United States within the intendment of § 271(f).FN16

AT & T alternately contends that the presumption holds no sway here given that § 271(f), by its terms, applies only to domestic conduct, i.e., to the supply of a patented invention's components “from the United States.” § 271(f)(1). AT & T's reading, however, “converts a single act of supply from the United States into a **1759 springboard for liability each time a copy of the software is subsequently made [abroad] and combined with computer hardware [abroad] for sale [abroad.]” Brief for United States as Amicus Curiae 29; see 414 F.3d, at 1373, 1375 (Rader, J., dissenting). In short, foreign law alone, not United States law, currently governs the manufacture and sale of components of patented inventions in foreign countries. If AT & T desires to prevent copying in foreign countries, its remedy today lies in obtaining and enforcing foreign patents. See Deepsouth, 406 U.S., at 531, 92 S.Ct. 1700. FN17

There is no dispute, we note again, that § 271(f) is inapplicable to the export of design tools-blueprints, schematics, templates, and prototypes-all of which may provide the information required to construct and combine overseas the components of inventions patented under United States law. See supra, at 1755 - 1756. We have no license to attribute to Congress an unstated intention to place the information Microsoft dispatched from the United States in a separate category.

Congress is doubtless aware of the ease with which software (and other electronic media) can be copied, and has not left the matter untouched. In 1998, Congress addressed “the ease with which pirates could copy and distribute a copyrightable work in digital form.” Universal City Studios, Inc. v. Corley, 273 F.3d 429, 435 (C.A.2 2001). The resulting measure, the Digital Millennium Copyright Act, 17 U.S.C. § 1201 et seq., “backed with legal sanctions the efforts of copyright owners to protect their works from piracy behind digital walls such as encryption codes or password protections.” Universal City Studios, 273 F.3d, at 435. If *459 the patent law is to be adjusted better “to account for the realities of software distribution,” 414 F.3d, at 1370, the alteration should be made after focused legislative consideration, and not by the Judiciary forecasting Congress' likely disposition.

Because no physical object originating in the United States was combined with these computers, there was no violation of § 271(f). Accordingly, it is irrelevant that the Windows software was not copied onto the foreign-made computers directly from the master disk or from an electronic transmission that originated in the United States. To be sure, if these computers could not run Windows without inserting and keeping a CD-ROM in the appropriate drive, then the CD-ROMs might be components of the computer. But that is not the case here.

Justice STEVENS, dissenting.

I disagree with the Court's suggestion that because software is analogous to an abstract set of instructions, it cannot be regarded as a “component” within the meaning of § 271(f). See ante, at 1754 - 1755. Whether attached or detached from any medium, software plainly satisfies the dictionary definition of that word. See ante, at 1755, n. 11 (observing that “ ‘[c]omponent’ is commonly defined as ‘a constituent part,’ ‘element,’ or ‘ingredient’ ”). And unlike a blueprint that merely instructs a user how to do something, software actually causes infringing conduct to occur. It is more like a roller that causes a player piano to produce sound than sheet music that tells a pianist what to do. Moreover, it is surely not “a staple article or commodity of commerce suitable for substantial noninfringing use” as that term is used in § 271(f)(2). On the contrary, its sole intended use is an infringing use.

Microsoft Corp v. At&T Corp.

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Microsoft Corp v. At&T Corp., 550 U.S. 437 (2007)

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Supreme Court of the United States
MICROSOFT CORPORATION, Petitioner,
v.
AT & T CORP.

No. 05-1056.
Argued Feb. 21, 2007.
Decided April 30, 2007.

Justice Alito filed opinion concurring as to all but footnote 14, in which Justices Thomas and Breyer joined.

Justice Stevens filed dissenting opinion.

Chief Justice Roberts took no part in consideration or decision of case.

Justice GINSBURG delivered the opinion of the Court, except as to footnote 14.

It is the general rule under United States patent law that no infringement occurs when a patented product is made and sold in another country. There is an exception. Section 271(f) of the Patent Act, adopted in 1984, provides that infringement does occur when one “supplies ... from the United States,” for “combination” abroad, a patented invention's “components.” 35 U.S.C. § 271(f)(1). This case concerns the applicability of § 271(f) to computer software first sent from the United States to a foreign manufacturer on a master disk, or by electronic transmission, then copied by the foreign recipient for installation on computers made and sold abroad.

AT & T holds a patent on an apparatus for digitally encoding and compressing recorded speech. Microsoft's Windows operating system, it is conceded, has the potential to infringe AT & T's patent, because Windows incorporates software code that, when installed, enables a computer to process speech in the manner claimed by that patent. It bears emphasis, however, that uninstalled Windows software does not infringe AT & T's patent any more than a computer standing alone does; instead, the patent is infringed only when a computer is loaded with Windows and is thereby rendered capable of performing as the patented speech processor. The question before us: Does Microsoft's liability extend to computers made in another country when loaded with Windows software copied abroad from a master disk or electronic transmission dispatched by Microsoft from the United States? Our answer is “No.”

The master disk or electronic transmission Microsoft sends from the United States is never installed on any of the foreign-made computers in question. Instead, copies made abroad are used for installation. Because Microsoft does not export from the United States the copies actually installed, it does not “suppl[y] ... from the United States” “components” of the relevant computers, and therefore is not liable under § 271(f) as currently written.

Plausible arguments can be made for and against extending § 271(f) to the conduct charged in this case as infringing AT & T's patent. Recognizing that § 271(f) is an exception to the general rule that our patent law does not apply extraterritorially, we resist giving the language in which Congress cast § 271(f) an expansive interpretation. Our decision leaves to Congress' informed judgment any adjustment of § 271(f) it deems necessary or proper.

I
Our decision some 35 years ago in Deepsouth Packing Co. v. Laitram Corp., 406 U.S. 518, 92 S.Ct. 1700, 32 L.Ed.2d 273 (1972), a case about a shrimp deveining machine, led Congress to enact § 271(f). In that case, Laitram, holder of a patent on the time-and-expense-saving machine, sued Deepsouth, manufacturer of an infringing deveiner. Deepsouth conceded that the Patent Act barred it from making and selling its deveining machine in the United States, but sought to salvage a portion of its business: Nothing in United States patent law, Deepsouth urged, stopped it from making in the United States the parts of its deveiner, as opposed to the machine itself, and selling those parts to foreign buyers for assembly and use abroad. Id., at 522-524, 92 S.Ct. 1700<ref> Deepsouth shipped its deveining equipment “to foreign customers in three separate boxes, each containing only parts of the 1 3/4 -ton machines, yet the whole [was] assemblable in less than one hour.” Deepsouth Packing Co. v. Laitram Corp., 406 U.S. 518, 524, 92 S.Ct. 1700, 32 L.Ed.2d 273 (1972).</ref>1 We agreed.

Interpreting our patent law as then written, we reiterated in Deepsouth that it was “not an infringement to make or use a patented product outside of the United States.” Id., at 527, 92 S.Ct. 1700; see 35 U.S.C. § 271(a) (1970 ed.) (“[W]hoever without authority makes, uses or sells any patented invention, within the United States during the term of the patent therefor, infringes the patent.”). Deepsouth's foreign buyers did not infringe Laitram's patent, we held, because they assembled and used the deveining machines outside the United States. Deepsouth, we therefore concluded, could not be charged with inducing or contributing to an infringement. 406 U.S., at 526-527, 92 S.Ct. 1700.<ref>See 35 U.S.C. § 271(b) (1970 ed.) (“Whoever actively induces infringement of a patent shall be liable as an infringer.”); § 271(c) (rendering liable as a contributory infringer anyone who sells or imports a “component” of a patented invention, “knowing the same to be especially made or especially adapted for use in an infringement of such patent, and not a staple article or commodity of commerce suitable for substantial non-infringing use”).</ref> Nor could Deepsouth be held liable as a direct infringer, for it did not make, sell, or use the patented invention-the fully assembled deveining machine-within the United States. The parts of the machine were not themselves patented, we noted, hence export of those parts, unassembled, did not rank as an infringement of Laitram's patent. Id., at 527-529, 92 S.Ct. 1700.

Laitram had argued in Deepsouth that resistance to extension of the patent privilege to cover exported parts “derived from too narrow and technical an interpretation of the [Patent Act].” Id., at 529, 92 S.Ct. 1700. Rejecting that argument, we referred to prior decisions holding that “a combination patent protects only against the operable assembly of the whole and not the manufacture of its parts.” Id., at 528, 92 S.Ct. 1700. Congress' codification of patent law, we said, signaled no intention to broaden the scope of the privilege. Id., at 530, 92 S.Ct. 1700 (“When, as here, the Constitution is permissive, the sign of how far Congress has chosen to go can come only from Congress.”). And we again emphasized that

“[o]ur patent system makes no claim to extraterritorial effect; these acts of Congress do not, and were not intended to, operate beyond the limits of the United States; and we correspondingly reject the claims of others to such control over our markets.” Id., at 531, 92 S.Ct. 1700 (quoting Brown v. Duchesne, 19 How. 183, 195, 15 L.Ed. 595 (1857)).

Absent “a clear congressional indication of intent,” we stated, courts had no warrant to stop the manufacture and sale of the parts of patented inventions for assembly and use abroad. 406 U.S., at 532, 92 S.Ct. 1700.

Focusing its attention on Deepsouth, Congress enacted § 271(f). See Patent Law Amendments Act of 1984, § 101, 98 Stat. 3383; Fisch & Allen, The Application of Domestic Patent Law to Exported Software: 35 U.S.C. § 271(f), 25 U. Pa. J. Int'l Econ. L. 557, 565 (2004) (hereinafter Fisch & Allen) (“Congress specifically intended § 271(f) as a response to the Supreme Court's decision in Deepsouth”).<ref>See also, e.g., Patent Law Amendments of 1984, S.Rep. No. 98-663, pp. 2-3 (1984) (describing § 271(f) as “a response to the Supreme Court's 1972 Deepsouth decision which interpreted the patent law not to make it infringement where the final assembly and sale is abroad”); Section-by-Section Analysis of H.R. 6286, 130 Cong. Rec. 28069 (1984) ( “This proposal responds to the United States Supreme Court decision in Deepsouth ... concerning the need for a legislative solution to close a loophole in [the] patent law.”).</ref> The provision expands the definition of infringement to include supplying from the United States a patented invention's components:

“(1) Whoever without authority supplies or causes to be supplied in or from the United States all or a substantial portion of the components of a patented invention, where such components are uncombined in whole or in part, in such manner as to actively induce the combination of such components outside of the United States in a manner that would infringe the patent if such combination occurred within the United States, shall be liable as an infringer.
“(2) Whoever without authority supplies or causes to be supplied in or from the United States any component of a patented invention that is especially made or especially adapted for use in the invention and not a staple article or commodity of commerce suitable for substantial noninfringing use, where such component is uncombined in whole or in part, knowing that such component is so made or adapted and intending that such component will be combined outside of the United States in a manner that would infringe the patent if such combination occurred within the United States, shall be liable as an infringer.” 35 U.S.C. § 271(f).

II
Windows is designed, authored, and tested at Microsoft's Redmond, Washington, headquarters. Microsoft sells Windows to end users and computer manufacturers, both foreign and domestic. Purchasing manufacturers install the software onto the computers they sell. Microsoft sends to each of the foreign manufacturers a master version of Windows, either on a disk or via encrypted electronic transmission. The manufacturer uses the master version to generate copies. Those copies, not the master sent by Microsoft, are installed on the foreign manufacturer's computers. Once assembly is complete, the foreign-made computers are sold to users abroad. App. to Pet. for Cert. 45a-46a.<ref>Microsoft also distributes Windows to foreign manufacturers indirectly, by sending a master version to an authorized foreign “replicator”; the replicator then makes copies and ships them to the manufacturers. App. to Pet. for Cert. 45a-46a.</ref>

AT & T's patent ('580 patent) is for an apparatus (as relevant here, a computer) capable of digitally encoding and compressing recorded speech. Windows, the parties agree, contains software that enables a computer to process speech in the manner claimed by the '580 patent. In 2001, AT & T filed an infringement suit in the United States District Court for the Southern District of New York, charging Microsoft with liability for domestic and foreign installations of Windows.

Neither Windows software ( e.g., in a box on the shelf) nor a computer standing alone ( i.e., without Windows installed) infringes AT & T's patent. Infringement occurs only when Windows is installed on a computer, thereby rendering it capable of performing as the patented speech processor. Microsoft stipulated that by installing Windows on its own computers during the software development process, it directly infringed the '580 patent.<ref>See 35 U.S.C. § 271(a) (“[W]hoever without authority makes, uses, offers to sell, or sells any patented invention, within the United States or imports into the United States any patented invention during the term of the patent therefor, infringes the patent.”).</ref> Microsoft further acknowledged that by licensing copies of Windows to manufacturers of computers sold in the United States, it induced infringement of AT & T's patent.<ref>See § 271(b) (“Whoever actively induces infringement of a patent shall be liable as an infringer.”).</ref> Id., at 42a; Brief for Petitioner 3-4; Brief for Respondent 9, 19.

Microsoft denied, however, any liability based on the master disks and electronic transmissions it dispatched to foreign manufacturers, thus joining issue with AT & T. By sending Windows to foreign manufacturers, AT & T contended, Microsoft “supplie[d] ... from the United States,” for “ combination” abroad, “components” of AT & T's patented speech processor; accordingly, AT & T urged, Microsoft was liable under § 271(f). See supra, at 1752 - 1753 (reproducing text of § 271(f)). Microsoft responded that unincorporated software, because it is intangible information, cannot be typed a “component” of an invention under § 271(f). In any event, Microsoft urged, the foreign-generated copies of Windows actually installed abroad were not “supplie[d] ... from the United States.” Rejecting these responses, the District Court held Microsoft liable under § 271(f). 71 USPQ 2d 1118 (S.D.N.Y.2004). On appeal, a divided panel of the Court of Appeals for the Federal Circuit affirmed. 414 F.3d 1366 (2005). We granted certiorari, 549 U.S. 991, 127 S.Ct. 467, 166 L.Ed.2d 333 (2006), and now reverse.

III

A

This case poses two questions: First, when, or in what form, does software qualify as a “component” under § 271(f)? Second, were “components” of the foreign-made computers involved in this case “supplie[d]” by Microsoft “from the United States”?<ref>The record leaves unclear which paragraph of § 271(f) AT & T's claim invokes. While there are differences between § 271(f)(1) and (f)(2), see, e.g., infra, at 1760, n. 18, the parties do not suggest that those differences are outcome determinative. Cf. infra, at 1757 - 1758, n. 16 (explaining why both paragraphs yield the same result). For clarity's sake, we focus our analysis on the text of § 271(f)(1).</ref>

As to the first question, no one in this litigation argues that software can never rank as a “component” under § 271(f). The parties disagree, however, over the stage at which software becomes a component. Software, the “set of instructions, known as code, that directs a computer to perform specified functions or operations,” Fantasy Sports Properties, Inc. v. Sportsline.com, Inc., 287 F.3d 1108, 1118 (C.A.Fed.2002), can be conceptualized in (at least) two ways. One can speak of software in the abstract: the instructions themselves detached from any medium. (An analogy: The notes of Beethoven's Ninth Symphony.) One can alternatively envision a tangible “copy” of software, the instructions encoded on a medium such as a CD-ROM. (Sheet music for Beethoven's Ninth.) AT & T argues that software in the abstract, not simply a particular copy of software, qualifies as a “component” under § 271(f). Microsoft and the United States argue that only a copy of software, not software in the abstract, can be a component.<ref>Microsoft and the United States stress that to count as a component, the copy of software must be expressed as “object code.” “Software in the form in which it is written and understood by humans is called ‘source code.’ To be functional, however, software must be converted (or ‘compiled’) into its machine-usable version,” a sequence of binary number instructions typed “object code.” Brief for United States as Amicus Curiae 4, n. 1; 71 USPQ 2d 1118, 1119, n. 5, 2004 WL 406640 (S.D.N.Y.2004) (recounting Microsoft's description of the software development process). It is stipulated that object code was on the master disks and electronic transmissions Microsoft dispatched from the United States.</ref>

The significance of these diverse views becomes apparent when we turn to the second question: Were components of the foreign-made computers involved in this case “supplie[d]” by Microsoft “from the United States”? If the relevant components are the copies of Windows actually installed on the foreign computers, AT & T could not persuasively argue that those components, though generated abroad, were “supplie[d] ... from the United States” as § 271(f) requires for liability to attach.<ref>On this view of “component,” the copies of Windows on the master disks and electronic transmissions that Microsoft sent from the United States could not themselves serve as a basis for liability, because those copies were not installed on the foreign manufacturers' computers. See § 271(f)(1) (encompassing only those components “combin[ed] ... outside of the United States in a manner that would infringe the patent if such combination occurred within the United States”).</ref> If, on the other hand, Windows in the abstract qualifies as a component within § 271(f)'s compass, it would not matter that the master copies of Windows software dispatched from the United States were not themselves installed abroad as working parts of the foreign computers.<ref>The Federal Circuit panel in this case, relying on that court's prior decision in Eolas Technologies Inc. v. Microsoft Corp., 399 F.3d 1325 (2005), held that software qualifies as a component under § 271(f). We are unable to determine, however, whether the Federal Circuit panels regarded as a component software in the abstract, or a copy of software.</ref>

With this explanation of the relationship between the two questions in view, we further consider the twin inquiries.

B

First, when, or in what form, does software become a “component” under § 271(f)? We construe § 271(f)'s terms “in accordance with [their] ordinary or natural meaning.” FDIC v. Meyer, 510 U.S. 471, 476, 114 S.Ct. 996, 127 L.Ed.2d 308 (1994). Section 271(f) applies to the supply abroad of the “components of a patented invention, where such components are uncombined in whole or in part, in such manner as to actively induce the combination of such components.” § 271(f)(1) (emphasis added). The provision thus applies only to “such components” <ref>“Component” is commonly defined as “a constituent part,” “element,” or “ingredient.” Webster's Third New International Dictionary of the English Language 466 (1981).</ref> as are combined to form the “patented invention” at issue. The patented invention here is AT & T's speech-processing computer.

Until it is expressed as a computer-readable “copy,” e.g., on a CD-ROM, Windows software-indeed any software detached from an activating medium-remains uncombinable. It cannot be inserted into a CD-ROM drive or downloaded from the Internet; it cannot be installed or executed on a computer. Abstract software code is an idea without physical embodiment, and as such, it does not match § 271(f)'s categorization: “components” amenable to “combination.” Windows abstracted from a tangible copy no doubt is information-a detailed set of instructions-and thus might be compared to a blueprint (or anything containing design information, e.g., a schematic, template, or prototype). A blueprint may contain precise instructions for the construction and combination of the components of a patented device, but it is not itself a combinable component of that device. AT & T and its amici do not suggest otherwise. Cf. Pellegrini v. Analog Devices, Inc., 375 F.3d 1113, 1117-1119 (C.A.Fed.2004) (transmission abroad of instructions for production of patented computer chips not covered by § 271(f)).

AT & T urges that software, at least when expressed as machine-readable object code, is distinguishable from design information presented in a blueprint. Software, unlike a blueprint, is “modular”; it is a stand-alone product developed and marketed “for use on many different types of computer hardware and in conjunction with many other types of software.” Brief for Respondent 5; Tr. of Oral Arg. 46. Software's modularity persists even after installation; it can be updated or removed (deleted) without affecting the hardware on which it is installed. Ibid. Software, unlike a blueprint, is also “dynamic.” Tr. of Oral Arg. 46. After a device has been built according to a blueprint's instructions, the blueprint's work is done (as AT & T puts it, the blueprint's instructions have been “exhausted,” ibid.). Software's instructions, in contrast, are contained in and continuously performed by a computer. Brief for Respondent 27-28; Tr. of Oral Arg. 46. See also Eolas Technologies Inc. v. Microsoft Corp., 399 F.3d 1325, 1339 (C.A.Fed.2005) ( “[S]oftware code ... drives the functional nucleus of the finished computer product.” (quoting Imagexpo, L.L.C. v. Microsoft Corp., 299 F.Supp.2d 550, 553 (E.D.Va.2003))).

The distinctions advanced by AT & T do not persuade us to characterize software, uncoupled from a medium, as a combinable component. Blueprints too, or any design information for that matter, can be independently developed, bought, and sold. If the point of AT & T's argument is that we do not see blueprints lining stores' shelves, the same observation may be made about software in the abstract: What retailers sell, and consumers buy, are copies of software. Likewise, before software can be contained in and continuously performed by a computer, before it can be updated or deleted, an actual, physical copy of the software must be delivered by CD-ROM or some other means capable of interfacing with the computer.<ref>The dissent, embracing AT & T's argument, contends that, “unlike a blueprint that merely instructs a user how to do something, software actually causes infringing conduct to occur.” Post, at 1763 (STEVENS, J., dissenting). We have emphasized, however, that Windows can “caus[e] infringing conduct to occur”- i.e., function as part of AT & T's speech-processing computer-only when expressed as a computer-readable copy. Abstracted from a usable copy, Windows code is intangible, uncombinable information, more like notes of music in the head of a composer than “a roller that causes a player piano to produce sound.” Ibid.</ref>

Because it is so easy to encode software's instructions onto a medium that can be read by a computer, AT & T intimates, that extra step should not play a decisive role under § 271(f). But the extra step is what renders the software a usable, combinable part of a computer; easy or not, the copy-producing step is essential. Moreover, many tools may be used easily and inexpensively to generate the parts of a device. A machine for making sprockets might be used by a manufacturer to produce tens of thousands of sprockets an hour. That does not make the machine a “component” of the tens of thousands of devices in which the sprockets are incorporated, at least not under any ordinary understanding of the term “component.” Congress, of course, might have included within § 271(f)'s compass, for example, not only combinable “components” of a patented invention, but also “information, instructions, or tools from which those components readily may be generated.” It did not. In sum, a copy of Windows, not Windows in the abstract, qualifies as a “component” under § 271(f).<ref>We need not address whether software in the abstract, or any other intangible, can ever be a component under § 271(f). If an intangible method or process, for instance, qualifies as a “patented invention” under § 271(f) (a question as to which we express no opinion), the combinable components of that invention might be intangible as well. The invention before us, however, AT & T's speech-processing computer, is a tangible thing.</ref>

C

The next question, has Microsoft “supplie[d] ... from the United States” components of the computers here involved? Under a conventional reading of § 271(f)'s text, the answer would be “No,” for the foreign-made copies of Windows actually installed on the computers were “supplie[d]” from places outside the United States. The Federal Circuit majority concluded, however, that “for software ‘components,’ the act of copying is subsumed in the act of ‘supplying.’ ” 414 F.3d, at 1370. A master sent abroad, the majority observed, differs not at all from the exact copies, easily, inexpensively, and swiftly generated from the master; hence “sending a single copy abroad with the intent that it be replicated invokes § 271(f) liability for th[e] foreign-made copies.” Ibid.; cf. post, at 1762 - 1763 (STEVENS, J., dissenting) (“[A] master disk is the functional equivalent of a warehouse of components ... that Microsoft fully expects to be incorporated into foreign-manufactured computers.”).

Judge Rader, dissenting, noted that “supplying” is ordinarily understood to mean an activity separate and distinct from any subsequent “copying, replicating, or reproducing-in effect manufacturing.” 414 F.3d, at 1372-1373 (internal quotation marks omitted); see id., at 1373 (“[C]opying and supplying are separate acts with different consequences-particularly when the ‘supplying’ occurs in the United States and the copying occurs in Düsseldorf or Tokyo. As a matter of logic, one cannot supply one hundred components of a patented invention without first making one hundred copies of the component ... .”). He further observed: “The only true difference between making and supplying software components and physical components [of other patented inventions] is that copies of software components are easier to make and transport.” Id., at 1374. But nothing in § 271(f)'s text, Judge Rader maintained, renders ease of copying a relevant, no less decisive, factor in triggering liability for infringement. See ibid. We agree.

Section 271(f) prohibits the supply of components “from the United States ... in such manner as to actively induce the combination of such components.” § 271(f)(1) (emphasis added). Under this formulation, the very components supplied from the United States, and not copies thereof, trigger § 271(f) liability when combined abroad to form the patented invention at issue. Here, as we have repeatedly noted, see supra, at 1750 - 1751, 1752 - 1753, the copies of Windows actually installed on the foreign computers were not themselves supplied from the United States.<ref>In a footnote, Microsoft suggests that even a disk shipped from the United States, and used to install Windows directly on a foreign computer, would not give rise to liability under § 271(f) if the disk were removed after installation. See Brief for Petitioner 37, n. 11; cf. post, at 1761 - 1762 (ALITO, J., concurring). We need not and do not reach that issue here.</ref> Indeed, those copies did not exist until they were generated by third parties outside the United States.<ref>The dissent analogizes Microsoft's supply of master versions of Windows abroad to “the export of an inventory of ... knives to be warehoused until used to complete the assembly of an infringing machine.” Post, at 1761. But as we have underscored, foreign-made copies of Windows, not the masters Microsoft dispatched from the United States, were installed on the computers here involved. A more apt analogy, therefore, would be the export of knives for copying abroad, with the foreign-made copies “warehoused until used to complete the assembly of an infringing machine.” Ibid. Without stretching § 271(f) beyond the text Congress composed, a copy made entirely abroad does not fit the description “supplie [d] ... from the United States.”</ref> Copying software abroad, all might agree, is indeed easy and inexpensive. But the same could be said of other items: “Keys or machine parts might be copied from a master; chemical or biological substances might be created by reproduction; and paper products might be made by electronic copying and printing.” Brief for United States as Amicus Curiae 24. See also supra, at 1755 - 1756 (rejecting argument similarly based on ease of copying in construing “component”). Section 271(f) contains no instruction to gauge when duplication is easy and cheap enough to deem a copy in fact made abroad nevertheless “supplie[d] ... from the United States.” The absence of anything addressing copying in the statutory text weighs against a judicial determination that replication abroad of a master dispatched from the United States “supplies” the foreign-made copies from the United States within the intendment of § 271(f).<ref>Our analysis, while focusing on § 271(f)(1), is equally applicable to § 271(f)(2). But cf. post, at 1762 (STEVENS, J., dissenting) (asserting “paragraph (2) ... best supports AT & T's position here”). While the two paragraphs differ, among other things, on the quantity of components that must be “supplie[d] ... from the United States” for liability to attach, see infra, at 1760, n. 18, that distinction does not affect our analysis. Paragraph (2), like (1), covers only a “component” amenable to “combination.” § 271(f)(2); see supra, at 1754 - 1756 (explaining why Windows in the abstract is not a combinable component). Paragraph (2), like (1), encompasses only the “[s]uppl[y] ... from the United States” of “such [a] component” as will itself “be combined outside of the United States.” § 271(f)(2); see supra, at 1756 - 1757 and this page (observing that foreign-made copies of Windows installed on computers abroad were not “supplie[d] ... from the United States”). It is thus unsurprising that AT & T does not join the dissent in suggesting that the outcome might turn on whether we view the case under paragraph (1) or (2).</ref>

D

Any doubt that Microsoft's conduct falls outside § 271(f)'s compass would be resolved by the presumption against extraterritoriality, on which we have already touched. See supra, at 1750 - 1751, 1752. The presumption that United States law governs domestically but does not rule the world applies with particular force in patent law. The traditional understanding that our patent law “operate[s] only domestically and d[oes] not extend to foreign activities,” Fisch & Allen, supra, at 559, is embedded in the Patent Act itself, which provides that a patent confers exclusive rights in an invention within the United States. 35 U.S.C. § 154(a)(1) (patentee's rights over invention apply to manufacture, use, or sale “throughout the United States” and to importation “into the United States”). See Deepsouth, 406 U.S., at 531, 92 S.Ct. 1700 (“Our patent system makes no claim to extraterritorial effect”; our legislation “d[oes] not, and [was] not intended to, operate beyond the limits of the United States, and we correspondingly reject the claims of others to such control over our markets.” (quoting Brown, 19 How., at 195, 15 L.Ed. 595)).

As a principle of general application, moreover, we have stated that courts should “assume that legislators take account of the legitimate sovereign interests of other nations when they write American laws.” F. Hoffmann-La Roche Ltd. v. Empagran S. A., 542 U.S. 155, 164, 124 S.Ct. 2359, 159 L.Ed.2d 226 (2004); see EEOC v. Arabian American Oil Co., 499 U.S. 244, 248, 111 S.Ct. 1227, 113 L.Ed.2d 274 (1991). Thus, the United States accurately conveyed in this case: “Foreign conduct is [generally] the domain of foreign law,” and in the area here involved, in particular, foreign law “may embody different policy judgments about the relative rights of inventors, competitors, and the public in patented inventions.” Brief for United States as Amicus Curiae 28. Applied to this case, the presumption tugs strongly against construction of § 271(f) to encompass as a “component” not only a physical copy of software, but also software's intangible code, and to render “supplie [d] ... from the United States” not only exported copies of software, but also duplicates made abroad.

AT & T argues that the presumption is inapplicable because Congress enacted § 271(f) specifically to extend the reach of United States patent law to cover certain activity abroad. But as this Court has explained, “the presumption is not defeated ... just because [a statute] specifically addresses [an] issue of extraterritorial application,” Smith v. United States, 507 U.S. 197, 204, 113 S.Ct. 1178, 122 L.Ed.2d 548 (1993); it remains instructive in determining the extent of the statutory exception. See Empagran, 542 U.S., at 161-162, 164-165, 124 S.Ct. 2359; Smith, 507 U.S., at 204, 113 S.Ct. 1178.

AT & T alternately contends that the presumption holds no sway here given that § 271(f), by its terms, applies only to domestic conduct, i.e., to the supply of a patented invention's components “from the United States.” § 271(f)(1). AT & T's reading, however, “converts a single act of supply from the United States into a springboard for liability each time a copy of the software is subsequently made [abroad] and combined with computer hardware [abroad] for sale [abroad.]” Brief for United States as Amicus Curiae 29; see 414 F.3d, at 1373, 1375 (Rader, J., dissenting). In short, foreign law alone, not United States law, currently governs the manufacture and sale of components of patented inventions in foreign countries. If AT & T desires to prevent copying in foreign countries, its remedy today lies in obtaining and enforcing foreign patents. See Deepsouth, 406 U.S., at 531, 92 S.Ct. 1700. <ref>AT & T has secured patents for its speech processor in Canada, France, Germany, Great Britain, Japan, and Sweden. App. in No. 04-1285 (CA Fed.), p. 1477. AT & T and its amici do not relate what protections and remedies are, or are not, available under these foreign regimes. Cf. Brief for Respondent 46 (observing that “foreign patent protections are sometimes weaker than their U.S. counterparts” (emphasis added)).</ref>

IV

AT & T urges that reading § 271(f) to cover only those copies of software actually dispatched from the United States creates a “loophole” for software makers. Liability for infringing a United States patent could be avoided, as Microsoft's practice shows, by an easily arranged circumvention: Instead of making installation copies of software in the United States, the copies can be made abroad, swiftly and at small cost, by generating them from a master supplied from the United States. The Federal Circuit majority found AT & T's plea compelling:

“Were we to hold that Microsoft's supply by exportation of the master versions of the Windows & reg; software-specifically for the purpose of foreign replication-avoids infringement, we would be subverting the remedial nature of § 271(f), permitting a technical avoidance of the statute by ignoring the advances in a field of technology-and its associated industry practices-that developed after the enactment of § 271(f) .... Section § 271(f), if it is to remain effective, must therefore be interpreted in a manner that is appropriate to the nature of the technology at issue.” 414 F.3d, at 1371.

While the majority's concern is understandable, we are not persuaded that dynamic judicial interpretation of § 271(f) is in order. The “loophole,” in our judgment, is properly left for Congress to consider, and to close if it finds such action warranted.

There is no dispute, we note again, that § 271(f) is inapplicable to the export of design tools-blueprints, schematics, templates, and prototypes-all of which may provide the information required to construct and combine overseas the components of inventions patented under United States law. See supra, at 1755 - 1756. We have no license to attribute to Congress an unstated intention to place the information Microsoft dispatched from the United States in a separate category.

Section 271(f) was a direct response to a gap in our patent law revealed by this Court's Deepsouth decision. See supra, at 1752, and n. 3. The facts of that case were undeniably at the fore when § 271(f) was in the congressional hopper. In Deepsouth, the items exported were kits containing all the physical, readily assemblable parts of a shrimp deveining machine (not an intangible set of instructions), and those parts themselves (not foreign-made copies of them) would be combined abroad by foreign buyers. Having attended to the gap made evident in Deepsouth, Congress did not address other arguable gaps: Section 271(f) does not identify as an infringing act conduct in the United States that facilitates making a component of a patented invention outside the United States; nor does the provision check “suppl[ying] ... from the United States” information, instructions, or other materials needed to make copies abroad.<ref>Section 271(f)'s text does, in one respect, reach past the facts of Deepsouth. While Deepsouth exported kits containing all the parts of its deveining machines, § 271(f)(1) applies to the supply abroad of “all or a substantial portion of” a patented invention's components. And § 271(f)(2) applies to the export of even a single component if it is “especially made or especially adapted for use in the invention and not a staple article or commodity of commerce suitable for substantial noninfringing use.”</ref> Given that Congress did not home in on the loophole AT & T describes, and in view of the expanded extraterritorial thrust AT & T's reading of § 271(f) entails, our precedent leads us to leave in Congress' court the patent-protective determination AT & T seeks. Cf. Sony Corp. of America v. Universal City Studios, Inc., 464 U.S. 417, 431, 104 S.Ct. 774, 78 L.Ed.2d 574 (1984) (“In a case like this, in which Congress has not plainly marked our course, we must be circumspect in construing the scope of rights created by a legislative enactment which never contemplated such a calculus of interests.”).

Congress is doubtless aware of the ease with which software (and other electronic media) can be copied, and has not left the matter untouched. In 1998, Congress addressed “the ease with which pirates could copy and distribute a copyrightable work in digital form.” Universal City Studios, Inc. v. Corley, 273 F.3d 429, 435 (C.A.2 2001). The resulting measure, the Digital Millennium Copyright Act, 17 U.S.C. § 1201 et seq., “backed with legal sanctions the efforts of copyright owners to protect their works from piracy behind digital walls such as encryption codes or password protections.” Universal City Studios, 273 F.3d, at 435. If the patent law is to be adjusted better “to account for the realities of software distribution,” 414 F.3d, at 1370, the alteration should be made after focused legislative consideration, and not by the Judiciary forecasting Congress' likely disposition.

<nowiki>* * *</nowiki>

For the reasons stated, the judgment of the Court of Appeals for the Federal Circuit is

Reversed.

THE CHIEF JUSTICE took no part in the consideration or decision of this case.

Justice ALITO, with whom Justice THOMAS and Justice BREYER join, concurring as to all but footnote 14.

I agree with the Court that no “component[s]” of the foreign-made computers involved in this case were “supplie[d]” by Microsoft “from the United States.” 35 U.S.C. § 271(f)(1). I write separately because I reach this conclusion through somewhat different reasoning.

I

Computer programmers typically write programs in a “human readable” programming language. This “ ‘source code’ ” is then generally converted by the computer into a “machine readable code” or “machine language” expressed in a binary format. Brief for Respondent 5, n. 1 (citing R. White, How Computers Work 87, 94 (8th ed.2006)); E. Walters, Essential Guide to Computing 204-205 (2001). During the Windows writing process, the program exists in the form of machine readable code on the magnetic tape fields of Microsoft's computers' hard drives. White, supra, at 144-145; Walters, supra, at 54-55.

When Microsoft finishes writing its Windows program in the United States, it encodes Windows onto CD-ROMs known as “ ‘golden masters' ” in the form of machine readable code. App. 31, ¶ 4. This is done by engraving each disk in a specific way such that another computer can read the engravings, understand what they mean, and write the code onto the magnetic fields of its hard drive. Ibid.; Brief for Petitioner 4, n. 2.

Microsoft ships these disks (or sends the code via electronic transmission) abroad, where the code is copied onto other disks that are then placed into foreign-made computers for purposes of installing the Windows program. App. 31-32, ¶¶ 5-8. No physical aspect of a Windows CD-ROM-original disk or copy-is ever incorporated into the computer itself. See Stenograph L.L.C. v. Bossard Assocs., Inc., 144 F.3d 96, 100 (C.A.D.C.1998) (noting that, within the context of the Copyright Act, “installation of software onto a computer results in ‘copying’ ”); White, supra, at 144-145, 172-173. The intact CD-ROM is then removed and may be discarded without affecting the computer's implementation of the code.<ref> In a sense, the whole process is akin to an author living prior to the existence of the printing press, who created a story in his mind, wrote a manuscript, and sent it to a scrivener, who in turn copied the story by hand into a blank book.</ref> The parties agree for purposes of this litigation that a foreign-made computer containing the Windows code would violate AT & T's patent if present in the United States. Pet. for Cert. 42a, ¶ 5.

II

A

I agree with the Court that a component of a machine, whether a shrimp deveiner or a personal computer, must be something physical. Ante, at 1754 - 1756. This is because the word “component,” when concerning a physical device, is most naturally read to mean a physical part of the device. See Webster's Third New International Dictionary 466 (1976) (component is a “constituent part: Ingredient”); Random House Dictionary of the English Language 301 (1967) (component is a “a component part; constituent”). Furthermore, § 271(f) requires that the component be “combined” with other components to form the infringing device, meaning that the component must remain a part of any. Webster's, supra, at 452 (combine means “to join in physical or chemical union”; “to become one”; “to unite into a chemical compound”); Random House, supra, at 293 (combine means “to bring or join into a close union or whole”). For these reasons, I agree with the Court that a set of instructions on how to build an infringing device, or even a template of the device, does not qualify as a component. Ante, at 1754 - 1755.

B
As the parties agree, an inventor can patent a machine that carries out a certain process, and a computer may constitute such a machine when it executes commands-given to it by code-that allow it to carry out that process. Such a computer would not become an infringing device until enough of the code is installed on the computer to allow it to execute the process in question. The computer would not be an infringing device prior to the installation, or even during the installation. And the computer remains an infringing device after the installation process because, even though the original installation device (such as a CD-ROM) has been removed from the computer, the code remains on the hard drive.

III
Here, Windows software originating in the United States was sent abroad, whether on a master disk or by means of an electronic transmission, and eventually copied onto the hard drives of the foreign-made computers. Once the copying process was completed, the Windows program was recorded in a physical form, i.e., in magnetic fields on the computers' hard drives. See Brief for Respondent 5. The physical form of the Windows program on the master disk, i.e., the engravings on the CD-ROM, remained on the disk in a form unchanged by the copying process. See Brief for Petitioner 4, n. 2 (citing White, How Computers Work, at 144-145, 172-173). There is nothing in the record to suggest that any physical part of the disk became a physical part of the foreign-made computer, and such an occurrence would be contrary to the general workings of computers.

Because no physical object originating in the United States was combined with these computers, there was no violation of § 271(f). Accordingly, it is irrelevant that the Windows software was not copied onto the foreign-made computers directly from the master disk or from an electronic transmission that originated in the United States. To be sure, if these computers could not run Windows without inserting and keeping a CD-ROM in the appropriate drive, then the CD-ROMs might be components of the computer. But that is not the case here.

<nowiki>* * *</nowiki>

Because the physical incarnation of code on the Windows CD-ROM supplied from the United States is not a “component” of an infringing device under § 271(f), it logically follows that a copy of such a CD-ROM also is not a component. For this reason, I join the Court's opinion, except for footnote 14.

Justice STEVENS, dissenting.

As the Court acknowledges, “[p]lausible arguments can be made for and against extending § 271(f) to the conduct charged in this case as infringing AT & T's patent.” Ante, at 1751. Strong policy considerations, buttressed by the presumption against the application of domestic patent law in foreign markets, support Microsoft Corporation's position. I am, however, persuaded that an affirmance of the Court of Appeals' judgment is more faithful to the intent of the Congress that enacted § 271(f) than a reversal.

The provision was a response to our decision in Deepsouth Packing Co. v. Laitram Corp., 406 U.S. 518, 92 S.Ct. 1700, 32 L.Ed.2d 273 (1972), holding that a patent on a shrimp deveining machine had not been infringed by the export of components for assembly abroad. Paragraph (1) of § 271(f) would have been sufficient on its own to overrule Deepsouth,<ref>“Whoever without authority supplies or causes to be supplied in or from the United States all or a substantial portion of the components of a patented invention, where such components are uncombined in whole or in part, in such manner as to actively induce the combination of such components outside of the United States in a manner that would infringe the patent if such combination occurred within the United States, shall be liable as an infringer.” 35 U.S.C. § 271(f)(1).</ref> but it is paragraph (2) that best supports AT & T's position here. It provides:

“Whoever without authority supplies or causes to be supplied in or from the United States any component of a patented invention that is especially made or especially adapted for use in the invention and not a staple article or commodity of commerce suitable for substantial noninfringing use, where such component is uncombined in whole or in part, knowing that such component is so made or adapted and intending that such component will be combined outside of the United States in a manner that would infringe the patent if such combination occurred within the United States, shall be liable as an infringer.” § 271(f)(2).
Under this provision, the export of a specially designed knife that has no use other than as a part of a patented deveining machine would constitute infringement. It follows that § 271(f)(2) would cover the export of an inventory of such knives to be warehoused until used to complete the assembly of an infringing machine.
The relevant component in this case is not a physical item like a knife. Both Microsoft and the Court think that means it cannot be a “component.” See ante, at 1755. But if a disk with software inscribed on it is a “component,” I find it difficult to understand why the most important ingredient of that component is not also a component. Indeed, the master disk is the functional equivalent of a warehouse of components-components that Microsoft fully expects to be incorporated into foreign-manufactured computers. Put somewhat differently: On the Court's view, Microsoft could be liable under § 271(f) only if it sends individual copies of its software directly from the United States with the intent that each copy would be incorporated into a separate infringing computer. But it seems to me that an indirect transmission via a master disk warehouse is likewise covered by § 271(f).

I disagree with the Court's suggestion that because software is analogous to an abstract set of instructions, it cannot be regarded as a “component” within the meaning of § 271(f). See ante, at 1754 - 1755. Whether attached or detached from any medium, software plainly satisfies the dictionary definition of that word. See ante, at 1755, n. 11 (observing that “ ‘[c]omponent’ is commonly defined as ‘a constituent part,’ ‘element,’ or ‘ingredient’ ”). And unlike a blueprint that merely instructs a user how to do something, software actually causes infringing conduct to occur. It is more like a roller that causes a player piano to produce sound than sheet music that tells a pianist what to do. Moreover, it is surely not “a staple article or commodity of commerce suitable for substantial noninfringing use” as that term is used in § 271(f)(2). On the contrary, its sole intended use is an infringing use.

I would therefore affirm the judgment of the Court of Appeals.

U.S.,2007.
Microsoft Corp. v. AT & T Corp.
550 U.S. 437, 127 S.Ct. 1746, 167 L.Ed.2d 737, 75 USLW 4307, 82 U.S.P.Q.2d 1400, 07 Cal. Daily Op. Serv. 4660, 20 Fla. L. Weekly Fed. S 232, 33 A.L.R. Fed. 2d 745

===Footnotes===
<references/>

Microsoft Corp v. At&T Corp., 550 U.S. 437 (2007)

2015-04-02T19:39:50Z

Bill:

AME 40590 Intellectual Property for Engineers

2015-04-02T17:57:22Z

Bill: /* ALPHABETICAL LISTING OF CASES */

Cases to add:
* Damages:
** MINTZ V. DIETZ & WATSON, INC. (CAFC, May 2012)
** Monsanto Co. v. McFarling, 488 F.3d 973, 978-79 (Fed. Cir. 2007)
** Georgia-Pacific Corp. v. US Plywood Corp., 318 F. Supp. 1116 (SDNY 1970), modified, 446 F. 2d 295 (2d Cir. 1971)
** The Boeing Company v. The United States, 86 Fed. Cl. 303 (April 2, 2009)
** Mahurkar v. CR Bard, Inc. 79 F. 3d 1572, 1580 (Fed. Cir. 1996), adopting Panduit Corp. v. Stahlin Bros. Fibre Works, Inc.,575 F.2d 1152 (6th Cir. 1978)
** Depuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 567 F.3d 1314 (Fed. Cir. 2009)

* Software patents:
** In re Alappat, 33 F.3d 1526, 1545 (Fed. Cir. 1994).
** CyberSource Corporation v. Retail Decisions, Inc., Slip Op. at 19 (2011)
** Ultramercial, LLC v. Hulu, LLC (Fed. Cir. 2011)

=ALPHABETICAL LISTING OF CASES=

*[[A. & P. Tea Co. v. Supermarket Corp., 340 U.S. 147 (1950)]]
*[[Abbott Laboratories v. Geneva Pharmaceuticals, Inc., 182 F.3d 1315 (1999)]]
*[[Alza Corp. v. Mylan Laboratories, 464 F.3d 1286, (2006)]]
*[[Anderson's Black Rock, Inc. v. Pavement Co., 396 U.S. 57 (1969)]]
*[[Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336 (1961)]]
*[[Arrhythmia Research Technology, Inc. v. Corazonix Corp., 958 F.2d 1053 (1992)]]
*[[Asgrow Seed Co. v. Winterboer, 513 U.S. 179 (1994)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. (2013)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. CAFC (2012)]]
*[[Atlas Powder v. E.I. du Pont de Nemours, 750 F2d 1569 (1984)]]
*[[Bilski v. Kappos, 130 S.Ct. 3218 (2010)]]
*[[Bobbs-Merrill Co. v. Straus, 210 U.S. 339 (1908)]]
*[[Bonito Boats. v. Thunder Craft, 489 U.S. 141 (1989)]]
*[[Bowman v. Monsanto, 133 S.Ct. 1761 (2013)]]
*[[CCS Fitness, Inc. v. Brunswick Corporation, 288 F.3d 1359 (2002)]]
*[[Chester v. Miller, 906 F.2d 1574 (1990)]]
*[[D.L. Auld Co. v. Chroma Graphics Corp., 714 F.2d 1144 (1983)]]
*[[Diamond v. Chakrabarty, 100 S.Ct. 2204 (1980)]]
*[[Diamond v. Diehr, 450 U.S. 175 (1981)]]
*[[Egbert v. Lippmann, 104 U.S. 333 (1881)]]
*[[Electric Storage Battery Co. v. Shimadzu, 307 U.S. 5 (1939)]]
*[[Elizabeth v. American Nicholson Pavement Company, 97 U.S. 126 (1877)]]
*[[Filmtec Corp. v. Allied-Signal Inc., 939 F.2d 1568 (1991)]]
*[[Funk Bros. Seed Co. v. Kalo Inoculant Co. 333 U.S. 127 (1948)]]
*[[Gottschalk v. Benson, 409 U.S. 63 (1972)]]
*[[Gould v. Hellwarth, 472 F2d 1383 (1973)]]
*[[Graham v. John Deere, 383 U.S. 1 (1966)]]
*[[Graver Tank & Mfg. Co. v. Linde Air Products Co. 339 US 605 (1950)]]
*[[H.H. Robertson, Co. v. United Steel Deck, Inc., 820 F.2d 384 (1987)]]
*[[Hotchkiss v. Greenwood, 52 U.S. 11 (1850) ]]
*[[Hybritech v. Monoclonal Antiboties, 802 F.2d 1375 (1986)]]
*[[i4i Ltd. Partnership v. Microsoft Corp., 598 F.3d 831 (2010)]]
*[[In Re Bilski]]
**[[In Re Bilski, Dky concurring opinion]]
**[[In Re Bilski, Newman dissenting opinion]]
**[[In Re Bilski, Mayer dissenting opinion]]
**[[In Re Bilski, Rader dissenting opinion]]
*[[In re Brana, 51 F.3d 1560 (1995)]]
*[[In re Carlson, 983 F.2d 1032 (1992)]]
*[[In re Hall, 781 F.2d 897 (1986)]]
*[[In re Kahn, CAFC 04-1616 (2006)]]
*[[In Re Rouffet, 149 F.3d 1350 (1998)]]
*[[J.E.M. Ag Supply, Inc. v. Pioneer Hi-Bred International, Inc., 534 U.S. 124 (2001)]]
*[[Juicy Whip v. Orange Bang, 185 F.3d 1364 (1999)]]
*[[KSR International Co. v. Teleflex, Inc., 550 U.S. 398 (2007)]]
*[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]
*[[Lorenz v. Colgate-Palmolive-Peet Co., 167 F.2d 423 (1948)]]
*[[Lough v. Brunswick Corp., 86 F.3d 1113 (1996)]]
*[[Lyon v. Bausch & Lomb, 224 F.2d 530 (1955)]]
*[[Metabolit Laboratories, Inc. and Competitive Technologies, Inc. v. Laboratory Corporation of America Holdings, 370 F.3d 1354 (2004)]]
*[[Metallizing Engineering Co., Inc. v. Kenyon Bearing & Auto Parts Co., Inc., 153 F.2d 516 (1946)]]
*[[Microsoft Corp v. At&T Corp.]]
*[[Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (1978)]]
*[[Perkin-Elmer Corporation v. Computervision Corporation, 732 F2d 888 (1984)]]
*[[Pfaff vs. Wells Electronics, 525 U.S. 55 (1998)]]
*[[Philips Electric Co. v. Thermal Industries, Inc., 450 F.2d 1164 (1971)]]
*[[Quanta Computer, Inc. v. LG Electronics, Inc., 553 U.S. 617 (2008)]]
*[[Reiner v. I. Leon Co., 285 F.2d 501 (1960)]]
*[[South Corp. v. US]]
*[[South Corp. v. US 690 F.2d 1368 (1982)]]
*[[State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (1998)]]
*[[Traffix Devices, Inc. vs. Marketing Displays, Inc.]]
*[[TurboCare Div. of Demag Delaval Turbomachinery Corp. v. General Elec. Co., 264 F.3d 1111 (2001)]]
*[[UMC Electronics Co. v. U.S., 816 F.2d 647 (1987)]]
*[[US v. Adams, 383 U.S. 39 (1966)]]
*[[U.S. v. Univis Lens Co., 316 U.S. 241 (1942)]]
*[[Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530]]
*[[Vas-Cath Inc. v. Mahurkar, 935 F.2d 1555 (1991)]]
*[[Warner-Jenkinson Company v. Hilton Davis Chemical Co., 520 US 17 (1997)]]
**[[Warner-Jenkinson v. Hilton Davis Petitioner Brief]]
**[[Warner-Jenkinson v. Hilton Davis Respondent Brief]]
*[[Winner International Royalty Co. v. Wang, 202 F.3d 1340 (2000)]]
*[[W.L. Gore & Associates, Inc. v. Garlock, Inc., 721 F.2d 1540 (1983)]]

=[[INTRODUCTION]]=
This is a summary. Click on the title for the full chapter: [[INTRODUCTION]]

Outline:
*The main purpose for obtaining a patent is ''economic''.
*It grants the exclusive right to ''make, use or sell'' the invention for a limited period of time.
*The governing law is Title 35 of the United States Code (35 USC).
*The governing regulations are from Title 37 of the Code of Federal Regulations (37 CFR).
*The law is federal, so patent cases are resolved in the federal court system:
**district courts;
**circuit courts;
**the Court of Appeals for the Federal Circuit (CAFC), a special appeals court for patent cases; and,
**the Supreme Court.
*The US Patent and Trademark Office (PTO) processes patent applications.
*Patents last for 20 years from the date the application is filed with the PTO.
*Patents have the attributes of personal property.
*The foundation of the federal government's authority to create a patent system is in the Constitution. The purposes is explicitly economic, "to promote the progress of science and useful arts..."
*Other forms of intellectual property
**copyright;
**trademarks; and,
**trade secrets.

=[[NONOBVIOUSNESS]]=
This is a summary. Click on the title for the full chapter: [[NONOBVIOUSNESS]]

Outline:

*This is perhaps the most difficult factual patent issue. In addition to meeting the novelty requirements of 35 USC 102, 35 USC 103 requires that the claimed invention as a whole must have been nonobvious "at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains."
*There is a lot of historical confusion regarding this standard. Basically, it is a notion of something being meeting some type of sufficient inventive standard or nontriviality.
*To determine this, there are three fundamental lines of inquiry:
**the scope and content of the prior art;
**the differences between the prior art and claims at issue; and,
**the level of ordinary skill in the art.
*Secondary considerations include:
**a long-felt but unsatisfied need met by the invention;
**appreciation by those versed in the art that the need existed;
**substantial attempts to meet this need;
**commercial success of the invention;
**replacement in the industry by the claimed invention;
**acquiescence by the industry;
**''teaching away'' by those skilled in the art;
**unexpectedness of the results; and,
**disbelief or incredulity on the part of industry with respect to the new invention.

=[[INFRINGEMENT]]=
This is a summary. Click on the title for the full chapter: [[INFRINGEMENT]]

=[[THE PATENT DOCUMENT]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT DOCUMENT]]

Outline:
*A patent has several parts:
**specification: describes the invention;
**claims: delineates the ownership rights;
**drawings: not required, but if they are included then any element included in the claims must be shown in the drawings; and,
**other miscellaneous parts.
*Interpreting claims: claims are said to ''read on'' another device.
*The doctrine of equivalence, prevents something from being patented that only has minor alterations from the prior art.
*The date of the invention
**''reduction to practice'';
**''diligence'' requirement.
*The ''file wrapper''.

=[[NOVELTY]]=
This is a summary. Click on the title for the full chapter: [[NOVELTY]]

Outline:
*Specified in 35 USC 102.
*Fundamentally: an invention must be ''new''.
*Section 102 basically defines in a technical way what it means to not be new:
**Events prior to invention
***known or used by others in the US
***patented or in a printed publication in another country
**Events one year before filing the patent application
***patented or in a printed publication anywhere (''in this or a foreign country'')
***in public use or on sale in the US
**Other bars
*The applicant must be the inventor (not the employer)

Outline:
*Literal Infringement
*The Doctrine of Equivalents

=[[UTILITY]]=
This is a summary. Click on the title for the full chapter: [[UTILITY]]

=[[PATENTABLE SUBJECT MATTER]]=
This is a summary. Click on the title for the full chapter: [[PATENTABLE SUBJECT MATTER]]

Can computer programs, algorithms, laws of nature, life forms, plants, ''etc.'' be patented. In particular, are the following patentable:

* Plants
* Algorithms and Computer Programs
* Scientific Facts?

In a recent case
* State Street (1998)
the CAFC substantially broadened the subject matter of section 101 to include such things as methods of doing business, etc.

=[[FOREIGN AND DOMESTIC PRIORITY]]=
This is a summary. Click on the title for the full chapter: [[FOREIGN AND DOMESTIC PRIORITY]]

Outline:
*Priority in general
*Foreign priority
*International applications
*Domestic priority
*Provisional applications

=[[THE PATENT APPLICATION]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT APPLICATION]]

Outline:
*The Disclosure
*The Claims
*Other Sections
*New Matter
*The Examination Process

=[[INVENTOR ELIGIBILITY]]=
This is a summary. Click on the title for the full chapter: [[INVENTOR ELIGIBILITY]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972): full text]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981): (full text)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005): (full text)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]

[[METABOLITE LABORATORIES, INC. and Competitive Technologies, Inc. v. LABORATORY CORPORATION OF AMERICA HOLDINGS (doing business as LabCorp): the CAFC case (full text)]]

=[[ANTICIPATION]]=
This is a summary. Click on the title for the full chapter: [[ANTICIPATION]]

=[[PRIOR ART]]=
This is a summary. Click on the title for the full chapter: [[PRIOR ART]]

[[Pfaff v. Wells Electronics: full text]]

[[Perkin-Elmer Corporation v. Computervision Corporation (full text)]]

[[Perkin-Elmer Corporation v. Computervision Corporation]]

Talk:In Re Rouffet

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Talk:In Re Rouffet, 149 F.3d 1350 (1998)

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==Courtney==

Rouffet's application discloses technology to reduce the number of handovers between beams transmitted by the same satellite. In particular, Rouffet eliminates handovers caused solely by the satellite's motion. To accomplish this goal, Rouffet changes the shape of the beam transmitted by the satellite's antenna. Rouffet's satellites transmit fan-shaped beams.

The factual predicates underlying an obviousness determination include the scope and content of the prior art, the differences between the prior art and the claimed invention, and the level of ordinary skill in the art.

The Board, however, specifically found that artisans of ordinary skill in this field of art would know to shift the frame of reference from a ground station following a satellite to a satellite transmitting to the ground.

Obviousness is determined from the vantage point of a hypothetical person having ordinary skill in the art to which the patent pertains.

To prevent the use of hindsight based on the invention to defeat patentability of the invention, this court requires the examiner to show a motivation to combine the references that create the case of obviousness. In other words, the examiner must show reasons that the skilled artisan, confronted with the same problems as the inventor and with no knowledge of the claimed invention, would select the elements from the cited prior art references for combination in the manner claimed.

This court has identified three possible sources for a motivation to combine references: the nature of the problem to be solved, the teachings of the prior art, and the knowledge of persons of ordinary skill in the art.

Because the Board did not explain the specific understanding or principle within the knowledge of a skilled artisan that would motivate one with no knowledge of Rouffet's invention to make the combination, this court infers that the examiner selected these references with the assistance of hindsight. This court forbids the use of hindsight in the selection of references that comprise the case of obviousness.

The Board's naked invocation of skill in the art to supply a suggestion to combine the references cited in this case is therefore clearly erroneous. Absent any proper motivation to combine part of Levine's teachings with Freeburg's satellite system, the rejection of Rouffet's claim over these references was improper and is reversed.

The Board reversibly erred in determining that there was a motivation to combine either the teachings of King, Rosen, and Ruddy or of Freeburg and Levine in a manner that would render the claimed invention obvious. Because this predicate was missing in each case, the Board did not properly show that these references render the claimed invention obvious. Therefore this court reverses the Board's decision upholding the rejection of Rouffet's claims. In light of this disposition, Rouffet's pending motion to remand the case to the Board for further consideration is denied as moot.

== Maura ==

The Board of Patent Appeals and Interferences (the Board) affirmed final rejection of the application as obvious under 35 U.S.C. § 103(a). See Ex parte Rouffet, No. 96- 1553 (Bd. Pat.App. & Int. Apr. 16, 1997). Because the Board reversibly erred in identifying a motivation to combine the references, this court reverses.

To reject claims in an application under section 103, an examiner must show an unrebutted prima facie case of obviousness. See In re Deuel, 51 F.3d 1552, 1557, 34 U.S.P.Q.2d 1210, 1214 (Fed.Cir.1995). In the absence of a proper prima facie case of obviousness, an applicant who complies with the other statutory requirements is entitled to a patent. See In re Oetiker, 977 F.2d 1443, 1445, 24 U.S.P.Q.2d 1443, 1444 (Fed.Cir.1992). On appeal to the Board, an applicant can overcome a rejection by showing insufficient evidence of prima facie obviousness or by rebutting the prima facie case with evidence of secondary indicia of nonobviousness. See id.
While this court reviews the Board's determination in light of the entire record, an applicant may specifically challenge an obviousness rejection by showing that the Board reached an incorrect conclusion of obviousness or that the Board based its obviousness determination on incorrect factual predicates.

The factual predicates underlying an obviousness determination include the scope and content of the prior art, the differences between the prior art and the claimed invention, and the level of ordinary skill in the art.
'A finding is clearly erroneous when, although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.' " In re Graves, 69 F.3d 1147, 1151, 36 U.S.P.Q.2d 1697, 1700 (Fed.Cir.1995) (quoting United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 92 L.Ed. 746 (1948)).
This objective evidence of nonobviousness includes copying, long felt but unsolved need, failure of others, see Graham v. John Deere Co., 383 U.S. 1, 17-18, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966), commercial success, see In re Huang, 100 F.3d 135, 139-40, 40 U.S.P.Q.2d 1685, 1689-90 (Fed.Cir.1996), unexpected results created by the claimed invention, unexpected properties of the claimed invention, see In re Mayne, 104 F.3d 1339, 1342, 41 U.S.P.Q.2d 1451, 1454 (Fed.Cir.1997); In re Woodruff, 919 F.2d 1575, 1578, 16 U.S.P.Q.2d 1934, 1936-37 (Fed.Cir.1990), licenses showing industry respect for the invention, see Arkie Lures, Inc. v. Gene Larew Tackle, Inc., 119 F.3d 953, 957, 43 U.S.P.Q.2d 1294, 1297 (Fed.Cir.1997); Pentec, Inc. v. Graphic Controls Corp., 776 F.2d 309, 316, 227 U.S.P.Q. 766, 771 (Fed.Cir.1985), and skepticism of skilled artisans before the invention, see In re Dow Chem. Co., 837 F.2d 469, 473, 5 U.S.P.Q.2d 1529, 1532 (Fed.Cir.1988).

Therefore, "[w]hen determining the patentability of a claimed invention which combines two known elements, 'the question is whether there is something in the prior art as a whole to suggest the desirability, and thus the obviousness, of making the combination.

The Board provides no reasons that one of ordinary skill in this art, seeking to minimize handovers due to satellite motion, would combine Ruddy with Rosen and King in a manner that would render the claimed invention obvious.
Obviousness is determined from the vantage point of a hypothetical person having ordinary skill in the art to which the patent pertains. See 35 U.S.C. § 103(a). This legal construct is akin to the "reasonable person" used as a reference in negligence determinations. The legal construct also presumes that all prior art references in the field of the invention are available to this hypothetical skilled artisan. See In re Carlson, 983 F.2d 1032, 1038, 25 U.S.P.Q.2d 1207, 1211 (Fed.Cir.1993).

("Most, if not all, inventions are combinations and mostly of old elements."). Therefore an examiner may often find every element of a claimed invention in the prior art. If identification of each claimed element in the prior art were sufficient to negate patentability, very few patents would ever issue. Furthermore, rejecting patents solely by finding prior art corollaries for the claimed elements would permit an examiner to use the claimed invention itself as a blueprint for piecing together elements in the prior art to defeat the patentability of the claimed invention. Such an approach would be "an illogical and inappropriate process by which to determine patentability." Sensonics, Inc. v. Aerosonic Corp., 81 F.3d 1566, 1570, 38 U.S.P.Q.2d 1551, 1554 (Fed.Cir.1996).
To prevent the use of hindsight based on the invention to defeat patentability of the invention, this court requires the examiner to show a motivation to combine the references that create the case of obviousness. In other words, the examiner must show reasons that the skilled artisan, confronted with the same problems as the inventor and with no knowledge of the claimed invention, would select the elements from the cited prior art references for combination in the manner claimed.
This court has identified three possible sources for a motivation to combine references: the nature of the problem to be solved, the teachings of the prior art, and the knowledge of persons of ordinary skill in the art. In this case, the Board relied upon none of these. Rather, just as it relied on the high level of skill in the art to overcome the differences between the claimed invention and the selected elements in the references, it relied upon the high level of skill in the art to provide the necessary motivation. The Board did not, however, explain what specific understanding or technological principle within the knowledge of one of ordinary skill in the art would have suggested the combination. Instead, the Board merely invoked the high level of skill in the field of art. If such a rote invocation could suffice to supply a motivation to combine, the more sophisticated scientific fields would rarely, if ever, experience a patentable technical advance. Instead, in complex scientific fields, the Board could routinely identify the prior art elements in an application, invoke the lofty level of skill, and rest its case for rejection. To counter this potential weakness in the obviousness construct, the suggestion to combine requirement stands as a critical safeguard against hindsight analysis and rote application of the legal test for obviousness.

As noted above, the suggestion to combine requirement is a safeguard against the use of hindsight combinations to negate patentability. While the skill level is a component of the inquiry for a suggestion to combine, a lofty level of skill alone does not suffice to supply a motivation to combine. Otherwise a high level of ordinary skill in an art field would almost always preclude patentable inventions. As this court has often noted, invention itself is the process of combining prior art in a nonobvious manner. See, e.g., Richdel, 714 F.2d at 1579; Environmental Designs, 713 F.2d at 698. Therefore, even when the level of skill in the art is high, the Board must identify specifically the principle, known to one of ordinary skill, that suggests the claimed combination. Cf. Gechter v. Davidson, 116 F.3d 1454, 43 U.S.P.Q.2d 1030 (Fed.Cir.1997) (explaining that the Board's opinion must describe the basis for its decision). In other words, the Board must explain the reasons one of ordinary skill in the art would have been motivated to select the references and to combine them to render the claimed invention obvious.

== Kevin ==

The examiner initially rejected Rouffet's claims as unpatentable over U.S. Pat. No. 5,199,672 (King) in view of U.S. Pat. No. 4,872,015 (Rosen) and a conference report entitled "A Novel Non-Geostationary Satellite Communications System," Conference Record, International Conference on Communications, 1981 (Ruddy). On appeal to the Board, the examiner added an alternative ground for rejection, holding that the claims were obvious over U.S. Pat. No. 5,394,561 (Freeburg) in view of U.S. Pat. No. 5,170,485 (Levine).

To reject claims in an application under section 103, an examiner must show an unrebutted prima facie case of obviousness. See In re Deuel, 51 F.3d 1552, 1557, 34 U.S.P.Q.2d 1210, 1214 (Fed.Cir.1995). In the absence of a proper prima facie case of obviousness, an applicant who complies with the other statutory requirements is entitled to a patent. See In re Oetiker, 977 F.2d 1443, 1445, 24 U.S.P.Q.2d 1443, 1444 (Fed.Cir.1992). On appeal to the Board, an applicant can overcome a rejection by showing insufficient evidence of prima facie obviousness or by rebutting the prima facie case with evidence of secondary indicia of nonobviousness. See id.

When a rejection depends on a combination of prior art references, there must be some teaching, suggestion, or motivation to combine the references. See In re Geiger, 815 F.2d 686, 688, 2 U.S.P.Q.2d 1276, 1278 (Fed.Cir.1987). Although the suggestion to combine references may flow from the nature of the problem, see Pro-Mold & Tool Co. v. Great Lakes Plastics, Inc., 75 F.3d 1568, 1573, 37 U.S.P.Q.2d 1626, 1630 (Fed.Cir.1996), the suggestion more often comes from the teachings of the pertinent references, see In re Sernaker, 702 F.2d 989, 994, 217 U.S.P.Q. 1, 5 (Fed.Cir.1983), or from the ordinary knowledge of those skilled in the art that certain references are of special importance in a particular field, see Pro-Mold, 75 F.3d at 1573 (citing Ashland Oil, Inc. v. Delta Resins & Refractories, Inc., 776 F.2d 281, 297 n. 24, 227 U.S.P.Q. 657, 667 n. 24 (Fed.Cir.1985)). Therefore, "[w]hen determining the patentability of a claimed invention which combines two known elements, 'the question is whether there is something in the prior art as a whole to suggest the desirability, and thus the obviousness, of making the combination.' " See In re Beattie, 974 F.2d 1309, 1311-12, 24 U.S.P.Q.2d 1040, 1042 (Fed.Cir.1992) (quoting Lindemann Maschinenfabrik GMBH v. American Hoist & Derrick Co., 730 F.2d 1452, 1462, 221 U.S.P.Q. 481, 488 (Fed.Cir.1984)).
III

The parties agree that the five references asserted by the examiner are in the same field of endeavor as the invention. The parties also agree that the pertinent level of skill in the art--design of satellite communications systems--is high. On appeal, Rouffet asserts that the examiner and the Board erred by improperly combining references to render the claimed invention obvious.
The Combination of King, Rosen, and Ruddy
The Board first affirmed the rejection of Rouffet's claims over a combination of King, Rosen, and Ruddy. King discloses a system for launching a plurality of satellites into low Earth orbits from a single launch vehicle. Rosen teaches a geostationary satellite that uses a plurality of fan beams with their long axes oriented in an east-west direction to communicate with mobile and fixed terminals on the Earth.

Obviousness is determined from the vantage point of a hypothetical person having ordinary skill in the art to which the patent pertains. See 35 U.S.C. § 103(a). This legal construct is akin to the "reasonable person" used as a reference in negligence determinations. The legal construct also presumes that all prior art references in the field of the invention are available to this hypothetical skilled artisan. See In re Carlson, 983 F.2d 1032, 1038, 25 U.S.P.Q.2d 1207, 1211 (Fed.Cir.1993).
As this court has stated, "virtually all [inventions] are combinations of old elements." Environmental Designs, Ltd. v. Union Oil Co., 713 F.2d 693, 698, 218 U.S.P.Q. 865, 870 (Fed.Cir.1983); see also Richdel, Inc. v. Sunspool Corp., 714 F.2d 1573, 1579-80, 219 U.S.P.Q. 8, 12 (Fed.Cir.1983) ("Most, if not all, inventions are combinations and mostly of old elements."). Therefore an examiner may often find every element of a claimed invention in the prior art. If identification of each claimed element in the prior art were sufficient to negate patentability, very few patents would ever issue. Furthermore, rejecting patents solely by finding prior art corollaries for the claimed elements would permit an examiner to use the claimed invention itself as a blueprint for piecing together elements in the prior art to defeat the patentability of the claimed invention. Such an approach would be "an illogical and inappropriate process by which to determine patentability." Sensonics, Inc. v. Aerosonic Corp., 81 F.3d 1566, 1570, 38 U.S.P.Q.2d 1551, 1554 (Fed.Cir.1996).
To prevent the use of hindsight based on the invention to defeat patentability of the invention, this court requires the examiner to show a motivation to combine the references that create the case of obviousness. In other words, the examiner must show reasons that the skilled artisan, confronted with the same problems as the inventor and with no knowledge of the claimed invention, would select the elements from the cited prior art references for combination in the manner claimed.
This court has identified three possible sources for a motivation to combine references: the nature of the problem to be solved, the teachings of the prior art, and the knowledge of persons of ordinary skill in the art. In this case, the Board relied upon none of these. Rather, just as it relied on the high level of skill in the art to overcome the differences between the claimed invention and the selected elements in the references, it relied upon the high level of skill in the art to provide the necessary motivation. The Board did not, however, explain what specific understanding or technological principle within the knowledge of one of ordinary skill in the art would have suggested the combination. Instead, the Board merely invoked the high level of skill in the field of art. If such a rote invocation could suffice to supply a motivation to combine, the more sophisticated scientific fields would rarely, if ever, experience a patentable technical advance. Instead, in complex scientific fields, the Board could routinely identify the prior art elements in an application, invoke the lofty level of skill, and rest its case for rejection. To counter this potential weakness in the obviousness construct, the suggestion to combine requirement stands as a critical safeguard against hindsight analysis and rote application of the legal test for obviousness.

As noted above, the suggestion to combine requirement is a safeguard against the use of hindsight combinations to negate patentability. While the skill level is a component of the inquiry for a suggestion to combine, a lofty level of skill alone does not suffice to supply a motivation to combine. Otherwise a high level of ordinary skill in an art field would almost always preclude patentable inventions. As this court has often noted, invention itself is the process of combining prior art in a nonobvious manner. See, e.g., Richdel, 714 F.2d at 1579; Environmental Designs, 713 F.2d at 698. Therefore, even when the level of skill in the art is high, the Board must identify specifically the principle, known to one of ordinary skill, that suggests the claimed combination.

In Re Rouffet

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In Re Rouffet, 149 F.3d 1350 (1998)

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In Re Denis Rouffet Yannick Tanguy and Frederic Berthault

149 F.3d 1350

47 U.S.P.Q.2d 1453

In re Denis ROUFFET, Yannick Tanguy and Frederic Berthault.

No. 97-1492.

United States Court of Appeals,
Federal Circuit.

July 15, 1998.

Richard C. Turner and Grant K. Rowan, Sughrue, Mion, Zinn, Macpeak & Seas, PLLC, Washington, DC, argued for appellants.

David J. Ball, Jr., Associate Solicitor, Office of the Solicitor, Patent and Trademark Office, Arlington, Virginia, argued for appellee. With him on the brief were Nancy J. Linck, Solicitor, Albin F. Drost, Deputy Solicitor, and Craig R. Kaufman, Associate Solicitor. Of counsel was Scott A. Chambers, Associate Solicitor, Office of the Solicitor.

Before PLAGER, Circuit Judge, ARCHER, Senior Circuit Judge, and RADER, Circuit Judge.

RADER, Circuit Judge.

Denis Rouffet, Yannick Tanguy, and Frederic Bethault (collectively, Rouffet) submitted application 07/888,791 (the application) on May 27, 1992. The Board of Patent Appeals and Interferences (the Board) affirmed final rejection of the application as obvious under 35 U.S.C. § 103(a). See Ex parte Rouffet, No. 96-1553 (Bd. Pat.App. & Int. Apr. 16, 1997). Because the Board reversibly erred in identifying a motivation to combine the references, this court reverses.

I.

Satellites in a geosynchronous or geostationary orbit remain over the same point on the Earth's surface. Their constant position above the Earth's surface facilitates communications. These satellites project a number of beams to the Earth. Each beam transmits to its area of coverage, or footprint, on the Earth's surface. In order to provide complete coverage, adjacent footprints overlap slightly and therefore must use different frequencies to avoid interference. However, two or more non-overlapping footprints can use the same set of frequencies in order to use efficiently the limited radio spectrum. Figure 1 from the application shows the coverage of a portion of the Earth's surface provided by multiple cone shaped beams:FIG. 1

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Frequency reuse techniques, however, have a limited ability to compensate for congestion in geostationary orbits. To alleviate the orbit congestion problem, new telecommunications systems use a network of satellites in low Earth orbit. When viewed from a fixed point on the Earth's surface, such satellites do not remain stationary but move overhead. A satellite's motion as it transmits a plurality of cone-shaped beams creates a new problem. The satellite's movement causes a receiver on the Earth's surface to move from the footprint of one beam into a second beam transmitted by the same satellite. Eventually, the satellite's motion causes the receiver to move from the footprint of a beam transmitted by one satellite into the footprint of a beam transmitted by a second satellite. Each switch from one footprint to another creates a "handover" event analogous to that which occurs when a traditional cellular phone travels from one cell to another. Handovers are undesirable because they can cause interruptions in signal transmission and reception.

Rouffet's application discloses technology to reduce the number of handovers between beams transmitted by the same satellite. In particular, Rouffet eliminates handovers caused solely by the satellite's motion. To accomplish this goal, Rouffet changes the shape of the beam transmitted by the satellite's antenna. Rouffet's satellites transmit fan-shaped beams. A fan beam has an elliptical footprint. Rouffet aligns the long axis of his beams parallel to the direction of the satellite's motion across the Earth's surface. By elongating the beam's footprint in the direction of satellite travel, Rouffet's invention ensures that a fixed point on the Earth's surface likely will remain within a single footprint until it is necessary to switch to another satellite. Because Rouffet's invention does not address handovers caused by the motion of the receiver across the Earth's surface. his arrangement reduces, but does not eliminate, handovers. Figure 3 from the application shows the footprints 12 from six beams aligned in the direction of satellite motion 15:

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The application contains ten claims that stand or fall as a group. Claim 1 is representative:

A low orbit satellite communications system for mobile terminals, wherein the communications antenna system of each satellite provides isoflux coverage made up of a plurality of fan beams that are elongate in the travel direction of the satellite.

The examiner initially rejected Rouffet's claims as unpatentable over U.S. Pat. No. 5,199,672 (King) in view of U.S. Pat. No. 4,872,015 (Rosen) and a conference report entitled "A Novel Non-Geostationary Satellite Communications System," Conference Record, International Conference on Communications, 1981 (Ruddy). On appeal to the Board, the examiner added an alternative ground for rejection, holding that the claims were obvious over U.S. Pat. No. 5,394,561 (Freeburg) in view of U.S. Pat. No. 5,170,485 (Levine).

On April 16, 1997, the Board issued its decision. Because Rouffet had specified that the claims would stand or fall as a group based on the patentability of claim 1, the Board limited its opinion to that claim. The Board unanimously determined that the examiner had properly rejected claim 1 as obvious over King in view of Rosen and Ruddy. The Board, on a split vote, also affirmed the rejection over Freeburg in view of Levine.II

To reject claims in an application under section 103, an examiner must show an unrebutted prima facie case of obviousness. See In re Deuel, 51 F.3d 1552, 1557, 34 U.S.P.Q.2d 1210, 1214 (Fed.Cir.1995). In the absence of a proper prima facie case of obviousness, an applicant who complies with the other statutory requirements is entitled to a patent. See In re Oetiker, 977 F.2d 1443, 1445, 24 U.S.P.Q.2d 1443, 1444 (Fed.Cir.1992). On appeal to the Board, an applicant can overcome a rejection by showing insufficient evidence of prima facie obviousness or by rebutting the prima facie case with evidence of secondary indicia of nonobviousness. See id.

While this court reviews the Board's determination in light of the entire record, an applicant may specifically challenge an obviousness rejection by showing that the Board reached an incorrect conclusion of obviousness or that the Board based its obviousness determination on incorrect factual predicates. This court reviews the ultimate determination of obviousness as a question of law. See In re Lueders, 111 F.3d 1569, 1571, 42 U.S.P.Q.2d 1481, 1482 (Fed.Cir.1997). The factual predicates underlying an obviousness determination include the scope and content of the prior art, the differences between the prior art and the claimed invention, and the level of ordinary skill in the art. See Monarch Knitting Mach. Corp. v. Sulzer Morat GmbH, 139 F.3d 877, 881, 45 U.S.P.Q.2d 1977, 1981 (Fed.Cir.1998). This court reviews the Board's factual findings for clear error. See In re Zurko, 142 F.3d, 1447, 1449, 46 U.S.P.Q.2d 1691, 1693 (Fed.Cir.1998) (in banc); Lueders, 111 F.3d at 1571-72. " 'A finding is clearly erroneous when, although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.' " In re Graves, 69 F.3d 1147, 1151, 36 U.S.P.Q.2d 1697, 1700 (Fed.Cir.1995) (quoting United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 92 L.Ed. 746 (1948)).

The secondary considerations are also essential components of the obviousness determination. See In re Emert, 124 F.3d 1458, 1462, 44 U.S.P.Q.2d 1149, 1153 (Fed.Cir.1997) ("Without Emert providing rebuttal evidence, this prima facie case of obviousness must stand."). This objective evidence of nonobviousness includes copying, long felt but unsolved need, failure of others, see Graham v. John Deere Co., 383 U.S. 1, 17-18, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966), commercial success, see In re Huang, 100 F.3d 135, 139-40, 40 U.S.P.Q.2d 1685, 1689-90 (Fed.Cir.1996), unexpected results created by the claimed invention, unexpected properties of the claimed invention, see In re Mayne, 104 F.3d 1339, 1342, 41 U.S.P.Q.2d 1451, 1454 (Fed.Cir.1997); In re Woodruff, 919 F.2d 1575, 1578, 16 U.S.P.Q.2d 1934, 1936-37 (Fed.Cir.1990), licenses showing industry respect for the invention, see Arkie Lures, Inc. v. Gene Larew Tackle, Inc., 119 F.3d 953, 957, 43 U.S.P.Q.2d 1294, 1297 (Fed.Cir.1997); Pentec, Inc. v. Graphic Controls Corp., 776 F.2d 309, 316, 227 U.S.P.Q. 766, 771 (Fed.Cir.1985), and skepticism of skilled artisans before the invention, see In re Dow Chem. Co., 837 F.2d 469, 473, 5 U.S.P.Q.2d 1529, 1532 (Fed.Cir.1988). The Board must consider all of the applicant's evidence. See Oetiker, 977 F.2d at 1445 ("An observation by the Board that the examiner made a prima facie case is not improper, as long as the ultimate determination of patentability is made on the entire record."); In re Piasecki, 745 F.2d 1468, 1472, 223 U.S.P.Q. 785, 788 (Fed.Cir.1984). The court reviews factual conclusions drawn from this evidence for clear error. Whether the evidence presented suffices to rebut the prima facie case is part of the ultimate conclusion of obviousness and is therefore a question of law.

When a rejection depends on a combination of prior art references, there must be some teaching, suggestion, or motivation to combine the references. See In re Geiger, 815 F.2d 686, 688, 2 U.S.P.Q.2d 1276, 1278 (Fed.Cir.1987). Although the suggestion to combine references may flow from the nature of the problem, see Pro-Mold & Tool Co. v. Great Lakes Plastics, Inc., 75 F.3d 1568, 1573, 37 U.S.P.Q.2d 1626, 1630 (Fed.Cir.1996), the suggestion more often comes from the teachings of the pertinent references, see In re Sernaker, 702 F.2d 989, 994, 217 U.S.P.Q. 1, 5 (Fed.Cir.1983), or from the ordinary knowledge of those skilled in the art that certain references are of special importance in a particular field, see Pro-Mold, 75 F.3d at 1573 (citing Ashland Oil, Inc. v. Delta Resins & Refractories, Inc., 776 F.2d 281, 297 n. 24, 227 U.S.P.Q. 657, 667 n. 24 (Fed.Cir.1985)). Therefore, "[w]hen determining the patentability of a claimed invention which combines two known elements, 'the question is whether there is something in the prior art as a whole to suggest the desirability, and thus the obviousness, of making the combination.' " See In re Beattie, 974 F.2d 1309, 1311-12, 24 U.S.P.Q.2d 1040, 1042 (Fed.Cir.1992) (quoting Lindemann Maschinenfabrik GMBH v. American Hoist & Derrick Co., 730 F.2d 1452, 1462, 221 U.S.P.Q. 481, 488 (Fed.Cir.1984)).

III

The parties agree that the five references asserted by the examiner are in the same field of endeavor as the invention. The parties also agree that the pertinent level of skill in the art--design of satellite communications systems--is high. On appeal, Rouffet asserts that the examiner and the Board erred by improperly combining references to render the claimed invention obvious.

The Combination of King, Rosen, and Ruddy

The Board first affirmed the rejection of Rouffet's claims over a combination of King, Rosen, and Ruddy. King discloses a system for launching a plurality of satellites into low Earth orbits from a single launch vehicle. Rosen teaches a geostationary satellite that uses a plurality of fan beams with their long axes oriented in an east-west direction to communicate with mobile and fixed terminals on the Earth.

The final, and most important, reference in this combination is Ruddy. Ruddy describes a television broadcast system that uses a series of satellites to retransmit signals sent from a ground station over a wide area. Rather than using a geostationary orbit, Ruddy teaches the use of a series of satellites in Molniya orbits. A satellite in a Molniya orbit always follows the same path through the sky when viewed from a fixed point on the ground. Viewed from the Earth, the orbital path includes a narrow, elliptical apogee loop. In order to transmit to these moving satellites from a ground station, Ruddy uses a fan beam with a long axis aligned with the long axis of the orbit's apogee loop. This alignment places the entire apogee loop within the footprint of the beam and eliminates the need for the ground station's antenna to track the satellite's motion around the apogee loop. Ruddy further teaches orbit parameters and spacing of multiple satellites to ensure that a satellite is always in the loop to receive and rebroadcast signals from the Earth station.

King and Rosen together teach the use of a network of satellites in low Earth orbit. Thus, Ruddy becomes the piece of the prior art mosaic that shows, in the reading of the Board, the use of "a plurality of fan beams that are elongate in the travel direction of the satellite." Ruddy, however, is different from the claimed invention in several respects. Specifically, the application claims the projection of multiple elliptical fan-shaped footprints from the satellite to the ground. See Claim 1, supra, see also Application at 6, lines 9-11 ("In addition, in this system, the geometrical shape of the beams 12 is changed: instead of being circular they are now elongate ellipses."). The application's written description further teaches that the invention's fan-shaped satellite beams will minimize handovers. See id. at lines 11-16 ("This considerably increases call durations between handovers.").

In contrast, Ruddy teaches that a ground station may use a single fan-shaped beam to transmit to a satellite in a unique Molniya orbit. The ground station transmits a beam into which a series of satellites in Molniya orbits will successively enter. At least two differences are evident: the application teaches projection of multiple beams from a satellite to the Earth, while Ruddy teaches projection of a single beam from the Earth to satellites. Moreover to the extent Ruddy contains a teaching about handovers, its teachings focus on use of the unique Molniya orbit to ensure that a satellite always falls within the beam transmitted by the ground station.

These differences suggest some difficulty in showing a prima facie case of obviousness. The Board, however, specifically found that artisans of ordinary skill in this field of art would know to shift the frame of reference from a ground station following a satellite to a satellite transmitting to the ground. According proper deference to the Board's finding of a lofty skill level for ordinary artisans in this field, this court discerns no clear error in the Board's conclusion that these differences would not preclude a finding of obviousness. While Ruddy does not expressly teach alignment of the fan beam with the apparent direction of the satellite's motion, this court perceives no clear error in the Board's determination that Ruddy would suggest such an alignment to one of skill in this art. Therefore, the Board did not err in finding that the combination of King, Rosen, and Ruddy contains all of the elements claimed in Rouffet's application.

However, the Board reversibly erred in determining that one of skill in the art would have been motivated to combine these references in a manner that rendered the claimed invention obvious. Indeed, the Board did not identify any motivation to choose these references for combination. Ruddy does not specifically address handover minimization. To the extent that Ruddy at all addresses handovers due to satellite motion, it addresses this subject through the selection of orbital parameters. Ruddy does not teach the choice of a particular shape and alignment of the beam projected by the satellite. Thus Ruddy addresses the handover problem with an orbit selection, not a beam shape. The Board provides no reasons that one of ordinary skill in this art, seeking to minimize handovers due to satellite motion, would combine Ruddy with Rosen and King in a manner that would render the claimed invention obvious.

Obviousness is determined from the vantage point of a hypothetical person having ordinary skill in the art to which the patent pertains. See 35 U.S.C. § 103(a). This legal construct is akin to the "reasonable person" used as a reference in negligence determinations. The legal construct also presumes that all prior art references in the field of the invention are available to this hypothetical skilled artisan. See In re Carlson, 983 F.2d 1032, 1038, 25 U.S.P.Q.2d 1207, 1211 (Fed.Cir.1993).

As this court has stated, "virtually all [inventions] are combinations of old elements." Environmental Designs, Ltd. v. Union Oil Co., 713 F.2d 693, 698, 218 U.S.P.Q. 865, 870 (Fed.Cir.1983); see also Richdel, Inc. v. Sunspool Corp., 714 F.2d 1573, 1579-80, 219 U.S.P.Q. 8, 12 (Fed.Cir.1983) ("Most, if not all, inventions are combinations and mostly of old elements."). Therefore an examiner may often find every element of a claimed invention in the prior art. If identification of each claimed element in the prior art were sufficient to negate patentability, very few patents would ever issue. Furthermore, rejecting patents solely by finding prior art corollaries for the claimed elements would permit an examiner to use the claimed invention itself as a blueprint for piecing together elements in the prior art to defeat the patentability of the claimed invention. Such an approach would be "an illogical and inappropriate process by which to determine patentability." Sensonics, Inc. v. Aerosonic Corp., 81 F.3d 1566, 1570, 38 U.S.P.Q.2d 1551, 1554 (Fed.Cir.1996).

To prevent the use of hindsight based on the invention to defeat patentability of the invention, this court requires the examiner to show a motivation to combine the references that create the case of obviousness. In other words, the examiner must show reasons that the skilled artisan, confronted with the same problems as the inventor and with no knowledge of the claimed invention, would select the elements from the cited prior art references for combination in the manner claimed.

This court has identified three possible sources for a motivation to combine references: the nature of the problem to be solved, the teachings of the prior art, and the knowledge of persons of ordinary skill in the art. In this case, the Board relied upon none of these. Rather, just as it relied on the high level of skill in the art to overcome the differences between the claimed invention and the selected elements in the references, it relied upon the high level of skill in the art to provide the necessary motivation. The Board did not, however, explain what specific understanding or technological principle within the knowledge of one of ordinary skill in the art would have suggested the combination. Instead, the Board merely invoked the high level of skill in the field of art. If such a rote invocation could suffice to supply a motivation to combine, the more sophisticated scientific fields would rarely, if ever, experience a patentable technical advance. Instead, in complex scientific fields, the Board could routinely identify the prior art elements in an application, invoke the lofty level of skill, and rest its case for rejection. To counter this potential weakness in the obviousness construct, the suggestion to combine requirement stands as a critical safeguard against hindsight analysis and rote application of the legal test for obviousness.

Because the Board did not explain the specific understanding or principle within the knowledge of a skilled artisan that would motivate one with no knowledge of Rouffet's invention to make the combination, this court infers that the examiner selected these references with the assistance of hindsight. This court forbids the use of hindsight in the selection of references that comprise the case of obviousness. See In re Gorman, 933 F.2d 982, 986, 18 U.S.P.Q.2d 1885, 1888 (Fed.Cir.1991). Lacking a motivation to combine references, the Board did not show a proper prima facie case of obviousness. This court reverses the rejection over the combination of King, Rosen, and Ruddy.

The Combination of Freeburg and Levine

Freeburg teaches a cellular radiotelephone system based on a constellation of low Earth orbit satellites that use conical beams to transmit from the satellite to both fixed and mobile Earth stations. Levine teaches an Earth-based cellular radio system that uses fan beams broadcast from antenna towers. Levine's elliptical footprints are aligned with the road grid. To increase the capacity of traditional ground-based systems through frequency reuse techniques, Levine teaches the use of antennas that broadcast signals with smaller footprints than the prior art system. Thus, Levine actually increases the number of overlap regions between cells and, hence, the number of potential handovers. Figure 1 of the Levine patent illustrates its alignment of beam footprints:

NOTE: OPINION CONTAINS TABLE OR OTHER DATA THAT IS NOT VIEWABLEAs a mobile unit (e.g., a driver using a car phone) moves though a succession of overlapping zones, Levine uses selection algorithms to determine which of the cells is aligned with the travel direction of the mobile unit. These algorithms then select this cell for use while continually monitoring intersecting cells in the event that the mobile unit changes direction.

Once again, this court notes significant differences between the teachings of the application and the Levine-Freeburg combination. The critical Levine reference again involves a beam from an Earth station without any reference to the "travel direction of [a] satellite." Moreover, Levine actually multiplies the number of potential handovers and then uses software to sort out the necessary handovers from the unnecessary. However, the Board explains the reasons that one possessing the lofty skills characteristic of this field would know to account for the differences between the claimed invention and the prior art combination. This court discerns no clear error in that reliance on the considerable skills in this field.

This court does, however, discern reversible error in the Board's identification of a motivation to combine Levine and Freeburg. In determining that one of skill in the art would have had motivation to combine Levine and Freeburg, the Board noted that "[t]he level of skill in the art is very high." As noted before, this observation alone cannot supply the required suggestion to combine these references. The Board posits that the high level of skill in the art overcomes the absence of any actual suggestion that one could select part of the teachings of Levine for combination with the satellite system disclosed by Freeburg.

As noted above, the suggestion to combine requirement is a safeguard against the use of hindsight combinations to negate patentability. While the skill level is a component of the inquiry for a suggestion to combine, a lofty level of skill alone does not suffice to supply a motivation to combine. Otherwise a high level of ordinary skill in an art field would almost always preclude patentable inventions. As this court has often noted, invention itself is the process of combining prior art in a nonobvious manner. See, e.g., Richdel, 714 F.2d at 1579; Environmental Designs, 713 F.2d at 698. Therefore, even when the level of skill in the art is high, the Board must identify specifically the principle, known to one of ordinary skill, that suggests the claimed combination. Cf. Gechter v. Davidson, 116 F.3d 1454, 43 U.S.P.Q.2d 1030 (Fed.Cir.1997) (explaining that the Board's opinion must describe the basis for its decision). In other words, the Board must explain the reasons one of ordinary skill in the art would have been motivated to select the references and to combine them to render the claimed invention obvious.

The Board's naked invocation of skill in the art to supply a suggestion to combine the references cited in this case is therefore clearly erroneous. Absent any proper motivation to combine part of Levine's teachings with Freeburg's satellite system, the rejection of Rouffet's claim over these references was improper and is reversed.

IV

The Board reversibly erred in determining that there was a motivation to combine either the teachings of King, Rosen, and Ruddy or of Freeburg and Levine in a manner that would render the claimed invention obvious. Because this predicate was missing in each case, the Board did not properly show that these references render the claimed invention obvious. Therefore this court reverses the Board's decision upholding the rejection of Rouffet's claims. In light of this disposition, Rouffet's pending motion to remand the case to the Board for further consideration is denied as moot.

COSTS

Each party shall bear its own costs.

REVERSED.

In Re Bilski, Rader dissenting opinion

2015-04-02T17:54:55Z

Bill:

RADER, Circuit Judge, dissenting.

This court labors for page after page, paragraph after paragraph, explanation after explanation to say what could have been said in a single sentence: “Because Bilski claims merely an abstract idea, this court affirms the Board's rejection.” If the only problem of this vast judicial tome were its circuitous path, I would not dissent, but this venture also disrupts settled and wise principles of law.

Much of the court's difficulty lies in its reliance on dicta taken out of context from numerous Supreme Court opinions dealing with the technology of the past. In other words, as innovators seek the path to the next tech no-revolution, this court ties our patent system to dicta from an industrial age decades removed from the bleeding edge. A direct reading of the Supreme Court's principles and cases on patent eligibility would yield the one-sentence resolution suggested above. Because this court, however, links patent eligibility to the age of iron and steel at a time of subatomic particles and terabytes, I must respectfully dissent.

I

The Patent Law of the United States has always embodied the philosophy that “ingenuity should receive a liberal encouragement.” Writings of Thomas Jefferson 75-76 (Washington ed. 1871); see also Diamond v. Chakrabarty, 447 U.S. 303, 308-09, 100 S.Ct. 2204, 65 L.Ed.2d 144 (1980). True to this principle, the original Act made “ any new and useful art, machine, manufacture or composition of matter” patent eligible. Act of Feb. 21, 1793, ch. 11, § 1, 1 Stat. 318 (emphasis supplied). Even as the laws have evolved, that bedrock principle remains at their foundation. Thus, the Patent Act from its inception focused patentability on the specific characteristics of the claimed invention-its novelty and utility-not on its particular subject matter category.

The modern incarnation of section 101 holds fast to that principle, setting forth the broad categories of patent eligible subject matter, and conditioning patentability on the characteristics, not the category, of the claimed invention:

Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.

35 U.S.C. § 101 (2006) (emphases supplied). As I have suggested, the Supreme Court requires this court to rely on the “ordinary, contemporary, common meaning” of these words. Diamond v. Diehr, 450 U.S. 175, 182, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981). If this court would follow that Supreme Court rule, it would afford broad patent protection to new and useful inventions that fall within the enumerated categories and satisfy the other conditions of patentability. That is, after all, precisely what the statute says.

In Diehr, the Supreme Court adopted a very useful algorithm for determining patentable subject matter, namely, follow the Patent Act itself. After setting forth the procedural history of that case, the Supreme Court stated: “In cases of statutory construction, we begin with the language of the statute.” Diehr, 450 U.S. at 182, 101 S.Ct. 1048. With an eye to the Benson language (so central to this court's reasoning) that “[t]ransformation and reduction of an article ‘to a different state or thing’ is the clue to the patentability of a process claim that does not include particular machines,” Gottschalk v. Benson, 409 U.S. 63, 72, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972), the Court then noted:

[I]n dealing with the patent laws, we have more than once cautioned that “courts ‘should not read into the patent laws limitations and conditions which the legislature has not expressed.’ ”

Diehr, 450 U.S. at 182, 101 S.Ct. 1048 (citations omitted). Indeed section 101's term “process” contains no hint of an exclusion for certain types of methods. This court today nonetheless holds that a process is eligible only if it falls within certain subsets of “process.” Ironically the Patent Act itself specifically defines “process” without any of these judicial innovations. 35 U.S.C. § 100(b). Therefore, as Diehr commands, this court should refrain from creating new circuitous judge-made tests.

Read in context, section 101 gives further reasons for interpretation without innovation. Specifically, section 101 itself distinguishes patent eligibility from the conditions of patentability-providing generously for patent eligibility, but noting that patentability requires substantially more. The language sweeps in “ any new and useful process ... [and] any improvement.” 35 U.S.C. § 101 (emphasis supplied). As an expansive modifier, “any” embraces the broad and ordinary meanings of the term “process,” for instance. The language of section 101 conveys no implication that the Act extends patent protection to some subcategories of processes but not others. It does not mean “some” or even “most,” but all.

Unlike the laws of other nations that include broad exclusions to eligible subject matter, such as European restrictions on software and other method patents, see European Patent Convention of 1973, Art. 52(2)(c) and (3), and prohibitions against patents deemed contrary to the public morality, see id. at Art. 53(a), U.S. law and policy have embraced advances without regard to their subject matter. That promise of protection, in turn, fuels the research that, at least for now, makes this nation the world's innovation leader.

II

With all of its legal sophistry, the court's new test for eligibility today does not answer the most fundamental question of all: why would the expansive language of section 101 preclude protection of innovation simply because it is not transformational or properly linked to a machine (whatever that means)? Stated even more simply, why should some categories of invention deserve no protection?

This court, which reads the fine print of Supreme Court decisions from the Industrial Age with admirable precision, misses the real import of those decisions. The Supreme Court has answered the fundamental question above many times. The Supreme Court has counseled that the only limits on eligibility are inventions that embrace natural laws, natural phenomena, and abstract ideas. See, e.g., Diehr, 450 U.S. at 185, 101 S.Ct. 1048 (“This Court has undoubtedly recognized limits to § 101 and every discovery is not embraced within the statutory terms. Excluded from such patent protection are laws of nature, natural phenomena, and abstract ideas.”). In Diehr, the Supreme Court's last pronouncement on eligibility for “processes,” the Court said directly that its only exclusions from the statutory language are these three common law exclusions: “Our recent holdings ... stand for no more than these long-established principles.” Id. at 185, 101 S.Ct. 1048.

This point deserves repetition. The Supreme Court stated that all of the transformation and machine linkage explanations simply restated the abstractness rule. In reading Diehr to suggest a non-statutory transformation or preemption test, this court ignores the Court's admonition that all of its recent holdings do no more than restate the natural laws and abstractness exclusions. Id.; see also Chakrabarty, 447 U.S. at 310, 100 S.Ct. 2204 (“Here, by contrast, the patentee has produced a new bacterium with markedly different characteristics from any found in nature and one having the potential for significant utility. His discovery is not nature's handiwork, but his own; accordingly it is patentable subject matter under § 101.”); Parker v. Flook, 437 U.S. 584, 591-594, 98 S.Ct. 2522, 57 L.Ed.2d 451 (1978) (“Even though a phenomenon of nature or mathematical formula may be well known, an inventive application of the principle may be patented. Conversely, the discovery of such a phenomenon cannot support a patent unless there is some other inventive concept in its application.”); In re Taner, 681 F.2d 787, 791 (C.C.P.A 1982) (“In Diehr, the Supreme Court made clear that Benson stands for no more than the long-established principle that laws of nature, natural phenomena, and abstract ideas are excluded from patent protection.”).

The abstractness and natural law preclusions not only make sense, they explain the purpose of the expansive language of section 101. Natural laws and phenomena can never qualify for patent protection because they cannot be invented at all. After all, God or Allah or Jahveh or Vishnu or the Great Spirit provided these laws and phenomena as humanity's common heritage. Furthermore, abstract ideas can never qualify for patent protection because the Act intends, as section 101 explains, to provide “useful” technology. An abstract idea must be applied to (transformed into) a practical use before it qualifies for protection. The fine print of Supreme Court opinions conveys nothing more than these basic principles. Yet this court expands (transforms?) some Supreme Court language into rules that defy the Supreme Court's own rule.

When considering the eligibility of “processes,” this court should focus on the potential for an abstract claim. Such an abstract claim would appear in a form that is not even susceptible to examination against prior art under the traditional tests for patentability. Thus this court would wish to ensure that the claim supplied some concrete, tangible technology for examination. Indeed the hedging claim at stake in this appeal is a classic example of abstractness. Bilski's method for hedging risk in commodities trading is either a vague economic concept or obvious on its face. Hedging is a fundamental economic practice long prevalent in our system of commerce and taught in any introductory finance class. In any event, this facially abstract claim does not warrant the creation of new eligibility exclusions.

III

This court's willingness to venture away from the statute follows on the heels of an oft-discussed dissent from the Supreme Court's dismissal of its grant of certiorari in Lab. Corp. of Am. Holdings v. Metabolite Labs., Inc., 548 U.S. 124, 126 S.Ct. 2921, 165 L.Ed.2d 399 (2006). That dissent is premised on a fundamental misapprehension of the distinction between a natural phenomenon and a patentable process.

The distinction between “phenomena of nature,” “mental processes,” and “abstract intellectual concepts” is not difficult to draw. The fundamental error in that Lab. Corp. dissent is its failure to recognize the difference between a patent ineligible relationship-i.e., that between high homocysteine levels and folate and cobalamin deficiencies-and a patent eligible process for applying that relationship to achieve a useful, tangible, and concrete result-i.e., diagnosis of potentially fatal conditions in patients. Nothing abstract here. Moreover, testing blood for a dangerous condition is not a natural phenomenon, but a human invention.

The distinction is simple but critical: A patient may suffer from the unpatentable phenomenon of nature, namely high homocysteine levels and low folate. But the invention does not attempt to claim that natural phenomenon. Instead the patent claims a process for assaying a patient's blood and then analyzing the results with a new process that detects the life-threatening condition. Moreover, the sick patient does not practice the patented invention. Instead the patent covers a process for testing blood that produces a useful, concrete, and tangible result: incontrovertible diagnostic evidence to save lives. The patent does not claim the patent ineligible relationship between folate and homocysteine, nor does it foreclose future inventors from using that relationship to devise better or different processes. Contrary to the language of the dissent, it is the sick patient who “embod[ies] only the correlation between homocysteine and vitamin deficiency,” Lab. Corp., 548 U.S. at 137, 126 S.Ct. 2921, not the claimed process.

From the standpoint of policy, the Lab. Corp. dissent avoids the same fundamental question that the Federal Circuit does not ask or answer today: Is this entire field of subject matter undeserving of incentives for invention? If so, why? In the context of Lab. Corp. that question is very telling: the natural condition diagnosed by the invention is debilitating and even deadly. See U.S. Patent No. 4,940,658, col. 1, ll. 32-40 (“Accurate and early diagnosis of cobalamin and folate deficiencies ... is important because these deficiencies can lead to life-threatening hematologic abnormalities.... Accurate and early diagnosis of cobalamin deficiency is especially important because it can also lead to incapacitating and life-threatening neuropsychiatric abnormalities.”). Before the invention featured in Lab. Corp., medical science lacked an affordable, reliable, and fast means to detect this debilitating condition. Denial of patent protection for this innovation-precisely because of its elegance and simplicity (the chief aims of all good science)-would undermine and discourage future research for diagnostic tools. Put another way, does not Patent Law wish to encourage researchers to find simple blood tests or urine tests that predict and diagnose breast cancers or immunodeficiency diseases? In that context, this court might profitably ask whether its decisions incentivize research for cures and other important technical advances. Without such attention, this court inadvertently advises investors that they should divert their unprotectable investments away from discovery of “scientific relationships” within the body that diagnose breast cancer or Lou Gehrig's disease or Parkinson's or whatever.

IV

In sum, this court today invents several circuitous and unnecessary tests. It should have merely noted that Bilski attempts to patent an abstract idea. Nothing more was needed. Instead this opinion propagates unanswerable questions: What form or amount of “transformation” suffices? When is a “representative” of a physical object sufficiently linked to that object to satisfy the transformation test? (e.g., Does only vital sign data taken directly from a patient qualify, or can population data derived in part from statistics and extrapolation be used?) What link to a machine is sufficient to invoke the “or machine” prong? Are the “specific” machines of Benson required, or can a general purpose computer qualify? What constitutes “extra-solution activity?” If a process may meet eligibility muster as a “machine,” why does the Act “require” a machine link for a “process” to show eligibility? Does the rule against redundancy itself suggest an inadequacy in this complex spider web of tests supposedly “required” by the language of section 101?

One final point, reading section 101 as it is written will not permit a flurry of frivolous and useless inventions. Even beyond the exclusion for abstractness, the final clause of section 101-“subject to the conditions and requirements of this title”-ensures that a claimed invention must still satisfy the “conditions and requirements” set forth in the remainder title 35. Id. These statutory conditions and requirements better serve the function of screening out unpatentable inventions than some vague “transformation” or “proper machine link” test.

In simple terms, the statute does not mention “transformations” or any of the other Industrial Age descriptions of subject matter categories that this court endows with inordinate importance today. The Act has not empowered the courts to impose limitations on patent eligible subject matter beyond the broad and ordinary meaning of the terms process, machine, manufacture, and composition of matter. It has instead preserved the promise of patent protection for still unknown fields of invention.

Innovation has moved beyond the brick and mortar world. Even this court's test, with its caveats and winding explanations seems to recognize this. Today's software transforms our lives without physical anchors. This court's test not only risks hobbling these advances, but precluding patent protection for tomorrow's technologies. “We still do not know one thousandth of one percent of what nature has revealed to us.” Attributed to Albert Einstein. If this court has its way, the Patent Act may not incentivize, but complicate, our search for the vast secrets of nature. When all else fails, consult the statute.

545 F.3d 943, 2008-2 USTC P 50,621, 88 U.S.P.Q.2d 1385

In Re Bilski, Mayer dissenting opinion

2015-04-02T17:53:53Z

Bill:

MAYER, Circuit Judge, dissenting.

The en banc order in this case asked: “Whether it is appropriate to reconsider State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (Fed.Cir.1998), and AT & T Corp. v. Excel Communications, Inc., 172 F.3d 1352 (Fed.Cir.1999), in this case and, if so, whether those cases should be overruled in any respect?” I would answer that question with an emphatic “yes.” The patent system is intended to protect and promote advances in science and technology, not ideas about how to structure commercial transactions. Claim 1 of the application of Bernard L. Bilski and Rand A. Warsaw (“Bilski”) is not eligible for patent protection because it is directed to a method of conducting business. Affording patent protection to business methods lacks constitutional and statutory support, serves to hinder rather than promote innovation and usurps that which rightfully belongs in the public domain. State Street and AT & T should be overruled.

I.

In discussing the scope of copyright protection, the Supreme Court has noted that “ ‘a page of history is worth a volume of logic.’ ” Eldred v. Ashcroft, 537 U.S. 186, 200, 123 S.Ct. 769, 154 L.Ed.2d 683 (2003) (quoting New York Trust Co. v. Eisner, 256 U.S. 345, 349, 41 S.Ct. 506, 65 L.Ed. 963 (1921)). The same holds true with respect to patent protection. From a historical perspective, it is highly unlikely that the framers of the Constitution's intellectual property clause intended to grant patent protection to methods of conducting business. To the contrary, “those who formulated the Constitution were familiar with the long struggle over monopolies so prominent in English history, where exclusive rights to engage even in ordinary business activities were granted so frequently by the Crown for the financial benefits accruing to the Crown only.” In re Yuan, 38 C.C.P.A. 967, 188 F.2d 377, 380 (1951). The Statute of Monopolies,<ref>The Statute of Monopolies “grew out of abuses in the grant of exclusive franchises in various lines of business such as trading cards, alehouses and various staple products.” Robert P. Merges, As Many as Six Impossible Patents Before Breakfast: Property Rights for Business Concepts and Patent System Reform, 14 Berkeley Tech. L.J. 577, 585 (1999).</ref> enacted in 1624, curtailed the Crown's ability to grant “monopolies to court favorites in goods or businesses which had long before been enjoyed by the public.” Graham v. John Deere Co., 383 U.S. 1, 5, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966). When drafting the Constitution, the framers were well aware of the abuses that led to the English Statute of Monopolies and therefore “consciously acted to bar Congress from granting letters patent in particular types of business.” In re Comiskey, 499 F.3d 1365, 1375 (Fed.Cir.2007); see also Malla Pollack, The Multiple Unconstitutionality of Business Method Patents: Common Sense, Congressional Consideration, and Constitutional History, 28 Rutgers Computer & Tech. L.J. 61, 90 (2002) (“[T]he ratifying generation did not agree to invention patents on advances in trade itself, because trade monopolies were odious.”).

There is nothing in the early patent statutes to indicate that Congress intended business methods to constitute patentable subject matter. See Patent Act of 1790 § 4, 1 Stat. 109, 111 (1790); Patent Act of 1793 § 1, 1 Stat. 318, 319 (1793); Pollack, supra at 106 (“[I]f any nation was ripe for invention patents on business methods, it was the newly freed colonies of British North America.... [H]owever, no business method patents seem to have been granted.”). As early as 1869, the Commissioner of Patents said that “[i]t is contrary ... to the spirit of the law, as construed by the office for many years, to grant patents for methods of book-keeping,” Ex parte Abraham, 1869 Dec. Comm'r Pat. 59, 59 (1869), and by 1893 the courts had concluded that “a method of transacting common business ... does not seem to be patentable as an art,” United States Credit Sys. Co. v. Am. Credit Indem. Co., 53 F. 818, 819 (C.C.S.D.N.Y.1893), aff'd on other grounds, 59 F. 139 (2d Cir.1893). By 1952, when Congress enacted the current Patent Act, it was widely acknowledged that methods of doing business were ineligible for patent protection. See, e.g., Loew's Drive-In Theatres, Inc. v. Park-In Theatres, Inc., 174 F.2d 547, 552 (1st Cir.1949) (“[A] system for the transaction of business ... however novel, useful, or commercially successful is not patentable apart from the means for making the system practically useful, or carrying it out.”); In re Patton, 29 C.C.P.A. 982, 127 F.2d 324 (1942) (noting that “a system of transacting business, apart from the means for carrying out such system” is not patentable); Hotel Sec. Checking Co. v. Lorraine Co., 160 F. 467, 469 (2d Cir.1908) (“A system of transacting business disconnected from the means for carrying out the system is not, within the most liberal interpretation of the term, an art.”); In re Moeser, 27 App. D.C. 307, 310 (1906) (holding that a system for burial insurance contracts was not patentable because “contracts or proposals for contracts, devised or adopted as a method of transacting a particular class of ... business, [are] not patentable as an art”); see also 145 Cong. Rec. H6,947 (Aug. 3, 1999) (statement of Rep. Manzullo) (“Before the State Street Bank and Trust case ... it was universally thought that methods of doing or conducting business were not patentable items.”).

In passing the 1952 Act, Congress re-enacted statutory language that had long existed,<ref>Congress did substitute the word “process” for “art” in the 1952 Act, but “[a]nalysis of the eligibility of a claim of patent protection for a ‘process' did not change with the addition of that term to § 101.” Diamond v. Diehr, 450 U.S. 175, 184, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981).</ref> thus signaling its intent to carry forward the body of case law that had developed under prior versions of the statute. Because there is nothing in the language of the 1952 Act, or its legislative history, to indicate that Congress intended to modify the rule against patenting business methods, we must presume that no change in the rule was intended. See, e.g., Astoria Fed. Sav. & Loan Ass'n v. Solimino, 501 U.S. 104, 108, 111 S.Ct. 2166, 115 L.Ed.2d 96 (1991) (“[W]here a common-law principle is well established ... the courts may take it as given that Congress has legislated with an expectation that the principle will apply except when a statutory purpose to the contrary is evident.” (citations and internal quotation marks omitted)); Isbrandtsen Co. v. Johnson, 343 U.S. 779, 783, 72 S.Ct. 1011, 96 L.Ed. 1294 (1952) (“Statutes which invade the common law ... are to be read with a presumption favoring the retention of long-established and familiar principles, except when a statutory purpose to the contrary is evident.”); see also In re Schrader, 22 F.3d 290, 295 (Fed.Cir.1994) (“When Congress approved the addition of the term ‘process' to the categories of patentable subject matter in 1952, it incorporated the definition of ‘process' that had evolved in the courts.” (footnote omitted)). If Congress had wished to change the established practice of disallowing patents on business methods, it was quite capable of doing so explicitly. See Parker v. Flook, 437 U.S. 584, 596, 98 S.Ct. 2522, 57 L.Ed.2d 451 (1978) (stressing that courts “must proceed cautiously when ... asked to extend patent rights into areas wholly unforeseen by Congress”).

State Street's decision to jettison the prohibition against patenting methods of doing business contravenes congressional intent. Because (1) “the framers consciously acted to bar Congress from granting letters patent in particular types of business,” Comiskey, 499 F.3d at 1375, and (2) Congress evidenced no intent to modify the long-established rule against business method patents when it enacted the 1952 Patent Act, it is hard to fathom how the issuance of patents on business methods can be supported.

II.

Business method patents have been justified, in significant measure, by a misapprehension of the legislative history of the 1952 Patent Act. In particular, proponents of such patents have asserted that the Act's legislative history states that Congress intended statutory subject matter to “include anything under the sun that is made by man.” AT & T, 172 F.3d at 1355 (Fed.Cir.1999) (citations and internal quotation marks omitted); see also Diamond v. Chakrabarty, 447 U.S. 303, 309, 100 S.Ct. 2204, 65 L.Ed.2d 144 (1980). Read in context, however, the legislative history says no such thing. The full statement from the committee report reads: “A person may have ‘invented’ a machine or a manufacture, which may include anything under the sun that is made by man, but it is not necessarily patentable under section 101 unless the conditions of the title are fulfilled.” S.Rep. No.1979, 82d Cong., 2d Sess. 5 (1952), U.S.Code Cong. & Admin.News 1952, pp. 2394, 2399 (emphasis added); H.R.Rep. No.1923, 82d Cong., 2d Sess. 6 (1952) (emphasis added).

This statement does not support the contention that Congress intended “anything under the sun” to be patentable. To the contrary, the language supports the opposite view: a person may have “invented” anything under the sun, but it is “not necessarily patentable” unless the statutory requirements for patentability have been satisfied. Thus, the legislative history oft-cited to support business method patents undercuts, rather than supports, the notion that Congress intended to extend the scope of section 101 to encompass such methods.

Moreover, the cited legislative history is not discussing process claims at all. The quoted language is discussing “machines” and “manufactures;” it is therefore surprising that it has been thought a fit basis for allowing patents on business processes.

III.

The Constitution does not grant Congress unfettered authority to issue patents. See U.S. Const. art. I, § 8.<ref>Article I, § 8 provides that “The Congress shall have Power ... To promote the Progress of Science and useful Arts by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.” The patent power “is the only one of the several powers conferred upon the Congress which is accompanied by a specific statement of the reason for it.” Yuan, 188 F.2d at 380.</ref> Instead, the patent power is a “qualified authority ... [which] is limited to the promotion of advances in the ‘useful arts.’ ” Graham, 383 U.S. at 5, 86 S.Ct. 684; see also KSR Int'l Co. v. Teleflex Inc., 550 U.S. 398, 127 S.Ct. 1727, 1746, 167 L.Ed.2d 705 (2007) (reaffirming that patents are designed to promote “the progress of useful arts”). What the framers described as “useful arts,” we in modern times call “technology.” Paulik v. Rizkalla, 760 F.2d 1270, 1276 (Fed.Cir.1985) (en banc). Therefore, by mandating that patents advance the useful arts, “[t]he Constitution explicitly limited patentability to ... ‘the process today called technological innovation.’ ” Comiskey, 499 F.3d at 1375 (quoting Paulik, 760 F.2d at 1276); see also In re Foster, 58 C.C.P.A. 1001, 438 F.2d 1011 (1971) (“All that is necessary ... to make a sequence of operational steps a statutory ‘process' within 35 U.S.C. § 101 is that it be in the technological arts.”); Karl B. Lutz, Patents and Science: A Clarification of the Patent Clause of the U.S. Constitution, 18 Geo. Wash. L.Rev. 50, 54 (1949) (“The term ‘useful arts' as used in the Constitution ... is best represented in modern language by the word ‘technology.’ ”); James S. Sfekas, Controlling Business Method Patents: How the Japanese Standard for Patenting Software Could Bring Reasonable Limitations to Business Method Patents in the United States, 16 Pac. Rim. L. & Pol'y J. 197, 214 (2007) (At the time the Patent Clause was adopted, “the term ‘useful arts' was commonly used in contrast to the ideas of the ‘liberal arts' and the ‘fine arts,’ which were well-known ideas in the eighteenth century.”).

Before State Street led us down the wrong path, this court had rightly concluded that patents were designed to protect technological innovations, not ideas about the best way to run a business.<ref>“[D]espite the assertions in State Street and Schrader, very few in the patent community believe that business methods have always been patentable. To the contrary, the dominant view is that the law has changed, and that the definition of patentable subject matter is now wider than it once was.” R. Carl Moy, Subjecting Rembrandt to the Rule of Law: Rule-Based Solutions for Determining the Patentability of Business Methods, 28 Wm. Mitchell L.Rev. 1047, 1060 (2002) (footnotes omitted); see also Rochelle Cooper Dreyfuss, Are Business Method Patents Bad for Business?, 16 Santa Clara Computer & High Tech. L.J. 263, 265-66 (2000) ( State Street gave “judicial recognition to business method patents.”). Over the course of two centuries, a few patents issued on what could arguably be deemed methods of doing business, see, e.g., U.S. Patent No. 5,664,115 (“Interactive Computer System to Match Buyers and Sellers of Real Estate, Businesses and Other Property Using the Internet”), but these patents were aberrations and the general rule, prior to State Street, was that methods of engaging in business were ineligible for patent protection. See Comiskey, 499 F.3d at 1374 (noting that “[a]t one time, ‘[t]hough seemingly within the category of process or method, a method of doing business [was] rejected as not being within the statutory classes.’ ” (quoting State Street, 149 F.3d at 1377)). One commentator has noted that although the United States Patent and Trademark Office (“USPTO”) “in an attempt to deflect criticism [has] issued an apologia ... asserting that business method patents are as old as the United States patent system,” this document is fundamentally flawed. See Pollack, supra at 73-75. She explains:
The USPTO wants us to believe that it found no records of patents whose points of invention were business methods, because no one had time to invent any new business methods until the human race had run its mechanical ingenuity to the peak of computer software; seemingly we were all too busy inventing the computer to think about anything else-especially new ways of doing business. I thought that we granted patents because, otherwise, people would be too busy making money by running businesses to take time out to invent anything except business methods. The USPTO [document], furthermore, is eliding the printed matter exception to patentable subject matter with the business method exception.
Id. at 75 (footnote omitted). </ref> We had thus rejected as unpatentable a method for coordinating firefighting efforts, Patton, 127 F.2d at 326-27, a method for deciding how salesmen should best handle customers, In re Maucorps, 609 F.2d 481 (CCPA 1979), and a computerized method for aiding a neurologist in diagnosing patients, In re Meyer, 688 F.2d 789 (CCPA 1982).<ref>The claims in Patton were explicitly rejected on the basis that they were directed to a business method, while the claims in Maucorps and Meyer were rejected as attempts to patent mathematical algorithms. Subsequently, however, this court stated that the claimed processes in Maucorps and Meyer were directed toward business systems and should therefore not be considered patent eligible. In re Alappat, 33 F.3d 1526, 1541 (Fed.Cir.1994) (en banc). We noted that “ Maucorps dealt with a business methodology for deciding how salesmen should best handle respective customers and Meyer involved a ‘system’ for aiding a neurologist in diagnosing patients. Clearly, neither of the alleged ‘inventions' in those cases falls within any § 101 category.” Id.</ref> We stated that patentable processes must “be in the technological arts so as to be in consonance with the Constitutional purpose to promote the progress of ‘useful arts.’ ” In re Musgrave, 57 C.C.P.A. 1352, 431 F.2d 882, 893 (CCPA 1970) (emphasis added).

Business method patents do not promote the “useful arts” because they are not directed to any technological or scientific innovation. Although business method applications may use technology-such as computers-to accomplish desired results, the innovative aspect of the claimed method is an entrepreneurial rather than a technological one. Thus, although Bilski's claimed hedging method could theoretically be implemented on a computer, that alone does not render it patentable. See Diehr, 450 U.S. at 192 n. 14, 101 S.Ct. 1048 (Patentability cannot be established by the “token” use of technology.); Gottschalk v. Benson, 409 U.S. 63, 64-66, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972) (finding unpatentable a method of programming a general purpose digital computer to convert signals from binary-coded decimal to pure binary form). Where a claimed business method simply uses a known machine to do what it was designed to do, such as using a computer to gather data or perform calculations, use of that machine will not bring otherwise unpatentable subject matter within the ambit of section 101. See Benson, 409 U.S. at 67, 93 S.Ct. 253 (finding a process unpatentable where “[t]he mathematical procedures [could] be carried out in existing computers long in use, no new machinery being necessary”).

Although the Supreme Court has not directly addressed the patentability of business methods, several of its decisions implicitly tether patentability to technological innovation. See Pfaff v. Wells Elecs., Inc., 525 U.S. 55, 63, 119 S.Ct. 304, 142 L.Ed.2d 261 (1998) (“[T]he patent system represents a carefully crafted bargain that encourages both the creation and the public disclosure of new and useful advances in technology, in return for an exclusive monopoly for a limited period of time.” (emphasis added)); Markman v. Westview Instruments, Inc., 517 U.S. 370, 390, 116 S.Ct. 1384, 134 L.Ed.2d 577 (1996) (“Congress created the Court of Appeals for the Federal Circuit as an exclusive appellate court for patent cases ... observing that increased uniformity would strengthen the United States patent system in such a way as to foster technological growth and industrial innovation.” (citations and internal quotation marks omitted) (emphasis added)); Benson, 409 U.S. at 71, 93 S.Ct. 253 (refusing to “freeze [the patentability of] process patents to old technologies, leaving no room for the revelations of the new, onrushing technology ” (emphases added)). Indeed, the Supreme Court has repeatedly emphasized that what renders subject matter patentable is “the application of the law of nature to a new and useful end.” Funk Bros. Seed Co. v. Kalo Inoculant Co., 333 U.S. 127, 130, 68 S.Ct. 440, 92 L.Ed. 588 (1948); see Diehr, 450 U.S. at 188 n. 11, 101 S.Ct. 1048; Benson, 409 U.S. at 67, 93 S.Ct. 253.<ref>Laws of nature are those laws pertaining to the “natural sciences,” such as biology, chemistry, or physics. See, e.g., Webster's New International Dictionary 1507 (3d ed. 2002) (“Natural sciences” are the “branches of science ( [such] as physics, chemistry, [or] biology) that deal with matter, energy, and their interrelations and transformations or with objectively measured phenomena.”). They must be distinguished from other types of law, such as laws of economics or statutory enactments. Laws of nature do not involve “judgments on human conduct, ethics, morals, economics, politics, law, aesthetics, etc.” Musgrave, 431 F.2d at 890; see also Joy Y. Xiang, How Wide Should the Gate of “Technology” Be? Patentability of Business Methods in China, 11 Pac. Rim L. & Pol'y J. 795, 807 (2002) (noting that State Street's “ ‘useful, concrete and tangible result’ test is inconsistent with the ‘application of the law of nature’ patent eligibility scope outlined by the U.S. Supreme Court and [the Federal Circuit prior to State Street ].”).</ref> Applying laws of nature to new and useful ends is nothing other than “technology.”<ref>One commentator notes that both Japan and the Republic of Korea explicitly define an “invention” as the application of a law of nature, and argues that the United States should follow a similar approach to patentability. See Andrew A. Schwartz, The Patent Office Meets the Poison Pill: Why Legal Methods Cannot be Patented, 20 Harv. J. Law & Tech. 333, 357 (2007).</ref> See, e.g., Microsoft Computer Dictionary 513 (5th ed. 2002) (The definition of “technology” is the “application of science and engineering to the development of machines and procedures in order to enhance or improve human conditions.”); American Heritage Dictionary of the English Language 1777 (4th ed. 2000) (“Technology” is the “application of science, especially to industrial or commercial objectives.”); see also Sfekas, supra at 214-15 (“The [Supreme] Court's holdings in Benson and Diehr are really stating a requirement that inventions must be technological.”); Schwartz, supra at 357 (The “clear and consistent body of Supreme Court case law establishes that the term ‘invention’ encompasses anything made by man that utilizes or harnesses one or more ‘laws of nature’ for human benefit.”). As the Supreme Court has made clear, “the act of invention ... consists neither in finding out the laws of nature, nor in fruitful research as to the operation of natural laws, but in discovering how those laws may be utilized or applied for some beneficial purpose, by a process, a device or a machine.” United States v. Dubilier Condenser Corp., 289 U.S. 178, 188, 53 S.Ct. 554, 77 L.Ed. 1114 (1933).

Methods of doing business do not apply “the law of nature to a new and useful end.” Because the innovative aspect of such methods is an entrepreneurial rather than a technological one, they should be deemed ineligible for patent protection. See, e.g., John R. Thomas, The Patenting of the Liberal Professions, 40 B.C. L.Rev. 1139 (1999) (arguing that affording patentability to business methods opens the door to obtaining patent protection for all aspects of human thought and behavior, and that patents should remain grounded in science and technology) (hereinafter “Thomas (1999)”). “[T]he primary purpose of our patent laws is not the creation of private fortunes for the owners of patents but is ‘to promote the progress of science and useful arts.’ ” Motion Picture Patents Co. v. Universal Film Mfg. Co., 243 U.S. 502, 511, 37 S.Ct. 416, 61 L.Ed. 871 (1917). Although business method patents may do much to enrich their owners, they do little to promote scientific research and technological innovation.

IV.

State Street has launched a legal tsunami, inundating the patent office with applications seeking protection for common business practices.<ref>Congress has acted to ameliorate some of the negative effects of granting patents on methods of doing business. It passed the American Inventors Protection Act (commonly referred to as the First Inventor Defense Act) which provides an affirmative defense against a business method patent infringement action if the defendant “acting in good faith, actually reduced the subject matter to practice at least 1 year before the effective filing date of such patent, and commercially used the subject matter before the effective filing date of such patent.” See 35 U.S.C. § 273. Even where a defendant may qualify for this defense, however, he “still must engage in expensive litigation where [he] bears the burden of affirmatively raising and proving the defense.” See Nicholas A. Smith, Business Method Patents and Their Limits: Justifications, History, and the Emergence of A Claim Construction Jurisprudence, 9 Mich. Telecomm. & Tech. L.Rev. 171, 199 (2002).</ref> Applications for Class 705 (business method) patents increased from fewer than 1,000 applications in 1997 to more than 11,000 applications in 2007. See United States Patent and Trademark Office, Class 705 Application Filings and Patents Issued Data, available at http:// www. uspto. gov/ web/ menu/ pbmethod/ application filing. htm (information available as of Jan. 2008); see Douglas L. Price, Assessing the Patentability of Financial Services and Products, 3 J. High Tech. L. 141, 153 (2004) (“The State Street case has opened the floodgates on business method patents.”).

Patents granted in the wake of State Street have ranged from the somewhat ridiculous to the truly absurd. See, e.g., U.S. Patent No. 5,851,117 (method of training janitors to dust and vacuum using video displays); U.S. Patent No. 5,862,223 (method for selling expert advice); U.S. Patent No. 6,014,643 (method for trading securities); U.S. Patent No. 6,119,099 (method of enticing customers to order additional food at a fast food restaurant); U.S. Patent No. 6,329,919 (system for toilet reservations); U.S. Patent No. 7,255,277 (method of using color-coded bracelets to designate dating status in order to limit “the embarrassment of rejection”). There has even been a patent issued on a method for obtaining a patent. See U.S. Patent No. 6,049,811. Not surprisingly, State Street and its progeny have generated a thundering chorus of criticism. See Leo J. Raskind, The State Street Bank Decision: The Bad Business of Unlimited Patent Protection for Methods of Doing Business, 10 Fordham Intell. Prop. Media & Ent. L.J. 61, 61 (1999) (“The Federal Circuit's recent endorsement of patent protection for methods of doing business marks so sweeping a departure from precedent as to invite a search for its justification.”); Pollack, supra at 119-20 (arguing that State Street was based upon a misinterpretation of both the legislative history and the language of section 101 and that “business method patents are problematical both socially and constitutionally”); Price, supra at 155 (“The fall out from State Street has created a gold-rush mentality toward patents and litigation in which companies .... gobble up patents on anything and everything.... It is a mad rush to get as many dumb patents as possible.” (citations and internal quotation marks omitted)); Thomas (1999), supra at 1160 (“After State Street, it is hardly an exaggeration to say that if you can name it, you can claim it.”); Sfekas, supra at 226 (“[T]he U.S. courts have set too broad a standard for patenting business methods.... These business method patents tend to be of lower quality and are unnecessary to achieve the goal of encouraging innovation in business.”); William Krause, Sweeping the E-Commerce Patent Minefield: The Need for a Workable Business Method Exception, 24 Seattle U.L.Rev. 79, 101 (2000) ( State Street “opened up a world of unlimited possession to anyone quick enough to take a business method and put it to use via computer software before anyone else.”); Moy, supra at 1051 (“To call [the situation following State Street ] distressing is an understatement. The consensus ... appears to be that patents should not be issuing for new business methods.”).

There are a host of difficulties associated with allowing patents to issue on methods of conducting business. Not only do such patents tend to impede rather than promote innovation, they are frequently of poor quality. Most fundamentally, they raise significant First Amendment concerns by imposing broad restrictions on speech and the free flow of ideas.

A.
“[T]he underlying policy of the patent system [is] that ‘the things which are worth to the public the embarrassment of an exclusive patent,’ ... must outweigh the restrictive effect of the limited patent monopoly.” Graham, 383 U.S. at 10-11, 86 S.Ct. 684 (quoting letter from Thomas Jefferson to Isaac McPherson (Aug. 1813)). Thus, Congress may not expand the scope of “the patent monopoly without regard to the ... advancement or social benefit gained thereby.” Id. at 6, 86 S.Ct. 684.

Patents should be granted to those inventions “which would not be disclosed or devised but for the inducement of a patent.” Id. at 11, 86 S.Ct. 684. Methods of doing business have existed since the earliest days of the Patent Act and have flourished even in the absence of patent protection. See Brian P. Biddinger, Limiting the Business Method Patent: A Comparison and Proposed Alignment of European, Japanese and United States Patent Law, 69 Fordham L.Rev. 2523, 2544-50 (2001). Commentators have argued that “the broad grant of patent protection for methods of doing business is something of a square peg in a sinkhole of uncertain dimensions” since “[n]owhere in the substantial literature on innovation is there a statement that the United States economy suffers from a lack of innovation in methods of doing business.” Raskind, supra at 92-93. Instead, “the long history of U.S. business is one of innovation, emulation, and innovation again. It also is a history of remarkable creativity and success, all without business method patents until the past few years.” Smith, supra at 178; see also Sfekas, supra at 213 (“While innovation in business methods is a good thing, it is likely that there would be the same level of innovation even without patents on [such methods].”).

Business innovations, by their very nature, provide a competitive advantage and thus generate their own incentives. See Xiang, supra at 813 (“A business entity improves the way it does business in order to be more effective and efficient, to stay ahead of [the] competition, and to make more profit.”). The rapid “growth of fast food restaurants, self-service gasoline stations, quick oil change facilities ... automatic teller devices ... and alternatives for long-distance telephone services” casts real doubt about the need for the additional incentive of patent protection in the commercial realm. Raskind, supra at 93.

Although patents are not a prerequisite to business innovation, they are of undeniable importance in promoting technological advances. For example, the pharmaceutical industry relies on patent protection in order to recoup the large sums it invests to develop life-saving and life-enhancing drugs:

[T]he “fully loaded” cost of developing a single new pharmaceutical molecule, taking it though laboratory and clinical trials, and securing FDA approval for its marketing is today about $800 million (including the cost of project failures). Furthermore, fewer than one in five drug candidates that make it out of the laboratory survive this tortuous process and reach the marketplace in the form of FDA-approved pharmaceuticals.... Only patent protection can make the innovator's substantial investment in development and clinical testing economically rational.

Jay Dratler, Jr., Alice in Wonderland Meets the U.S. Patent System, 38 Akron L.Rev. 299, 313-14 (2005) (footnotes omitted).

Business method patents, unlike those granted for pharmaceuticals and other products, offer rewards that are grossly disproportionate to the costs of innovation. In contrast to technological endeavors, business innovations frequently involve little or no investment in research and development. Bilski, for example, likely spent only nominal sums to develop his hedging method. The reward he could reap if his application were allowed-exclusive rights over methods of managing risks in a wide array of commodity transactions-vastly exceeds any costs he might have incurred in devising his “invention.”

B.
“[S]ometimes too much patent protection can impede rather than ‘promote the Progress of Science and useful Arts,’ the constitutional objective of patent and copyright protection.” Lab. Corp. of Am. Holdings v. Metabolite Labs., Inc., 548 U.S. 124, 126, 126 S.Ct. 2921, 165 L.Ed.2d 399 (2006) (Breyer, J., joined by Stevens and Souter, JJ., dissenting from dismissal of writ of certiorari) (emphasis in original). This is particularly true in the context of patents on methods of conducting business. Instead of providing incentives to competitors to develop improved business techniques, business method patents remove building blocks of commercial innovation from the public domain. Dreyfuss, supra at 275-77. Because they restrict competitors from using and improving upon patented business methods, such patents stifle innovation. When “we grant rights to exclude unnecessarily, we ... limit competition with no quid pro quo. Retarding competition retards further development.” Pollack, supra at 76. “Think how the airline industry might now be structured if the first company to offer frequent flyer miles had enjoyed the sole right to award them or how differently mergers and acquisitions would be financed ... if the use of junk bonds had been protected by a patent.” Dreyfuss, supra at 264. By affording patent protection to business practices, “the government distorts the operation of the free market system and reduces the gains from the operation of the market.” Sfekas, supra at 214.

It is often consumers who suffer when business methods are patented. See Raskind, supra at 82. Patented products are more expensive because licensing fees are often passed on to consumers. See Lois Matelan, The Continuing Controversy Over Business Method Patents, 18 Fordham Intell. Prop. Med. & Ent. L.J. 189, 201 (2007). Further, as a general matter, “quantity and quality [of patented products] are less than they would be in a competitive market.” Dreyfuss, supra at 275.

Patenting business methods makes American companies less competitive in the global marketplace. American companies can now obtain exclusionary rights on methods of conducting business, but their counterparts in Europe and Japan generally cannot. See Biddinger, supra at 2546-47. Producing products in the United States becomes more expensive because American companies, unlike their overseas counterparts, must incur licensing fees in order to use patented business methods:

[O]nce a United States patent application for a new method of doing business becomes publicly available, companies in Europe and Japan may begin using the method outside the United States, while American companies in competition with the patentee would be unable to use the method in the United States without incurring licensing fees. The result is that companies outside of the United States receive the benefit of the novel method without incurring either the research and development costs of the inventor, or the licensing fees of the patentee's American competitors.

Id. at 2545-46.

C.
Another significant problem that plagues business method patents is that they tend to be of poor overall quality. See eBay Inc. v. MercExchange, L.L.C., 547 U.S. 388, 397, 126 S.Ct. 1837, 164 L.Ed.2d 641 (2006) (Kennedy, J., joined by Stevens, Souter, and Breyer, JJ., concurring) (noting the “potential vagueness and suspect validity” of some of “the burgeoning number of patents over business methods”). Commentators have lamented “the frequency with which the Patent Office issues patents on shockingly mundane business inventions.” Dreyfuss, supra at 268; see also Pollack, supra at 106 (“[M]any of the recently-issued business method patents are facially (even farcically) obvious to persons outside the USPTO.”). One reason for the poor quality of business method patents is the lack of readily accessible prior art references. Because business methods were not patentable prior to State Street, “there is very little patent-related prior art readily at hand to the examiner corps.” Dreyfuss, supra at 269.

Furthermore, information about methods of conducting business, unlike information about technological endeavors, is often not documented or published in scholarly journals. See Russell A. Korn, Is Legislation the Answer? An Analysis of the Proposed Legislation for Business Method Patents, 29 Fla. St. U.L.Rev. 1367, 1372-73 (2002). The fact that examiners lack the resources to weed out undeserving applications “has led to the improper approval of a large number of patents, leaving private parties to clean up the mess through litigation.” Krause, supra at 97.

Allowing patents to issue on business methods shifts critical resources away from promoting and protecting truly useful technological advances. As discussed previously, the patent office has been deluged with business method applications in recent years. Time spent on such applications is time not spent on applications which claim true innovations. When already overburdened examiners are forced to devote significant time to reviewing large numbers of business method applications, the public's access to new and beneficial technologies is unjustifiably delayed.

D.
Patenting business methods allows private parties to claim exclusive ownership of ideas and practices which rightfully belong in the public domain. “It is a matter of public interest that [economic] decisions, in the aggregate, be intelligent and well informed. To this end, the free flow of commercial information is indispensable.” Virginia State Bd. of Pharmacy v. Virginia Citizens Consumer Council, Inc., 425 U.S. 748, 765, 96 S.Ct. 1817, 48 L.Ed.2d 346 (1976). Thus, “the stringent requirements for patent protection seek to assure that ideas in the public domain remain there for the free use of the public.” Aronson v. Quick Point Pencil Co., 440 U.S. 257, 262, 99 S.Ct. 1096, 59 L.Ed.2d 296 (1979).

Bilski's claimed method consists essentially of two conversations. The first conversation is between a commodity provider and a commodity consumer, while the second conversation is between the provider and “market participants” who have “a counter-risk position to ... consumers.” His claims provide almost no details as to the contents of these conversations.

Like many business method applications, Bilski's application is very broadly drafted. It covers a wide range of means for “hedging” in commodity transactions. If his application were allowed, anyone who discussed ways to balance market risks in any sort of commodity could face potential infringement liability. By adopting overly expansive standards for patentability, the government enables private parties to impose broad and unwarranted burdens on speech and the free flow of ideas. See Thomas F. Cotter, A Burkean Perspective on Patent Eligibility, 22 Berkeley Tech. L.J. 855, 880-82 (2007) (arguing that overly expansive patent eligibility standards can result in the granting of patents that threaten free speech, privacy and other constitutionally-protected rights); John R. Thomas, The Future of Patent Law: Liberty and Property in the Patent Law, 39 Hous. L.Rev. 569, 589 (2002) (arguing that “the patent law allows private actors to impose more significant restraints on speech than has ever been possible through copyright”); see also Cent. Hudson Gas & Elec. Corp. v. Pub. Serv. Comm'n of New York, 447 U.S. 557, 569-70, 100 S.Ct. 2343, 65 L.Ed.2d 341 (1980) (The First Amendment mandates that restrictions on free speech in commercial transactions be “no more extensive than necessary.”).

To the extent that business methods are deemed patentable, individuals can face unexpected potential infringement liability for everyday conversations and commercial interactions. “[I]mplicit in the Patent Clause itself [is the understanding] that free exploitation of ideas will be the rule, to which the protection of a federal patent is the exception.” Bonito Boats, Inc. v. Thunder Craft Boats, Inc., 489 U.S. 141, 151, 109 S.Ct. 971, 103 L.Ed.2d 118 (1989). In the wake of State Street, too many patent holders have been allowed to claim exclusive ownership of subject matter that rightfully belongs in the public domain.

V.
The majority's proposed “machine-or-transformation test” for patentability will do little to stem the growth of patents on non-technological methods and ideas. Quite simply, in the context of business method patent applications, the majority's proposed standard can be too easily circumvented. See Cotter, supra at 875 (noting that the physical transformation test for patentability can be problematic because “[i]n a material universe, every process will cause some sort of physical transformation, if only at the microscopic level or within the human body, including the brain”). Through clever draftsmanship, nearly every process claim can be rewritten to include a physical transformation. Bilski, for example, could simply add a requirement that a commodity consumer install a meter to record commodity consumption. He could then argue that installation of this meter was a “physical transformation,” sufficient to satisfy the majority's proposed patentability test.

Even as written, Bilski's claim arguably involves a physical transformation. Prior to utilizing Bilski's method, commodity providers and commodity consumers are not involved in transactions to buy and sell a commodity at a fixed rate. By using Bilski's claimed method, however, providers and consumers enter into a series of transactions allowing them to buy and sell a particular commodity at a particular price. Entering into a transaction is a physical process: telephone calls are made, meetings are held, and market participants must physically execute contracts. Market participants go from a state of not being in a commodity transaction to a state of being in such a transaction. The majority, however, fails to explain how this sort of physical transformation is insufficient to satisfy its proposed patent eligibility standard.

The majority suggests that a technological arts test is nothing more that a “shortcut” for its machine-or-transformation test. Ante at 964. To the contrary, however, the two tests are fundamentally different. Consider U.S. Patent No. 7,261,652, which is directed to a method of putting a golf ball, U.S. Patent No. 6,368,227, which is directed to a method of swinging on a swing suspended on a tree branch, and U.S. Patent No. 5,443,036, which is directed to a method of “inducing cats to exercise.” Each of these “inventions” involves a physical transformation that is central to the claimed method: the golfer's stroke is changed, a person on a swing starts swinging, and the sedentary cat becomes a fit feline. Thus, under the majority's approach, each of these inventions is patent eligible. Under a technological arts test, however, none of these inventions is eligible for patent protection because none involves any advance in science or technology.<ref>The majority's approach will encourage rent-seeking on a broad range of human thought and behavior. For example, because organizing a country into a democratic or socialist regime clearly involves a physical transformation, what is to prevent patents from issuing on forms of government?</ref>

Regardless of whether a claimed process involves a “physical transformation,” it should not be patent eligible unless it is directed to an advance in science or technology. See Benson, 409 U.S. at 64-71, 93 S.Ct. 253 (finding a process unpatentable even though it “transformed” binary-coded decimals into pure binary numbers using a general purpose computer). Although the Supreme Court has stated that a patentable process will usually involve a transformation of physical matter, see id. at 70, 93 S.Ct. 253, it has never found a process patent eligible which did not involve a scientific or technological innovation. See Diehr, 450 U.S. at 192-93, 101 S.Ct. 1048 (finding a process patentable where it involved new technology for curing rubber).

The majority refuses to inject a technology requirement into the section 101 analysis because it believes that the terms “technological arts” and “technology” are “ambiguous.” See ante at 960. To the contrary, however, the meaning of these terms is not particularly difficult to grasp. “The need to apply some sort of ‘technological arts' criterion has hardly led other countries' and regions' patent systems to grind to a halt; it is hard to see why it should be an insurmountable obstacle for ours.” Cotter, supra at 885. As discussed more fully in section III, a claimed process is technological to the extent it applies laws of nature to new ends. See Benson, 409 U.S. at 67, 93 S.Ct. 253 (“ ‘If there is to be invention from ... a discovery, it must come from the application of the law of nature to a new and useful end.’ ” (quoting Funk Bros., 333 U.S. at 130, 68 S.Ct. 440)). By contrast, a process is non-technological where its inventive concept is the application of principles drawn not from the natural sciences but from disciplines such as business, law, sociology, or psychology. See Thomas (1999), supra at 1168 (“[F]ew of us would suppose that inventions within the domain of business, law or fine arts constitute technology, much less patentable technology.”). The inventive aspect of Bilski's claimed process is the application of business principles, not laws of nature; it is therefore non-technological and ineligible for patent protection.

Unlike a technological standard for patentability, the majority's proposed test will be exceedingly difficult to apply. The standard that the majority proposes for inclusion in the patentability lexicon-“transformation of any physical object or substance, or an electronic signal representative of any physical object or substance,” ante at 964-is unnecessarily complex and will only lead to further uncertainty regarding the scope of patentable subject matter. As noted in In re Nuijten, 500 F.3d 1346, 1353 (Fed.Cir.2007), defining the term “physical” can be an “esoteric and metaphysical” inquiry. Indeed, although this court has struggled for years to set out what constitutes sufficient physical transformation to render a process patentable, we have yet to provide a consistent or satisfactory resolution of this issue.

We took this case en banc in a long-overdue effort to resolve primal questions on the metes and bounds of statutory subject matter. The patent system has run amok, and the USPTO, as well as the larger patent community, has actively sought guidance from this court in making sense of our section 101 jurisprudence. See Supplemental Br. of Appellee at 3 (“[The Federal Circuit] should clarify the meaning of State Street and AT & T, as they have been too often misunderstood.”); Br. of Fin. Serv. Indus. at 1 (“The rise of [business method patents] in recent years has ... led to uncertainty over the scope of the patents granted and, more fundamentally, the definition of patentable subject matter itself. [We] seek a workable standard defining the scope of patentable subject matter, one that ... provides clear guidance to the Patent and Trademark Office ... and the public.”); Br. of Samuelson Law, Tech. and Public Policy Clinic at 1 (“Ever since State Street, the [USPTO] has been flooded with applications for a wide variety of non-technological ‘inventions' such as arbitration methods, dating methods, tax-planning methods, legal methods, and novel-writing methods. These applications have eroded public confidence in the patent system and driven up the cost and decreased the return for applicants seeking legitimate technological patents.” (footnote omitted)); Br. of Assoc. of Am. Medical Colleges at 29 (arguing that “broad swaths of the public and certain industry sectors” have lost respect for the patent system and that “[the Federal Circuit] should act, even if its actions mean unsettling the settled expectations of some”). The majority, however, fails to enlighten three of the thorniest issues in the patentability thicket: (1) the continued viability of business method patents, (2) what constitutes sufficient physical transformation or machine-implementation to render a process patentable, and (3) the extent to which computer software and computer-implemented processes constitute statutory subject matter. The majority's “measured approach” to the section 101 analysis, see ante at 962, will do little to restore public confidence in the patent system or stem the growth of patents on business methods and other non-technological ideas.

VI.

Where the advance over the prior art on which the applicant relies to make his invention patentable is an advance in a field of endeavor such as law (like the arbitration method in Comiskey ), business (like the method claimed by Bilski) or other liberal-as opposed to technological-arts, the application falls outside the ambit of patentable subject matter. The time is ripe to repudiate State Street and to recalibrate the standards for patent eligibility, thereby ensuring that the patent system can fulfill its constitutional mandate to protect and promote truly useful innovations in science and technology. I dissent from the majority's failure to do so.

===Footnotes===
<references/>

In Re Bilski, Mayer dissenting opinion

2015-04-02T17:53:27Z

Bill:

In Re Bilski, Newman dissenting opinion

2015-04-02T17:48:26Z

Bill:

NEWMAN, Circuit Judge, dissenting.

The court today acts en banc to impose a new and far-reaching restriction on the kinds of inventions that are eligible to participate in the patent system. The court achieves this result by redefining the word “process” in the patent statute, to exclude all processes that do not transform physical matter or that are not performed by machines. The court thus excludes many of the kinds of inventions that apply today's electronic and photonic technologies, as well as other processes that handle data and information in novel ways. Such processes have long been patent eligible, and contribute to the vigor and variety of today's Information Age. This exclusion of process inventions is contrary to statute, contrary to precedent, and a negation of the constitutional mandate. Its impact on the future, as well as on the thousands of patents already granted, is unknown.

This exclusion is imposed at the threshold, before it is determined whether the excluded process is new, non-obvious, enabled, described, particularly claimed, etc.; that is, before the new process is examined for patentability. For example, we do not know whether the Bilski process would be found patentable under the statutory criteria, for they were never applied.

The innovations of the “knowledge economy”-of “digital prosperity”-have been dominant contributors to today's economic growth and societal change. Revision of the commercial structure affecting major aspects of today's industry should be approached with care, for there has been significant reliance on the law as it has existed, as many amici curiae pointed out. Indeed, the full reach of today's change of law is not clear, and the majority opinion states that many existing situations may require reassessment under the new criteria.

Uncertainty is the enemy of innovation. These new uncertainties not only diminish the incentives available to new enterprise, but disrupt the settled expectations of those who relied on the law as it existed. I respectfully dissent.

DISCUSSION

The court's exclusion of specified process inventions from access to the patent system is achieved by redefining the word “process” in the patent statute. However, the court's redefinition is contrary to statute and to explicit rulings of the Supreme Court and this court. I start with the statute:

Section 101 is the statement of statutory eligibility
From the first United States patent act in 1790, the subject matter of the “useful arts” has been stated broadly, lest advance restraints inhibit the unknown future. The nature of patent-eligible subject matter has received judicial attention over the years, as new issues arose with advances in science and technology. The Supreme Court has consistently confirmed the constitutional and legislative purpose of providing a broadly applicable incentive to commerce and creativity, through this system of limited exclusivity. Concurrently, the Court early explained the limits of patentable subject matter, in that “fundamental truths” were not intended to be included in a system of exclusive rights, for they are the general foundations of knowledge. Thus laws of nature, natural phenomena, and abstract ideas are not subject to patenting. Several rulings of the Court have reviewed patent eligibility in light of these fundamentals. However, the Court explicitly negated today's restrictions. My colleagues in the majority are mistaken in finding that decisions of the Court require the per se limits to patent eligibility that the Federal Circuit today imposes. The patent statute and the Court's decisions neither establish nor support the exclusionary criteria now adopted.

The court today holds that any process that does not transform physical matter or require performance by machine is not within the definition of “process” in any of the patent statutes since 1790. All of the statutes contained a broad definition of patent-eligible subject matter, like that in the current Patent Act of 1952:

35 U.S.C § 101 Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.

In Diamond v. Diehr, 450 U.S. 175, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981) the Court explained that Section 101 is not an independent condition of patentability, but a general statement of subject matter eligibility. The Court stated:

Section 101, however, is a general statement of the type of subject matter that is eligible for patent protection “subject to the conditions and requirements of this title.” Specific conditions for patentability follow and § 102 covers in detail the conditions relating to novelty. The question therefore of whether a particular invention is novel is “wholly apart from whether the invention falls in a category of statutory subject matter.”

Id. at 189-90, 101 S.Ct. 1048 (footnote omitted) (quoting In re Bergy, 596 F.2d 952, 961 (C.C.P.A.1979)).

“Process” is defined in the 1952 statute as follows:

35 U.S.C. § 100(b) The term “process” means process, art or method, and includes a new use of a known process, machine, manufacture, composition of matter, or material.

The 1952 Patent Act replaced the word “art” in prior statutes with the word “process,” while the rest of Section 101 was unchanged from earlier statutes. The legislative history for the 1952 Act explained that “art” had been “interpreted by courts to be practically synonymous with process or method.” S.Rep. No. 82-1979 (1952), reprinted in 1952 U.S.C.C.A.N. 2394, 2398, 2409-10. In Diehr the Court explained that a process “has historically enjoyed patent protection because it was considered a form of ‘art’ as that term was used in the 1793 Act.” 450 U.S. at 182, 101 S.Ct. 1048.

The definition of “process” provided at 35 U.S.C. § 100(b) is not “unhelpful,” as this court now states, maj. op. at 951 n. 3, but rather points up the errors in the court's new statutory interpretation. Section 100(b) incorporates the prior usage “art” and the term “method,” and places no restriction on the definition. This court's redefinition of “process” as limiting access to the patent system to those processes that use specific machinery or that transform matter, is contrary to two centuries of statutory definition.

The breadth of Section 101 and its predecessor provisions reflects the legislative intention to accommodate not only known fields of creativity, but also the unknown future. The Court has consistently refrained from imposing unwarranted restrictions on statutory eligibility, and for computer-implemented processes the Court has explicitly rejected the direction now taken. Nonetheless, this court now adopts a redefinition of “process” in Section 101 that excludes forms of information-based and software-implemented inventions arising from new technological capabilities, stating that this result is required by the Court's computer-related cases, starting with Gottschalk v. Benson, 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972). However, the Court in Benson rejected the restriction that is imposed today:

This court's new definition of “process” was rejected in Gottschalk v. Benson
In Benson the claimed invention was a mathematical process for converting binary-coded decimal numerals into pure binary numbers. The Court explained that a mathematical formula unlimited to a specific use was simply an abstract idea of the nature of “fundamental truths,” “phenomena of nature,” and “abstract intellectual concepts,” as have traditionally been outside of patent systems. 409 U.S. at 67, 93 S.Ct. 253. However, the Court explicitly declined to limit patent-eligible processes in the manner now adopted by this court, stating:

It is argued that a process patent must either be tied to a particular machine or apparatus or must operate to change articles or materials to a “different state or thing.” We do not hold that no process patent could ever qualify if it did not meet the requirements of our prior precedents. It is said that the decision precludes a patent for any program servicing a computer. We do not so hold.

Id. at 71, 93 S.Ct. 253. The Court explained that “the requirements of our prior precedents” did not preclude patents on computer programs, despite the statement drawn from Cochrane v. Deener, 94 U.S. 780, 787-88, 24 L.Ed. 139 (1876), that “[t]ransformation and reduction of an article ‘to a different state or thing’ is the clue to the patentability of a process claim that does not include particular machines.” Benson, 409 U.S. at 70, 93 S.Ct. 253. Although this same statement is now relied upon by this court as requiring its present ruling, maj. op at 956 & n. 11, the Court in Benson was explicit that: “We do not hold that no process patent could ever qualify if it did not meet [the Court's] prior precedents.” The Court recognized that Cochrane's statement was made in the context of a mechanical process and a past era, and protested:

It is said we freeze process patents to old technologies, leaving no room for the revelations of the new, onrushing technology. Such is not our purpose.

Benson, 409 U.S. at 71, 93 S.Ct. 253. Instead, the Court made clear that it was not barring patents on computer programs, and rejected the “argu[ment] that a process patent must either be tied to a particular machine or apparatus or must operate to change articles or materials to a ‘different state or thing’ ” in order to satisfy Section 101. Id. Although my colleagues now describe these statements as “equivocal,” maj. op. at 956, there is nothing equivocal about “We do not so hold.” Benson, 409 U.S. at 71, 93 S.Ct. 253. Nonetheless, this court now so holds.

In Parker v. Flook the Court again rejected today's restrictions
The eligibility of mathematical processes next reached the Court in Parker v. Flook, 437 U.S. 584, 98 S.Ct. 2522, 57 L.Ed.2d 451 (1978), where the Court held that the “process” category of Section 101 was not met by a claim to a mathematical formula for calculation of alarm limits for use in connection with catalytic conversion of hydrocarbons and, as in Benson, the claim was essentially for the mathematical formula. The Court later summarized its Flook holding, stating in Diamond v. Diehr that:

The [Flook] application, however, did not purport to explain how these other variables were to be determined, nor did it purport “to contain any disclosure relating to the chemical processes at work, the monitoring of the process variables, nor the means of setting off an alarm or adjusting an alarm system. All that it provides is a formula for computing an updated alarm limit.”

Diehr, 450 U.S. at 186-87, 101 S.Ct. 1048 (quoting Flook, 437 U.S. at 586, 98 S.Ct. 2522).

The Court explained in Flook that a field-of-use restriction to catalytic conversion did not distinguish Flook's mathematical process from that in Benson. However, the Court reiterated that patent eligibility of computer-directed processes is not controlled by the “qualifications of our earlier precedents,” again negating any limiting effect of the usages of the past, on which this court now places heavy reliance. The Court stated:

The statutory definition of “process” is broad. An argument can be made, however, that this Court has only recognized a process as within the statutory definition when it either was tied to a particular apparatus or operated to change materials to a “different state or thing.” As in Benson, we assume that a valid process patent may issue even if it does not meet one of these qualifications of our earlier precedents.<ref> My colleagues cite only part of this quotation as the Court's holding in Flook, maj. op. at 955, ignoring the qualifying words “[a]n argument can be made” as well as the next sentence clarifying that this argument was rejected by the Court in Benson and is now again rejected in Flook.</ref>

Flook, 437 U.S. at 589 n. 9, 98 S.Ct. 2522 (quoting Cochrane, 94 U.S. at 787). This statement directly contravenes this court's new requirement that all processes must meet the court's “machine-or-transformation test” or be barred from access to the patent system.

The Court in Flook discussed that abstractions and fundamental principles have never been subject to patenting, but recognized the “unclear line” between an abstract principle and the application of such principle:

The line between a patentable “process” and an unpatentable “principle” is not always clear. Both are “conception[s] of the mind, seen only by [their] effects when being executed or performed.”

Flook, 437 U.S. at 589, 98 S.Ct. 2522 (alterations in original) (quoting Tilghman v. Proctor, 102 U.S. 707, 728, 26 L.Ed. 279 (1880)).

The decision in Flook has been recognized as a step in the evolution of the Court's thinking about computers. See Arrhythmia Res. Tech., Inc. v. Corazonix Corp., 958 F.2d 1053, 1057 n. 4 (Fed.Cir.1992) (“it appears to be generally agreed that these decisions represent evolving views of the Court”) (citing R.L. Gable & J.B. Leaheey, The Strength of Patent Protection for Computer Products, 17 Rutgers Computer & Tech. L.J. 87 (1991); D. Chisum, The Patentability of Algorithms, 47 U. Pitt. L.Rev. 959 (1986)). That Flook does not support today's per se exclusion of forms of process inventions from access to the patent system is reinforced in the next Section 101 case decided by the Court:

In Diamond v. Chakrabarty the Court again rejected per se exclusions of subject matter from Section 101
In Diamond v. Chakrabarty, 447 U.S. 303, 100 S.Ct. 2204, 65 L.Ed.2d 144 (1980), the scope of Section 101 was challenged as applied to the new fields of biotechnology and genetic engineering, with respect to the patent eligibility of a new bacterial “life form.” The Court explained the reason for the broad terms of Section 101:

The subject-matter provisions of the patent law have been cast in broad terms to fulfill the constitutional and statutory goal of promoting “the Progress of Science and the useful Arts” with all that means for the social and economic benefits envisioned by Jefferson. Broad general language is not necessarily ambiguous when congressional objectives require broad terms.

Id. at 315, 100 S.Ct. 2204 (quoting U.S. Const., art. I, § 8). The Court referred to the use of “any” in Section 101 (“Whoever invents or discovers any new and useful process ... or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title”), and reiterated that the statutory language shows that Congress “plainly contemplated that the patent laws would be given wide scope.” Id. at 308, 100 S.Ct. 2204. The Court referred to the legislative intent to include within the scope of Section 101 “anything under the sun that is made by man,” id. at 309, 100 S.Ct. 2204 (citing S. Rep. 82-1979, at 5, U.S.Code Cong. & Admin.News 1952, pp. 2394, 2399; H.R. Rep. 82-1923, at 6 (1952)), and stated that the unforeseeable future should not be inhibited by judicial restriction of the “broad general language” of Section 101:

A rule that unanticipated inventions are without protection would conflict with the core concept of the patent law that anticipation undermines patentability. Mr. Justice Douglas reminded that the inventions most benefiting mankind are those that push back the frontiers of chemistry, physics, and the like. Congress employed broad general language in drafting § 101 precisely because such inventions are often unforeseeable.

Id. at 315-16, 100 S.Ct. 2204 (citations and internal quotation marks omitted). The Court emphasized that its precedents did not alter this understanding of Section 101's breadth, stating that “ Flook did not announce a new principle that inventions in areas not contemplated by Congress when the patent laws were enacted are unpatentable per se.” Id. at 315, 100 S.Ct. 2204.

Whether the applications of physics and chemistry that are manifested in advances in computer hardware and software were more or less foreseeable than the advances in biology and biotechnology is debatable, but it is not debatable that these fields of endeavor have become primary contributors to today's economy and culture, as well as offering an untold potential for future advances. My colleagues offer no reason now to adopt a policy of exclusion of the unknown future from the subject matter now embraced in Section 101.

Soon after Chakrabarty was decided, the Court returned to patentability issues arising from computer capabilities:

In Diamond v. Diehr the Court directly held that computer-implemented processes are included in Section 101
The invention presented to the Court in Diehr was a “physical and chemical process for molding precision synthetic rubber products” where the process steps included using a mathematical formula. The Court held that the invention fit the “process” category of Section 101 although mathematical calculations were involved, and repeated its observation in Chakrabarty that “courts should not read into the patent laws limitations and conditions which the legislature has not expressed.” Diehr, 450 U.S. at 182, 101 S.Ct. 1048 (internal quotation marks omitted) (citing Chakrabarty, 447 U.S. at 308, 100 S.Ct. 2204).

The Court distinguished a claim that would cover all uses of a mathematical formula and thus is an abstract construct, as in Benson, from a claim that applies a mathematical calculation for a specified purpose, as in Diehr. The Court stated that “a claim drawn to subject matter otherwise statutory does not become nonstatutory simply because it uses a mathematical formula, computer program, or digital computer,” id. at 187, 101 S.Ct. 1048, and explained that the line between statutory and nonstatutory processes depends on whether the process is directed to a specific purpose, see id. (“It is now commonplace that an application of a law of nature or mathematical formula to a known structure or process may well be deserving of patent protection.” (emphasis in original)). The Court clarified that Flook did not hold that claims may be dissected into old and new parts to assess their patent eligibility. Id. at 189 n. 12, 101 S.Ct. 1048.

However, the Court did not propose the “machine-or-transformation” test that this court now insists was “enunciated” in Diehr as a specific limit to Section 101. Maj. op. at 953-54. In Diehr there was no issue of machine or transformation, for the Diehr process both employed a machine and produced a chemical transformation: the process was conducted in “an openable rubber molding press,” and it cured the rubber. In discussing the known mathematical formula used by Diehr to calculate the relation between temperature and the rate of a chemical reaction, the Court recited the traditional exceptions of “laws of nature, natural phenomena, and abstract ideas,” 450 U.S. at 185, 101 S.Ct. 1048, and explained that the entirety of the process must be considered, not an individual mathematical step.

The Court characterized the holdings in Benson and Flook as standing for no more than the continued relevance of these “long-established” judicial exclusions, id., and repeated that a practical application of pure science or mathematics may be patentable, citing Mackay Radio & Telegraph Co. v. Radio Corp. of America, 306 U.S. 86, 94, 59 S.Ct. 427, 83 L.Ed. 506 (1939) ( “While a scientific truth, or the mathematical expression of it, is not a patentable invention, a novel and useful structure created with the aid of knowledge and scientific truth may be.”). The Court explained that the presence of a mathematical formula does not preclude patentability when the structure or process is performing a function within the scope of the patent system, stating:

[W]hen a claim containing a mathematical formula implements or applies that formula in a structure or process which, when considered as a whole, is performing a function which the patent laws were designed to protect ( e.g., transforming or reducing an article to a different state or thing), then the claim satisfies the requirements of § 101.

450 U.S. at 192, 101 S.Ct. 1048. This statement's parenthetical “ e.g.” is relied on by the majority for its statement that Diehr requires today's “machine-or-transformation” test. However, this “ e.g.” does not purport to state the only “function which the patent laws were designed to protect.” Id. This “ e.g.” indeed describes the process in Diehr, but it does not exclude all other processes from access to patenting.

It cannot be inferred that the Court intended, by this “ e.g.” parenthetical, to require the far-reaching exclusions now attributed to it. To the contrary, the Court in Diehr was explicit that “an application of a law of nature or mathematical formula” may merit patent protection, 450 U.S. at 187, 101 S.Ct. 1048 (emphasis in original), and that the claimed process must be considered as a whole, id. at 188, 101 S.Ct. 1048. The Court recognized that a process claim may combine steps that were separately known, and that abstract ideas such as mathematical formulae may be combined with other steps to produce a patentable process. Id. at 187, 101 S.Ct. 1048. The steps are not to be “dissect[ed]” into new and old steps; it is the entire process that frames the Section 101 inquiry. Id. at 188, 101 S.Ct. 1048.

The Diehr Court did not hold, as the majority opinion states, that transformation of physical state is a requirement of eligibility set by Section 101 unless the process is performed by a machine. It cannot be inferred that the Court silently imposed such a rule. See maj. op. at 956 (relying on lack of repetition in Diehr of the Benson and Flook disclaimers of requiring machine or transformation, as an implicit rejection of these disclaimers and tacit adoption of the requirement). There was no issue in Diehr of the need for either machine or transformation, for both were undisputedly present in the process of curing rubber. It cannot be said that the Court “enunciated” today's “definitive test” in Diehr.<ref>Many amici curiae pointed out that the Supreme Court did not adopt the test that this court now attributes to it. See, e.g., Br. of Amicus Curiae Am. Intellectual Property Law Ass'n at 18 & n.16; Br. of Amicus Curiae Biotechnology Industry Org. at 17-21; Br. of Amicus Curiae Boston Patent Law Ass'n at 6-8; Br. of Amicus Curiae Business Software Alliance at 13; Br. of Amicus Curiae Federal Circuit Bar Ass'n at 21; Br. of Amicus Curiae Regulatory Datacorp, Inc. at 12-13; Br. of Amicus Curiae Accenture at 16-17; Br. of Amicus Curiae Washington State Patent Law Ass'n at 10-11.</ref>

Subsequent Supreme Court authority reinforced the breadth of Section 101

In J.E.M. Ag Supply, Inc. v. Pioneer Hi-Bred International, Inc., 534 U.S. 124, 122 S.Ct. 593, 151 L.Ed.2d 508 (2001), the Court described Section 101 as a “dynamic provision designed to encompass new and unforeseen inventions,” id. at 135, 122 S.Ct. 593, that case arising in the context of eligibility of newly developed plant varieties for patenting. The Court stated: “As in Chakrabarty, we decline to narrow the reach of § 101 where Congress has given us no indication that it intends this result.” Id. at 145-46, 122 S.Ct. 593. The Court reiterated that “Congress plainly contemplated that the patent laws would be given wide scope,” id. at 130, 122 S.Ct. 593 (quoting Chakrabarty, 447 U.S. at 308, 100 S.Ct. 2204), and that the language of Section 101 is “extremely broad,” id. This is not language of restriction, and it reflects the statutory policy and purpose of inclusion, not exclusion, in Section 101.

The Court's decisions of an earlier age do not support this court's restrictions of Section 101
My colleagues also find support for their restrictions on patent-eligible “process” inventions in the pre-Section 101 decisions O'Reilly v. Morse, 56 U.S. (15 How.) 62, 14 L.Ed. 601 (1853), Cochrane v. Deener, 94 U.S. 780, 24 L.Ed. 139 (1876), and Tilghman v. Proctor, 102 U.S. 707, 26 L.Ed. 279 (1880). Although the Court in Benson and in Flook took care to state that these early decisions do not require the restrictions that the Court was rejecting, this court now places heavy reliance on these early decisions, which this court describes as “consistent with the machine-or-transformation test later articulated in Benson and reaffirmed in Diehr.” Maj. op. at 955. As I have discussed, no such test was “articulated in Benson ” and “reaffirmed in Diehr.”

However, these early cases do show, contrary to the majority opinion, that a “process” has always been a distinct category of patentable invention, and not tied to either apparatus or transformation, as this court now holds. For example, in Tilghman v. Proctor the Court considered a patent on a process for separating fats and oils, and held that the process was not restricted to any particular apparatus. The Court held that a process is an independent category of invention, and stated:

That a patent can be granted for a process, there can be no doubt. The patent law is not confined to new machines and new compositions of matter, but extends to any new and useful art or manufacture.

102 U.S. at 722; see also Corning v. Burden, 56 U.S. (15 How.) 252, 268, 14 L.Ed. 683 (1853) (“It is for the discovery or invention of some practical method or means of producing a beneficial result or effect, that a patent is granted, and not for the result or effect itself.”) The difference between a process and the other categories of patent-eligible subject matter does not deprive process inventions of the independent status accorded by statute, by precedent, and by logic, all of which negate the court's new rule that a process must be tied to a particular machine or must transform physical matter.

The majority also relies on O'Reilly v. Morse, citing the Court's rejection of Morse's Claim 8 for “the use of the motive power of the electro or galvanic current, which I call electromagnetism, however developed, for making or printing intelligible characters, signs or letters at any distances....” The Court explained:

In fine he claims an exclusive right to use a manner and process which he has not described and indeed had not invented, and therefore could not describe when he obtained his patent. The Court is of the opinion that the claim is too broad, and not warranted by law.

56 U.S. (15 How.) at 113. However, the claims that were directed to the communication system that was described by Morse were held patentable, although no machine, transformation, or manufacture was required. See Morse's Claim 5 (“The system of signs, consisting of dots and spaces, and horizontal lines, for numerals, letters, words, or sentences, substantially as herein set forth and illustrated, for telegraphic purposes.”). I cannot discern how the Court's rejection of Morse's Claim 8 on what would now be Section 112 grounds, or the allowance of his other claims, supports this court's ruling today. Indeed, Morse's claim 5, to a system of signs, is no more “tangible” than the systems held patentable in Alappat and State Street Bank, discussed post and now cast into doubt, or the Bilski system here held ineligible for access to patenting.

The majority opinion also relies on Cochrane v. Deener, particularly on certain words quoted in subsequent opinions of the Court. In Cochrane the invention was a method for bolting flour, described as a series of mechanical steps in the processing of flour meal. The question before the Court was whether the patented process would be infringed if the same steps were performed using different machinery. The answer was “that a process may be patentable, irrespective of the particular form of the instrumentalities used.” 94 U.S. at 788. The Court stressed the independence of a process from the tools that perform it:

A process is a mode of treatment of certain materials to produce a given result. It is an act, or series of acts, performed upon the subject-matter to be transformed and reduced to a different state or thing. If new and useful, it is just as patentable as is a piece of machinery. In the language of the patent law, it is an art. The machinery pointed out as suitable to perform the process may or may not be new or patentable; whilst the process itself may be altogether new, and produce an entirely new result. The process requires that certain things should be done with certain substances, and in a certain order; but the tools to be used in doing this may be of secondary consequence.

94 U.S. at 788. The Court did not restrict the kinds of patentable processes; the issue in Cochrane was whether the process must be tied to the machinery that the patentee used to perform it.

This court now cites Cochrane's description of a process as “acts performed upon subject-matter to be transformed and reduced to a different state or thing,” id., this court stating that unless there is transformation there is no patentable process. That is not what this passage means. In earlier opinions this court and its predecessor court stated the correct view of this passage, as has the Supreme Court. The Court of Customs and Patent Appeals observed:

[This Cochrane passage] has sometimes been misconstrued as a ‘rule’ or ‘definition’ requiring that all processes, to be patentable, must operate physically on substances. Such a result misapprehends the nature of the passage quoted as dictum, in its context, and the question being discussed by the author of the opinion. To deduce such a rule from the statement would be contrary to its intendment which was not to limit process patentability but to point out that a process is not limited to the means used in performing it.

In re Prater, 56 C.C.P.A. 1381, 415 F.2d 1393, 1403 (1969). Again in In re Schrader, 22 F.3d 290, 295 n. 12 (Fed.Cir.1994) this court noted that Cochrane did not limit patent eligible subject matter to physical transformation, and that transformation of “intangibles” could qualify for patenting. In AT & T Corp. v. Excel Communications, Inc., 172 F.3d 1352, 1358 (Fed.Cir.1999), this court described physical transformation as “merely one example of how a mathematical algorithm may bring about a useful application.”

The Court saw the Cochrane decision in its proper perspective. Both Flook and Benson rejected the idea that Cochrane imposed the requirement of either specific machinery or the transformation of matter, as discussed ante. See Flook, 437 U.S. at 588 n. 9, 98 S.Ct. 2522; Benson, 409 U.S. at 71, 93 S.Ct. 253. Non-transformative processes were not at issue in either Cochrane or Diehr, and there is no endorsement in Diehr of a “machine-or-transformation” requirement for patentable processes.

These early cases cannot be held now to require exclusion, from the Section 101 definition of “process,” of all processes that deal with data and information, whose only machinery is electrons, photons, or waves, or whose product is not a transformed physical substance.

The English Statute of Monopolies and English common law do not limit “process” in Section 101

I comment on this aspect in view of the proposal in the concurring opinion that this court's new two-prong test for Section 101 process inventions was implicit in United States law starting with the Act of 1790, because of Congress's knowledge of and importation of English common law and the English Statute of Monopolies of 1623. The full history of patent law in England is too ambitious to be achieved within the confines of Bilski's appeal,<ref> Scholarly histories include M. Frumkin, The Origin of Patents, 27 J.P.O.S. 143 (1945); E. Wyndham Hulme, Privy Council Law and Practice of Letters Patent for Invention from the Restoration to 1794, 33 L.Q. Rev. 63 (Part I), 180 (Part II) (1917); Hulme, On the History of Patent Law in the Seventeenth and Eighteenth Centuries, 18 L.Q. Rev. 280 (1902); Hulme, The History of the Patent System Under the Prerogative and at Common Law, 12 L.Q. Rev. 141 (1896); Ramon A. Klitzke, Historical Background of the English Patent Law, 41 J.P.O.S 615 (1959); Christine MacLeod, Inventing the Industrial Revolution: The English Patent System 1660-1800 (1988); Frank D. Prager, Historic Background and Foundation of American Patent Law, 5 Am. J. Legal Hist. 309 (1961); Brad Sherman & Lionel Bently, The Making of Modern Intellectual Property Law: The British Experience, 1760-1911 (1999); Edward C. Walterscheid, The Early Evolution of the United States Patent Law: Antecedents, printed serially at J. Pat. & Trademark Off. Soc'y (“J.P.T.O.S.”) 76:697 (1994) (Part 1); 76:849 (1994) (Part 2); 77:771, 847 (1995) (Part 3); 78:77 (1996) (Part 4); 78:615 (1996) (Part 5, part I); and 78:665 (1996) (Part 5, part II) (hereinafter “ Early Evolution ”); and Edward C. Walterscheid, To Promote the Progress of Useful Arts: American Patent Law and Administration, 1798-1836 (1998).</ref> and the concurring opinion's selective treatment of this history may propagate misunderstanding.

The concurrence places primary reliance on the Statute of Monopolies, which was enacted in response to the monarchy's grant of monopolies “to court favorites in goods or businesses which had long before been enjoyed by the public.” Graham v. John Deere Co., 383 U.S. 1, 5, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966) (citing Peter Meinhardt, Inventions, Patents and Monopoly 30-35 (1946)). The Statute of Monopolies outlawed these “odious monopolies” or favors of the Crown, but, contrary to the concurring opinion, the Statute had nothing whatever to do with narrowing or eliminating categories of inventive subject matter eligible for a British patent. See Prager, Historical Background and Foundation of American Patent Law, 5 Am. J. Legal Hist. at 313 (“The statute [of Monopolies] said nothing about meritorious functions of patents, nothing about patent disclosures, and nothing about patent procedures; it was only directed against patent abuses.”).

Patents for inventions had been granted by the Crown long before 1623. See Hulme, The History of the Patent System Under the Prerogative and at Common Law, 12 L.Q. Rev. at 143 (the first patent grant to the “introducer of a newly-invented process” was in 1440); Klitzke, Historical Background of the English Patent Law, 41 J.P.O.S. at 626-27 (discussing first patents for “invention” in England in the fifteenth century). That practice was unaffected by the terms of the Statute of Monopolies, which rendered “utterly void” all “Monopolies and all Commissions, Grants, Licenses, Charters and Letters Patent” that were directed to “the sole Buying, Selling, Making, Working or Using any Thing within this Realm,” 21 Jac. 1, c.3, § I (Eng.), but which specifically excepted Letters Patent for inventions from that exclusion, id. § VI. The only new limitation on patents for invention was a fourteen-year limit on the term of exclusivity. See Klitzke, Historical Background of the English Patent Law, 41 J.P.O.S. at 649.

The usage “Letters Patent” described one of the forms of document whereby the Crown granted various rights, whether the grant was for an odious monopoly that the Statute of Monopolies eliminated, or for rights to an invention new to England. That usage was not changed by the Statute of Monopolies. Nor were other aspects of the British practice which differed from that enacted in the United States, particularly the aspect whereby a British patent could be granted to a person who imported something that was new to England, whether or not the import was previously known or the importer was the inventor thereof. In England, “[t]he rights of the inventor are derived from those of the importer, and not vice versa as is commonly supposed.” Hulme, The History of the Patent System Under the Prerogative and at Common Law, 12 L.Q.R. at 152; see also MacLeod, Inventing the Industrial Revolution 13 (“The rights of the first inventor were understood to derive from those of the first importer of the invention.”).

In contrast, in the United States the patent right has never been predicated upon importation, and has never been limited to “manufactures.” See, e.g., Walterscheid, To Promote the Progress of Useful Arts 93, 137-38, 224; see also Prager, Historic Background and Foundation of American Patent Law, 5 Am. J. Legal Hist. at 309 (“The American Revolution destroyed many of the ancient customs; it brought a sweeping reorientation of patent law, with new forms, new rules, new concepts, and new ideals.”). The differences between the American and English patent law at this nation's founding were marked, and English judicial decisions interpreting the English statute are of limited use in interpreting the United States statute. In all events, no English decision supports this court's new restrictive definition of “process.”

The concurrence proposes that the Statute of Monopolies provides a binding definition of the terms “manufacture,” “machine,” “composition of matter,” and “process” in Section 101 of the U.S. Patent Act. See concurring op. at 968-70. The only one of these terms that appears in the Statute of Monopolies is “manufacture”, a broad term that reflects the usage of the period. Even at the time of this country's founding, the usage was broad, as set forth in Samuel Johnson's Dictionary of the English Language (3d. ed. 1768), which defines “manufacture” as “any thing made by art,” and defines “art” as “the power of doing something not taught by nature and instinct”; “a science”; “a trade”; “artfulness”; “skill”; “dexterity.” Historians explain that England's primary motive for patenting was to promote “[a]cquisition of superior Continental technology” at a time when England lagged behind, see MacLeod, Inventing the Industrial Revolution 11; this cannot be interpreted to mean that England and perforce the United States intended to eliminate “processes” from this incentive system. It is inconceivable that on this background the Framers, and again the enactors of the first United States patent statutes in 1790 and 1793, intended sub silentio to impose the limitations on “process” now created by this court.

Congress' earliest known draft patent bill included the terms “art, manufacture, engine, machine, invention or device, or any improvement upon the same.” Walterscheid, To Promote the Progress of Useful Arts 92. The 1793 Act explicitly stated “any new and useful art,” § 1, 1 Stat. 318 (1793), a usage that was carried forward until “art” was replaced with “process” in 35 U.S.C. § 101 and defined in § 100(b). Historians discuss that Congress' inclusion of any “art” or “process” in the patent system was a deliberate clarification of the English practice. See Walterscheid, To Promote the Progress of Useful Arts 93 (“[The first patent bill] appears to be an obvious attempt to deal legislatively with issues that were beginning to be addressed by the English courts.... [I]t states unequivocally that improvement inventions are patentable and expands the definition of invention or discovery beyond simply ‘manufacture.’ ”); Karl B. Lutz, Patents and Science: A Clarification of the Patent Clause of the U.S. Constitution, 32 J.P.O.S. 83, 86 (1950) ( “By the year 1787 it was being recognized even in Great Britain that the phrase ‘new manufactures' was an unduly limited object for a patent system, since it seems to exclude new processes.... [This question was] resolved in the United States Constitution by broadening the field from ‘new manufactures' to ‘useful arts'....”).

In interpreting a statute, it is the language selected by Congress that occupies center stage: “[O]ur obligation is to take statutes as we find them, guided, if ambiguity appears, by the legislative history and statutory purpose.” Chakrabarty, 447 U.S. at 315, 100 S.Ct. 2204. The Court has “perceive[d] no ambiguity” in Section 101, leaving no need for foreign assistance. Id. The legislative choice to afford the patent system “wide scope,” id. at 308, 100 S.Ct. 2204, including “process” inventions, evolved in the United States independent of later developments of the common law in England.

The concurrence concludes that the Statute of Monopolies foreclosed the future patenting of anything that the concurrence calls a “business method”-the term is not defined-whether or not the method is new, inventive, and useful. But the Statute of Monopolies only foreclosed “odious” monopolies, illustrated by historical reports that Queen Elizabeth had granted monopolies on salt, ale, saltpeter, white soap, dredging machines, playing cards, and rape seed oil, and on processes and services such as Spanish leather-making, mining of various metals and ores, dying and dressing cloth, and iron tempering. See Walterscheid, Early Evolution (Part 2), 76 J.P.T.O.S. at 854 n.14; Klitzke, Historical Background of the English Patent Law, 41 J.P.O.S. at 634-35. These and other grants, many of which were implemented by Letters Patent, were the “odious monopolies” that were rendered illegal. They included several classes of known activity, product and process, and had nothing to do with new “inventions.” The Statute of Monopolies cannot be held to have restricted the kinds of new processes that can today be eligible for patenting in the United States, merely because it outlawed patents on non-novel businesses in England. The presence or absence of “organizing human activity,” a vague term created by the concurrence, has no connection or relevance to Parliament's elimination of monopoly patronage grants for old, established arts. The Statute of Monopolies neither excluded nor included inventions that involve human activity, although the words “the sole working or making in any manner of new manufactures” presuppose human activity. 21 Jac. 1, c.3, § VI (emphases added). We are directed to no authority for the proposition that a new and inventive process involving “human activity” has historically been treated differently from other processes; indeed, most inventions involve human activity.

The concurrence has provided hints of the complexity of the evolution of patent law in England, as in the United States, as the Industrial Revolution took hold. Historians have recognized these complexities. See, e.g., Walterscheid, To Promote the Progress of Useful Arts 5 (“[T]he American patent law almost from its inception departed from its common law counterpart in the interpretation that would be given to the definition of novelty....”); Klitzke, Historical Background of the English Patent Law, 41 J.P.O.S. at 638 (noting that in Elizabethan times, novelty only required a showing that “the industry had not been carried on within the realm within a reasonable period of time”, while today “the proof of a single public sale of an article” or a “printed publication” can negate patentability).

I caution against over-simplification, particularly in view of the uncertainties in English common law at the time of this country's founding. See Boulton v. Bull, 2 H. Bl. 463, 491 (C.P.1795) (Eyre, C.J.) (“Patent rights are no where that I can find accurately discussed in our books.”); MacLeod, Inventing the Industrial Revolution 61 (“It was only from the time when the Privy Council relinquished jurisdiction that a case law on patents began to develop.... But it was a slow process and even the spate of hard-fought patent cases at the end of the eighteenth century did little to establish a solid core of judicial wisdom.”). The English judicial opinions of the eighteenth century were not as limiting on the United States as my colleagues suggest. See Walterscheid, The Nature of the Intellectual Property Clause: A Study in Historical Perspective 355 (2002) (“In the eighteenth century, patentees and those who gave advice concerning patents were certainly of the view that the Statute did not preclude the patenting of general principles of operation.”); see also MacLeod, Inventing the Industrial Revolution 63-64.

It is reported that in the century and a half following enactment of the Statute of Monopolies, the English patent registers were replete with inventions claimed as “processes.” See Walterscheid, Early Evolution (Part 3), 77 J.P.T.O.S. at 856 (“As one of the earliest texts on the patent law stated in 1806: “most of the patents now taken out, are by name, for the method of doing particular things....”). The concurrence agrees; but it is also reported that because patents were not litigated in the common law courts until the Privy Council authorized such suits in 1752, judicial interpretation of various aspects of patent law were essentially absent until about the time this country achieved independence, leading to the variety of views expressed in Boulton v. Bull. The legislators in the new United States cannot now be assigned the straightjacket of law not yet developed in England. Indeed, the first patent granted by President Washington, upon examination by Secretary of State Jefferson, was for a method of “making Pot-ash and Pearl-ash,” a process patent granted during the period that the concurrence states was fraught with English uncertainty about process patents. See The First United States Patent, 36 J.P.O.S. 615, 616-17 (1954).

The concurrence lists some English process patents predating the United States' 1793 Patent Act, and argues that processes not sufficiently “like” these archaic inventions should not now be eligible for patenting. I refer simply to Flook, 437 U.S. at 588 n. 9, 98 S.Ct. 2522, where the Court stated: “As in Benson, we assume that a valid process patent may issue even if it does not meet one of the qualifications of our earlier precedents.” Similarly, the Chakrabarty Court stated: “[A] statute is not to be confined to the particular applications ... contemplated by the legislators. This is especially true in the field of patent law.” Chakrabarty, 447 U.S. at 315-16, 100 S.Ct. 2204 (citing Barr v. United States, 324 U.S. 83, 90, 65 S.Ct. 522, 89 L.Ed. 765 (1945); Browder v. United States, 312 U.S. 335, 339, 61 S.Ct. 599, 85 L.Ed. 862 (1941); Puerto Rico v. Shell Co., 302 U.S. 253, 257, 58 S.Ct. 167, 82 L.Ed. 235 (1937)). The meaning of the statutory term “process” is not limited by particular examples from more than two hundred years ago.

However, I cannot resist pointing to the “business method” patents on Woodcroft's list. See concurring op. at 973 (citing No. 1197 to John Knox (July 21, 1778) (“Plan for assurances on lives of persons from 10 to 80 years of age.”)). Several other process patents on Woodcroft's list appear to involve financial subject matter, and to require primarily human activity. See, e.g., No. 1170 to John Molesworth (Sept. 29, 1777) (“Securing to the purchasers of shares and chances of state-lottery tickets any prize drawn in their favor.”); No. 1159 to William Nicholson (July 14, 1777) (“Securing the property of persons purchasing shares of State-lottery tickets.”), cited in Bennet Woodcroft, Alphabetical Index of Patentees of Inventions 383, 410 (U.S. ed.1969). Other English process patents from the several decades following 1793 can aptly be described as “business methods,” although not performed with the aid of computers. E.g., No. 10,367 to George Robert D'Harcourt (Oct. 29, 1844) (“Ascertaining and checking the number of checks or tickets which have been used and marked, applicable for railway officers.”).

While most patents of an earlier era reflect the dominant mechanical and chemical technologies of that era, modern processes reflect the dramatic advances in telecommunications and computing that have occurred since the time of George III. See USPTO White Paper, Automated Financial or Management Data Processing Methods (Business Methods) 4 (2000), available at http:// www. uspto. gov/ web/ menu/ busmethp/ whitepaper. pdf (hereinafter USPTO White Paper) (“The full arrival of electricity as a component in business data processing system[s] was a watershed event.”). It is apparent that economic, or “business method,” or “human activity” patents were neither explicitly nor implicitly foreclosed from access to the English patent system.

Evolution of process patents in the United States

The United States' history of patenting establishes the same point. The PTO has located various patents predating modern computer usages that can be described as financial or business methods. The USPTO White Paper at 3-4 and appendix A describes the history of financial apparatus and method patents dating back to 1799, including patents on bank notes, bills of credit, bills of exchange, check blanks, detecting and preventing counterfeiting, coin counting, interest calculation tables, and lotteries, all within the first fifty years of the United States patent system. It is a distortion of these patents to describe the processes as “tied to” another statutory category-that is, paper and pencil. Concurring op. at 974-75 & n. 18. Replacement of paper with a computer screen, and pencil with electrons, does not “untie” the process. Fairly considered, the many older financial and business-oriented patents that the PTO and many of the amici have identified are of the same type as the Bilski claims; they were surely not rendered patent-eligible solely because they used “paper” to instantiate the financial strategies and transactions that comprised their contribution.

I do not disagree with the general suggestion that statutes intended to codify the existing common law are to be interpreted in light of then-contemporary practice, including, if relevant, the English cases. See concurring op. at 972-73. However, the court must be scrupulous in assessing the relevance of decisions that were formulated on particularized facts involving the technology of the period. The United States Supreme Court has never held that “process” inventions suffered a second-class status under our statutes, achieving patent eligibility only derivatively through an explicit “tie” to another statutory category. The Court has repeatedly disparaged efforts to read in restrictions not based on statutory language. See Diehr, 450 U.S. at 182, 101 S.Ct. 1048; Chakrabarty, 447 U.S. at 308, 100 S.Ct. 2204. Yet second-class status is today engrafted on “process” inventions. There is plainly no basis for such restriction, which is a direct path to the “gloomy thought” that concerned Senator O.H. Platt in his Remarks in Congress at the Centennial Proceedings of the United States Patent System:

For one, I cannot entertain the gloomy thought that we have come to that century in the world's life in which new and grander achievements are impossible.... Invention is a prolific mother; every inventive triumph stimulates new effort. Man never is and never will be content with success, and the great secrets of nature are as yet largely undiscovered.

Invention and Advancement (1891), reprinted in United States Bicentennial Commemorative Edition of Proceedings and Addresses: Celebration of the Beginning of the Second Century of the American Patent System 75-76 (1990).

In sum, history does not support the retrogression sponsored by the concurrence.

This court now rejects its own CCPA and Federal Circuit precedent

The majority opinion holds that there is a Supreme Court restriction on process patents, “enunciated” in Benson, Flook, and Diehr; and that this restriction was improperly ignored by the Federal Circuit and the Court of Customs and Patent Appeals, leading us into error which we must now correct. Thus this court announces that our prior decisions may no longer be relied upon. Maj. op. at 959-60 & nn. 17, 19. The effect on the patents and businesses that did rely on them is not considered.

The Court's decisions in Benson, Flook, and Diehr all reached the Supreme Court by way of the CCPA, and the CCPA successively implemented the Court's guidance in establishing the Freeman/Walter/Abele test for eligibility under Section 101. The Federal Circuit continued to consider computer-facilitated processes, as in Arrhythmia Research Technology, 958 F.2d at 1059-60, where patent-eligibility was confirmed for a computer-assisted mathematical analysis of electrocardiograph signals that determined the likelihood of recurrence of heart attack. This court now rules that this precedent “should no longer be relied on.” Maj. op. at 959 n. 17.

In In re Alappat, 33 F.3d 1526 (Fed.Cir.1994) ( en banc ) the question was the eligibility for patent of a rasterizer that mathematically transforms data to eliminate aliasing in a digital oscilloscope. The court held that a computer-implemented system that produces a “useful, concrete, and tangible result” is Section 101 subject matter. Id. at 1544. This court now rules that “a ‘useful, concrete and tangible result’ analysis should no longer be relied on.” Maj. op. at 960 n. 19.

The Alappat court stressed the intent, embodied in the language of the statute, that the patent system be broadly available to new and useful inventions:

The use of the expansive term “any” in § 101 represents Congress's intent not to place any restrictions on the subject matter for which a patent may be obtained beyond those specifically recited in § 101 and other parts of Title 35.

33 F.3d at 1542. This court looked to the Supreme Court's guidance in its Section 101 decisions, and explained:

A close analysis of Diehr, Flook, and Benson reveals that the Supreme Court never intended to create an overly broad, fourth category of [mathematical] subject matter excluded from § 101. Rather, at the core of the Court's analysis in each of these cases lies an attempt by the Court to explain a rather straightforward concept, namely, that certain types of mathematical subject matter, standing alone, represent nothing more than abstract ideas until reduced to some type of practical application, and thus that subject matter is not, in and of itself, entitled to patent protection.

Id. at 1543 (emphasis in original). The court cited the Supreme Court's distinction between abstract ideas and their practical application, and stated of the claimed rasterizer: “This is not a disembodied mathematical concept which may be characterized as an ‘abstract idea,’ but rather a specific machine to produce a useful, concrete, and tangible result.” Id. at 1544.

This principle was applied to a computer-implemented data processing system for managing pooled mutual fund assets in State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (Fed.Cir.1998), and to a method for recording and processing telephone data in AT & T v. Excel. The court explained that processes that include mathematical calculations in a practical application can produce a useful, concrete, and tangible result, which in State Street Bank was “expressed in numbers, such as price, profit, percentage, cost, or loss.” 149 F.3d at 1375. In AT & T v. Excel the court applied State Street Bank and Diehr, and stated that “physical transformation ... is not an invariable requirement, but merely one example of how a mathematical algorithm may bring about a useful application” and thus achieve a useful, concrete, and tangible result. 172 F.3d at 1358. This analysis, too, can no longer be relied on. Maj. op. at 960 n. 19.

The now-discarded criterion of a “useful, concrete, and tangible result” has proved to be of ready and comprehensible applicability in a large variety of processes of the information and digital ages. The court in State Street Bank reinforced the thesis that there is no reason, in statute or policy, to exclude computer-implemented and information-based inventions from access to patentability. The holdings and reasoning of Alappat and State Street Bank guided the inventions of the electronic age into the patent system, while remaining faithful to the Diehr distinction between abstract ideas such as mathematical formulae and their application in a particular process for a specified purpose. And patentability has always required compliance with all of the requirements of the statute, including novelty, non-obviousness, utility, and the provisions of Section 112.

The public has relied on the rulings of this court and of the Supreme Court

The decisions in Alappat and State Street Bank confirmed the patent eligibility of many evolving areas of commerce, as inventors and investors explored new technological capabilities. The public and the economy have experienced extraordinary advances in information-based and computer-managed processes, supported by an enlarging patent base. The PTO reports that in Class 705, the examination classification associated with “business methods” and most likely to receive inventions that may not use machinery or transform physical matter, there were almost 10,000 patent applications filed in FY 2006 alone, and over 40,000 applications filed since FY 98 when State Street Bank was decided. See Wynn W. Coggins, USPTO, Update on Business Methods for the Business Methods Partnership Meeting 6 (2007) (hereinafter “ PTO Report ”), available at http:// www. uspto. gov/ web/ menu/ pbmethod/ partnership. pps. An amicus in the present case reports that over 15,000 patents classified in Class 705 have issued. See Br. of Amicus Curiae Accenture, at 22 n.20.<ref>The PTO recognizes that patents on “business methods” have been eligible subject matter for two centuries. See USPTO White Paper 2 (“Financial patents in the paper-based technologies have been granted continuously for over two hundred years.”).</ref> The industries identified with information-based and data-handling processes, as several amici curiae explain and illustrate, include fields as diverse as banking and finance, insurance, data processing, industrial engineering, and medicine.

Stable law, on which industry can rely, is a foundation of commercial advance into new products and processes. Inventiveness in the computer and information services fields has placed the United States in a position of technological and commercial preeminence. The information technology industry is reported to be “the key factor responsible for reversing the 20-year productivity slow-down from the mid-1970s to the mid-1990s and in driving today's robust productivity growth.” R.D. Atkinson & A.S. McKay, Digital Prosperity: Understanding the Economic Benefits of the Information Technology Revolution 10 (Info. Tech. & Innovation Found.2007), available at http:// www. itif. org/ files/ digital_ prosperity. pdf. By revenue estimates, in 2005 the software and information sectors constituted the fourth largest industry in the United States, with significantly faster growth than the overall U.S. economy. Software & Info. Indus. Ass'n, Software and Information: Driving the Knowledge Economy 7-8 (2008), http:// www. siia. net/ estore/ globecon- 08. pdf. A Congressional Report in 2006 stated:

As recently as 1978, intangible assets, such as intellectual property, accounted for 20 percent of corporate assets with the vast majority of value (80 percent) attributed to tangible assets such as facilities and equipment. By 1997, the trend reversed; 73 percent of corporate assets were intangible and only 27 percent were tangible.

H.R.Rep. No. 109-673 (accompanying a bill concerning judicial resources).

This powerful economic move toward “intangibles” is a challenge to the backward-looking change of this court's ruling today. Until the shift represented by today's decision, statute and precedent have provided stability in the rapidly moving and commercially vibrant fields of the Information Age. Despite the economic importance of these interests, the consequences of our decision have not been considered. I don't know how much human creativity and commercial activity will be devalued by today's change in law; but neither do my colleagues.

The Section 101 interpretation that is now uprooted has the authority of years of reliance, and ought not be disturbed absent the most compelling reasons. “Considerations of stare decisis have special force in the area of statutory interpretation, for here, unlike in the context of constitutional interpretation, the legislative power is implicated, and Congress remains free to alter what [the courts] have done.” Shepard v. United States, 544 U.S. 13, 23, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005) (quoting Patterson v. McLean Credit Union, 491 U.S. 164, 172-73, 109 S.Ct. 2363, 105 L.Ed.2d 132 (1989)); see also Hilton v. S.C. Pub. Railways Comm'n, 502 U.S. 197, 205, 112 S.Ct. 560, 116 L.Ed.2d 560 (1991) (in cases of statutory interpretation the importance of adhering to prior rulings is “most compelling”). Where, as here, Congress has not acted to modify the statute in the many years since Diehr and the decisions of this court, the force of stare decisis is even stronger. See Shepard, 544 U.S. at 23, 125 S.Ct. 1254.

Adherence to settled law, resulting in settled expectations, is of particular importance “in cases involving property and contract rights, where reliance interests are involved.” Payne v. Tennessee, 501 U.S. 808, 828, 111 S.Ct. 2597, 115 L.Ed.2d 720 (1991); see also United States v. Title Ins. & Trust Co., 265 U.S. 472, 486, 44 S.Ct. 621, 68 L.Ed. 1110 (1924) (declining to overrule precedent where prior ruling “has become a rule of property, and to disturb it now would be fraught with many injurious results”). This rationale is given no weight by my colleagues, as this court gratuitously disrupts decades of law underlying our own rulings. The only announced support for today's change appears to be the strained new reading of Supreme Court quotations. But this court has previously read these decades-old opinions differently, without objection by either Congress or the Court. My colleagues do not state a reason for their change of heart. See Benjamin N. Cardozo, The Nature of the Judicial Process 149 (1921) (“[T]he labor of judges would be increased almost to the breaking point if every past decision could be reopened in every case, and one could not lay one's own course of bricks on the secure foundation of the courses laid by others who had gone before him.”).

It is the legislature's role to change the law if the public interest so requires. In Chakrabarty the Court stated: “The choice we are urged to make is a matter of high policy for resolution within the legislative process after the kind of investigation, examination, and study that legislative bodies can provide and courts cannot.” 447 U.S. at 317, 100 S.Ct. 2204; see also Flook, 437 U.S. at 595, 98 S.Ct. 2522 (“Difficult questions of policy concerning the kinds of programs that may be appropriate for patent protection and the form and duration of such protection can be answered by Congress on the basis of current empirical data not equally available to this tribunal.”).

It is, however, the judicial obligation to assure a correct, just, and reliable judicial process, and particularly to respect the principles of stare decisis in an area in which prior and repeated statutory interpretations have been relied upon by others. See, e.g., Shepard, 544 U.S. at 23, 125 S.Ct. 1254 (“[T]he claim to adhere to case law is generally powerful once a decision has settled statutory meaning.”); Hilton, 502 U.S. at 202, 112 S.Ct. 560 (“Adherence to precedent promotes stability, predictability, and respect for judicial authority.”); Payne, 501 U.S. at 827, 111 S.Ct. 2597 (“ Stare decisis is the preferred course because it promotes the evenhanded, predictable, and consistent development of legal principles, fosters reliance on judicial decisions, and contributes to the actual and perceived integrity of the judicial process.”). These considerations appear to be abandoned.

Uncertain guidance for the future

Not only past expectations, but future hopes, are disrupted by uncertainty as to application of the new restrictions on patent eligibility. For example, the court states that even if a process is “tied to” a machine or transforms matter, the machine or transformation must impose “meaningful limits” and cannot constitute “insignificant extra-solution activity”. Maj. op. at 961-62. We are advised that transformation must be “central to the purpose of the claimed process,” id., although we are not told what kinds of transformations may qualify, id. at 962-63. These concepts raise new conflicts with precedent.

This court and the Supreme Court have stated that “there is no legally recognizable or protected ‘essential’ element, ‘gist’ or ‘heart’ of the invention in a combination patent.” Allen Eng'g Corp. v. Bartell Industries, Inc., 299 F.3d 1336, 1345 (Fed.Cir.2002) (quoting Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336, 345, 81 S.Ct. 599, 5 L.Ed.2d 592 (1961)). This rule applies with equal force to process patents, see W.L. Gore & Associates, Inc. v. Garlock, Inc., 721 F.2d 1540, 1548 (Fed.Cir.1983) (there is no gist of the invention rule for process patents), and is in accord with the rule that the invention must be considered as a whole, rather than “dissected,” in assessing its patent eligibility under Section 101, see Diehr, 450 U.S. at 188, 101 S.Ct. 1048. It is difficult to predict an adjudicator's view of the “invention as a whole,” now that patent examiners and judges are instructed to weigh the different process components for their “centrality” and the “significance” of their “extra-solution activity” in a Section 101 inquiry.

As for whether machine implementation will impose “meaningful limits in a particular case,” the “meaningfulness” of computer usage in the great variety of technical and informational subject matter that is computer-facilitated is apparently now a flexible parameter of Section 101. Each patent examination center, each trial court, each panel of this court, will have a blank slate on which to uphold or invalidate claims based on whether there are sufficient “meaningful limits”, or whether a transformation is adequately “central,” or the “significance” of process steps. These qualifiers, appended to a novel test which itself is neither suggested nor supported by statutory text, legislative history, or judicial precedent, raise more questions than they answer. These new standards add delay, uncertainty, and cost, but do not add confidence in reliable standards for Section 101.

Other aspects of the changes of law also contribute uncertainty. We aren't told when, or if, software instructions implemented on a general purpose computer are deemed “tied” to a “particular machine,” for if Alappat's guidance that software converts a general purpose computer into a special purpose machine remains applicable, there is no need for the present ruling. For the thousands of inventors who obtained patents under the court's now-discarded criteria, their property rights are now vulnerable.

The court also avoids saying whether the State Street Bank and AT & T v. Excel inventions would pass the new test. The drafting of claims in machine or process form was not determinative in those cases, for “we consider the scope of § 101 to be the same regardless of the form-machine or process-in which a particular claim is drafted.” AT & T v. Excel, 172 F.3d at 1357. From either the machine or the transformation viewpoint, the processing of data representing “price, profit, percentage, cost, or loss” in State Street Bank is not materially different from the processing of the Bilski data representing commodity purchase and sale prices, market transactions, and risk positions; yet Bilski is held to fail our new test, while State Street is left hanging. The uncertainty is illustrated in the contemporaneous decision of In re Comiskey, 499 F.3d 1365, 1378-79 (Fed.Cir.2007), where the court held that “systems that depend for their operation on human intelligence alone” to solve practical problems are not within the scope of Section 101; and In re Nuijten, 500 F.3d 1346, 1353-54 (Fed.Cir.2007), where the court held that claims to a signal with an embedded digital watermark encoded according to a given encoding process were not directed to statutory subject matter under Section 101, although the claims included “physical but transitory forms of signal transmission such as radio broadcasts, electrical signals through a wire, and light pluses through a fiber-optic cable.”

Although this uncertainty may invite some to try their luck in court, the wider effect will be a disincentive to innovation-based commerce. For inventors, investors, competitors, and the public, the most grievous consequence is the effect on inventions not made or not developed because of uncertainty as to patent protection. Only the successes need the patent right.

The Bilski invention has not been examined for patentability

To be patentable, Bilski's invention must be novel and non-obvious, and the specification and claims must meet the requirements of enablement, description, specificity, best mode, etc. See 35 U.S.C. § 101 (“Whoever invents or discovers a new and useful process ... may obtain a patent therefor, subject to the conditions and requirements of this title.”); Diehr, 450 U.S. at 190, 101 S.Ct. 1048 (the question of whether an invention is novel is distinct from whether the subject matter is statutory); State Street Bank, 149 F.3d at 1377 (“Whether the patent's claims are too broad to be patentable is not to be judged under § 101, but rather under §§ 102, 103, and 112.”). I don't know whether Bilski can meet these requirements-but neither does this court, for the claims have not been examined for patentability, and no rejections apart from Section 101 are included in this appeal.

Instead, the court states the “true issue before us” is “whether Applicants are seeking to claim a fundamental principle (such as an abstract idea) or mental process,” maj. op. at 952, and answers “yes.” With respect, that is the wrong question, and the wrong answer. Bilski's patent application describes his process of analyzing the effects of supply and demand on commodity prices and the use of a coupled transaction strategy to hedge against these risks; this is not a fundamental principle or an abstract idea; it is not a mental process or a law of nature. It is a “process,” set out in successive steps, for obtaining and analyzing information and carrying out a series of commercial transactions for the purpose of “managing the consumption risk costs of a commodity sold by a commodity provider at a fixed price.” Claim 1, preamble.

Because the process Bilski describes employs complex mathematical calculations to assess various elements of risk, any practicable embodiment would be conducted with the aid of a machine-a programmed computer-but the court holds that since computer-implementation is not recited in claim 1, for that reason alone the process fails the “machine” part of the court's machine-or-transformation test. Maj. op. at 962. And the court holds that since Bilski's process involves the processing of data concerning commodity prices and supply and demand and other risk factors, the process fails the “transformation” test because no “physical objects or substances” are transformed. Maj. op. at 963-64. The court then concludes that because Bilski's Claim 1 fails the machine-or-transformation test it ipso facto preempts a “fundamental principle” and is thereby barred from the patent system under Section 101: an illogical leap that displays the flaws in the court's analysis.

If a claim is unduly broad, or if it fails to include sufficient specificity, the appropriate ground of rejection is Section 112, for claims must “particularly point out and distinctly claim[ ]” the invention. See In re Vaeck, 947 F.2d 488, 495-96 (Fed.Cir.1991) (affirming rejection under Section 112 where “[t]here is no reasonable correlation between the narrow disclosure in applicant's specification and the broad scope of protection sought in the claims”); In re Foster, 58 C.C.P.A. 1001, 438 F.2d 1011, 1016 (1971) (claims “not commensurate with appellants' own definition of what they are seeking to cover” are rejected under Section 112, rather than Section 101); In re Prater, 415 F.2d at 1403-04 (applying Section 112 to claims that included mental steps). The filing of a broader claim than is supported in the specification does not convert the invention into an abstraction and evict the application from eligibility for examination. A broad first claim in a patent application is routine; it is not the crisis event postulated in the court's opinion.

The role of examination is to determine the scope of the claims to which the applicant is entitled. See 37 C.F.R. § 1.104(a). The PTO's regulations provide:

On taking up an application for examination or a patent in a reexamination proceeding, the examiner shall make a thorough study thereof and shall make a thorough investigation of the available prior art relating to the subject matter of the claimed invention. The examination shall be complete with respect to both compliance of the application or patent under reexamination with the applicable statutes and rules and to the patentability of the invention as claimed, as well as with respect to matters of form, unless otherwise indicated.

Id. § 1.104(a)(1). The Manual of Patent Examining Procedure (MPEP) similarly instructs the examiners to conduct a “thorough search of the prior art” before evaluating the invention under Section 101. MPEP § 2106(III) (8th ed., rev.7, July.2008) (“Prior to evaluating the claimed invention under 35 U.S.C. § 101, USPTO personnel are expected to conduct a thorough search of the prior art.”). The MPEP also requires examiners to identify all grounds of rejection in the first official PTO action to avoid unnecessary delays in examination. Id. § 2106(II) (“Under the principles of compact prosecution, each claim should be reviewed for compliance with every statutory requirement for patentability in the initial review of the application, even if one or more claims are found to be deficient with respect to some statutory requirement.”). I note that this requirement does not appear to have been here met.

Several amici curiae referred to the difficulties that the PTO has reported in examining patents in areas where the practice has been to preserve secrecy, for published prior art is sparse. The Federal Trade Commission recognized that the problem of “questionable” patents stems mostly from “the difficulty patent examiners can have in considering all the relevant prior art in the field and staying informed about the rapid advance of computer science.” FTC, To Promote Innovation: The Proper Balance of Competition & Patent Law and Policy at ch. 3, pp. 44 (Oct.2003), available at http:// www. ftc. gov/ os/ 2003/ 10/ innovationrpt. pdf. However, this problem seems to be remedied, for the PTO reported in 2007 that for Class 705, “[t]he cases the examiners are now working on have noticeably narrower claims” than the cases filed in or before FY 2000. PTO Report at 9. The PTO reports that its search fields have been enlarged, staff added, and supervision augmented. FTC Report at ch. 1, p. 30. (“Since the PTO introduced [these changes] the allowance rate for business method patents has decreased, and the PTO believes that this decreased allowance rate indicates improved PTO searches for prior art.”). If this court's purpose now is to improve the quality of issued patents by eliminating access to patenting for large classes of past, present, and future inventions, the remedy would appear to be excessive.

A straightforward, efficient, and ultimately fair approach to the evaluation of “new and useful” processes-quoting Section 101-is to recognize that a process invention that is not clearly a “fundamental truth, law of nature, or abstract idea” is eligible for examination for patentability. I do not suggest that basic scientific discoveries are a proper subject matter of patents (the Court in Chakrabarty mentioned E=mc 2 and the law of gravity), and I do not attempt an all-purpose definition of the boundary between scientific theory and technological application. But it is rare indeed that a question arises at the boundary of basic science; more usual is the situation illustrated by Samuel Morse's telegraph, in which the Court simply held that Morse's general claim was “too broad,” exceeding the scope of his practical application.

Bilski's process for determining risk in commodity transactions does not become an abstraction because it is broadly claimed in his first claim. It may be claimed so broadly that it reads on the prior art, but it is neither a fundamental truth nor an abstraction. Bilski's ten other claims contain further details and limitations, removing them farther from abstraction. Although claim 1 may have been deemed “representative” with respect to Section 101, the differences among the claims may be significant with respect to Sections 102, 103, and 112. Bilski's application, now pending for eleven years, has yet to be examined for patentability.

CONCLUSION

In sum, the text of Section 101, its statutory history, its interpretation by the Supreme Court, and its application by the courts, contravene this court's redefinition of the statutory term “process.” The court's decision affects present and future rights and incentives, and usurps the legislative role. The judicial role is to support stability and predictability in the law, with fidelity to statute and precedent, and respect for the principles of stare decisis.

Patents provide an incentive to invest in and work in new directions. In United States v. Line Material Co., 333 U.S. 287, 332, 68 S.Ct. 550, 92 L.Ed. 701 (1948), Justice Burton, joined by Chief Justice Vinson and Justice Frankfurter, remarked that “the frontiers of science have expanded until civilization now depends largely upon discoveries on those frontiers to meet the infinite needs of the future. The United States, thus far, has taken a leading part in making those discoveries and in putting them to use.” This remains true today. It is antithetical to this incentive to restrict eligibility for patenting to what has been done in the past, and to foreclose what might be done in the future.

===Footnotes===
<references/>

In Re Bilski, Newman dissenting opinion

2015-04-02T17:47:14Z

Bill:

NEWMAN, Circuit Judge, dissenting.

The court today acts en banc to impose a new and far-reaching restriction on the kinds of inventions that are eligible to participate in the patent system. The court achieves this result by redefining the word “process” in the patent statute, to exclude all processes that do not transform physical matter or that are not performed by machines. The court thus excludes many of the kinds of inventions that apply today's electronic and photonic technologies, as well as other processes that handle data and information in novel ways. Such processes have long been patent eligible, and contribute to the vigor and variety of today's Information Age. This exclusion of process inventions is contrary to statute, contrary to precedent, and a negation of the constitutional mandate. Its impact on the future, as well as on the thousands of patents already granted, is unknown.

This exclusion is imposed at the threshold, before it is determined whether the excluded process is new, non-obvious, enabled, described, particularly claimed, etc.; that is, before the new process is examined for patentability. For example, we do not know whether the Bilski process would be found patentable under the statutory criteria, for they were never applied.

The innovations of the “knowledge economy”-of “digital prosperity”-have been dominant contributors to today's economic growth and societal change. Revision of the commercial structure affecting major aspects of today's industry should be approached with care, for there has been significant reliance on the law as it has existed, as many amici curiae pointed out. Indeed, the full reach of today's change of law is not clear, and the majority opinion states that many existing situations may require reassessment under the new criteria.

Uncertainty is the enemy of innovation. These new uncertainties not only diminish the incentives available to new enterprise, but disrupt the settled expectations of those who relied on the law as it existed. I respectfully dissent.

DISCUSSION
The court's exclusion of specified process inventions from access to the patent system is achieved by redefining the word “process” in the patent statute. However, the court's redefinition is contrary to statute and to explicit rulings of the Supreme Court and this court. I start with the statute:

Section 101 is the statement of statutory eligibility
From the first United States patent act in 1790, the subject matter of the “useful arts” has been stated broadly, lest advance restraints inhibit the unknown future. The nature of patent-eligible subject matter has received judicial attention over the years, as new issues arose with advances in science and technology. The Supreme Court has consistently confirmed the constitutional and legislative purpose of providing a broadly applicable incentive to commerce and creativity, through this system of limited exclusivity. Concurrently, the Court early explained the limits of patentable subject matter, in that “fundamental truths” were not intended to be included in a system of exclusive rights, for they are the general foundations of knowledge. Thus laws of nature, natural phenomena, and abstract ideas are not subject to patenting. Several rulings of the Court have reviewed patent eligibility in light of these fundamentals. However, the Court explicitly negated today's restrictions. My colleagues in the majority are mistaken in finding that decisions of the Court require the per se limits to patent eligibility that the Federal Circuit today imposes. The patent statute and the Court's decisions neither establish nor support the exclusionary criteria now adopted.

The court today holds that any process that does not transform physical matter or require performance by machine is not within the definition of “process” in any of the patent statutes since 1790. All of the statutes contained a broad definition of patent-eligible subject matter, like that in the current Patent Act of 1952:

35 U.S.C § 101 Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.

In Diamond v. Diehr, 450 U.S. 175, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981) the Court explained that Section 101 is not an independent condition of patentability, but a general statement of subject matter eligibility. The Court stated:

Section 101, however, is a general statement of the type of subject matter that is eligible for patent protection “subject to the conditions and requirements of this title.” Specific conditions for patentability follow and § 102 covers in detail the conditions relating to novelty. The question therefore of whether a particular invention is novel is “wholly apart from whether the invention falls in a category of statutory subject matter.”

Id. at 189-90, 101 S.Ct. 1048 (footnote omitted) (quoting In re Bergy, 596 F.2d 952, 961 (C.C.P.A.1979)).

“Process” is defined in the 1952 statute as follows:

35 U.S.C. § 100(b) The term “process” means process, art or method, and includes a new use of a known process, machine, manufacture, composition of matter, or material.

The 1952 Patent Act replaced the word “art” in prior statutes with the word “process,” while the rest of Section 101 was unchanged from earlier statutes. The legislative history for the 1952 Act explained that “art” had been “interpreted by courts to be practically synonymous with process or method.” S.Rep. No. 82-1979 (1952), reprinted in 1952 U.S.C.C.A.N. 2394, 2398, 2409-10. In Diehr the Court explained that a process “has historically enjoyed patent protection because it was considered a form of ‘art’ as that term was used in the 1793 Act.” 450 U.S. at 182, 101 S.Ct. 1048.

The definition of “process” provided at 35 U.S.C. § 100(b) is not “unhelpful,” as this court now states, maj. op. at 951 n. 3, but rather points up the errors in the court's new statutory interpretation. Section 100(b) incorporates the prior usage “art” and the term “method,” and places no restriction on the definition. This court's redefinition of “process” as limiting access to the patent system to those processes that use specific machinery or that transform matter, is contrary to two centuries of statutory definition.

The breadth of Section 101 and its predecessor provisions reflects the legislative intention to accommodate not only known fields of creativity, but also the unknown future. The Court has consistently refrained from imposing unwarranted restrictions on statutory eligibility, and for computer-implemented processes the Court has explicitly rejected the direction now taken. Nonetheless, this court now adopts a redefinition of “process” in Section 101 that excludes forms of information-based and software-implemented inventions arising from new technological capabilities, stating that this result is required by the Court's computer-related cases, starting with Gottschalk v. Benson, 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972). However, the Court in Benson rejected the restriction that is imposed today:

This court's new definition of “process” was rejected in Gottschalk v. Benson
In Benson the claimed invention was a mathematical process for converting binary-coded decimal numerals into pure binary numbers. The Court explained that a mathematical formula unlimited to a specific use was simply an abstract idea of the nature of “fundamental truths,” “phenomena of nature,” and “abstract intellectual concepts,” as have traditionally been outside of patent systems. 409 U.S. at 67, 93 S.Ct. 253. However, the Court explicitly declined to limit patent-eligible processes in the manner now adopted by this court, stating:

It is argued that a process patent must either be tied to a particular machine or apparatus or must operate to change articles or materials to a “different state or thing.” We do not hold that no process patent could ever qualify if it did not meet the requirements of our prior precedents. It is said that the decision precludes a patent for any program servicing a computer. We do not so hold.

Id. at 71, 93 S.Ct. 253. The Court explained that “the requirements of our prior precedents” did not preclude patents on computer programs, despite the statement drawn from Cochrane v. Deener, 94 U.S. 780, 787-88, 24 L.Ed. 139 (1876), that “[t]ransformation and reduction of an article ‘to a different state or thing’ is the clue to the patentability of a process claim that does not include particular machines.” Benson, 409 U.S. at 70, 93 S.Ct. 253. Although this same statement is now relied upon by this court as requiring its present ruling, maj. op at 956 & n. 11, the Court in Benson was explicit that: “We do not hold that no process patent could ever qualify if it did not meet [the Court's] prior precedents.” The Court recognized that Cochrane's statement was made in the context of a mechanical process and a past era, and protested:

It is said we freeze process patents to old technologies, leaving no room for the revelations of the new, onrushing technology. Such is not our purpose.

Benson, 409 U.S. at 71, 93 S.Ct. 253. Instead, the Court made clear that it was not barring patents on computer programs, and rejected the “argu[ment] that a process patent must either be tied to a particular machine or apparatus or must operate to change articles or materials to a ‘different state or thing’ ” in order to satisfy Section 101. Id. Although my colleagues now describe these statements as “equivocal,” maj. op. at 956, there is nothing equivocal about “We do not so hold.” Benson, 409 U.S. at 71, 93 S.Ct. 253. Nonetheless, this court now so holds.

In Parker v. Flook the Court again rejected today's restrictions
The eligibility of mathematical processes next reached the Court in Parker v. Flook, 437 U.S. 584, 98 S.Ct. 2522, 57 L.Ed.2d 451 (1978), where the Court held that the “process” category of Section 101 was not met by a claim to a mathematical formula for calculation of alarm limits for use in connection with catalytic conversion of hydrocarbons and, as in Benson, the claim was essentially for the mathematical formula. The Court later summarized its Flook holding, stating in Diamond v. Diehr that:

The [Flook] application, however, did not purport to explain how these other variables were to be determined, nor did it purport “to contain any disclosure relating to the chemical processes at work, the monitoring of the process variables, nor the means of setting off an alarm or adjusting an alarm system. All that it provides is a formula for computing an updated alarm limit.”

Diehr, 450 U.S. at 186-87, 101 S.Ct. 1048 (quoting Flook, 437 U.S. at 586, 98 S.Ct. 2522).

The Court explained in Flook that a field-of-use restriction to catalytic conversion did not distinguish Flook's mathematical process from that in Benson. However, the Court reiterated that patent eligibility of computer-directed processes is not controlled by the “qualifications of our earlier precedents,” again negating any limiting effect of the usages of the past, on which this court now places heavy reliance. The Court stated:

The statutory definition of “process” is broad. An argument can be made, however, that this Court has only recognized a process as within the statutory definition when it either was tied to a particular apparatus or operated to change materials to a “different state or thing.” As in Benson, we assume that a valid process patent may issue even if it does not meet one of these qualifications of our earlier precedents.<ref> My colleagues cite only part of this quotation as the Court's holding in Flook, maj. op. at 955, ignoring the qualifying words “[a]n argument can be made” as well as the next sentence clarifying that this argument was rejected by the Court in Benson and is now again rejected in Flook.</ref>

Flook, 437 U.S. at 589 n. 9, 98 S.Ct. 2522 (quoting Cochrane, 94 U.S. at 787). This statement directly contravenes this court's new requirement that all processes must meet the court's “machine-or-transformation test” or be barred from access to the patent system.

The Court in Flook discussed that abstractions and fundamental principles have never been subject to patenting, but recognized the “unclear line” between an abstract principle and the application of such principle:

The line between a patentable “process” and an unpatentable “principle” is not always clear. Both are “conception[s] of the mind, seen only by [their] effects when being executed or performed.”

Flook, 437 U.S. at 589, 98 S.Ct. 2522 (alterations in original) (quoting Tilghman v. Proctor, 102 U.S. 707, 728, 26 L.Ed. 279 (1880)).

The decision in Flook has been recognized as a step in the evolution of the Court's thinking about computers. See Arrhythmia Res. Tech., Inc. v. Corazonix Corp., 958 F.2d 1053, 1057 n. 4 (Fed.Cir.1992) (“it appears to be generally agreed that these decisions represent evolving views of the Court”) (citing R.L. Gable & J.B. Leaheey, The Strength of Patent Protection for Computer Products, 17 Rutgers Computer & Tech. L.J. 87 (1991); D. Chisum, The Patentability of Algorithms, 47 U. Pitt. L.Rev. 959 (1986)). That Flook does not support today's per se exclusion of forms of process inventions from access to the patent system is reinforced in the next Section 101 case decided by the Court:

In Diamond v. Chakrabarty the Court again rejected per se exclusions of subject matter from Section 101
In Diamond v. Chakrabarty, 447 U.S. 303, 100 S.Ct. 2204, 65 L.Ed.2d 144 (1980), the scope of Section 101 was challenged as applied to the new fields of biotechnology and genetic engineering, with respect to the patent eligibility of a new bacterial “life form.” The Court explained the reason for the broad terms of Section 101:

The subject-matter provisions of the patent law have been cast in broad terms to fulfill the constitutional and statutory goal of promoting “the Progress of Science and the useful Arts” with all that means for the social and economic benefits envisioned by Jefferson. Broad general language is not necessarily ambiguous when congressional objectives require broad terms.

Id. at 315, 100 S.Ct. 2204 (quoting U.S. Const., art. I, § 8). The Court referred to the use of “any” in Section 101 (“Whoever invents or discovers any new and useful process ... or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title”), and reiterated that the statutory language shows that Congress “plainly contemplated that the patent laws would be given wide scope.” Id. at 308, 100 S.Ct. 2204. The Court referred to the legislative intent to include within the scope of Section 101 “anything under the sun that is made by man,” id. at 309, 100 S.Ct. 2204 (citing S. Rep. 82-1979, at 5, U.S.Code Cong. & Admin.News 1952, pp. 2394, 2399; H.R. Rep. 82-1923, at 6 (1952)), and stated that the unforeseeable future should not be inhibited by judicial restriction of the “broad general language” of Section 101:

A rule that unanticipated inventions are without protection would conflict with the core concept of the patent law that anticipation undermines patentability. Mr. Justice Douglas reminded that the inventions most benefiting mankind are those that push back the frontiers of chemistry, physics, and the like. Congress employed broad general language in drafting § 101 precisely because such inventions are often unforeseeable.

Id. at 315-16, 100 S.Ct. 2204 (citations and internal quotation marks omitted). The Court emphasized that its precedents did not alter this understanding of Section 101's breadth, stating that “ Flook did not announce a new principle that inventions in areas not contemplated by Congress when the patent laws were enacted are unpatentable per se.” Id. at 315, 100 S.Ct. 2204.

Whether the applications of physics and chemistry that are manifested in advances in computer hardware and software were more or less foreseeable than the advances in biology and biotechnology is debatable, but it is not debatable that these fields of endeavor have become primary contributors to today's economy and culture, as well as offering an untold potential for future advances. My colleagues offer no reason now to adopt a policy of exclusion of the unknown future from the subject matter now embraced in Section 101.

Soon after Chakrabarty was decided, the Court returned to patentability issues arising from computer capabilities:

In Diamond v. Diehr the Court directly held that computer-implemented processes are included in Section 101
The invention presented to the Court in Diehr was a “physical and chemical process for molding precision synthetic rubber products” where the process steps included using a mathematical formula. The Court held that the invention fit the “process” category of Section 101 although mathematical calculations were involved, and repeated its observation in Chakrabarty that “courts should not read into the patent laws limitations and conditions which the legislature has not expressed.” Diehr, 450 U.S. at 182, 101 S.Ct. 1048 (internal quotation marks omitted) (citing Chakrabarty, 447 U.S. at 308, 100 S.Ct. 2204).

The Court distinguished a claim that would cover all uses of a mathematical formula and thus is an abstract construct, as in Benson, from a claim that applies a mathematical calculation for a specified purpose, as in Diehr. The Court stated that “a claim drawn to subject matter otherwise statutory does not become nonstatutory simply because it uses a mathematical formula, computer program, or digital computer,” id. at 187, 101 S.Ct. 1048, and explained that the line between statutory and nonstatutory processes depends on whether the process is directed to a specific purpose, see id. (“It is now commonplace that an application of a law of nature or mathematical formula to a known structure or process may well be deserving of patent protection.” (emphasis in original)). The Court clarified that Flook did not hold that claims may be dissected into old and new parts to assess their patent eligibility. Id. at 189 n. 12, 101 S.Ct. 1048.

However, the Court did not propose the “machine-or-transformation” test that this court now insists was “enunciated” in Diehr as a specific limit to Section 101. Maj. op. at 953-54. In Diehr there was no issue of machine or transformation, for the Diehr process both employed a machine and produced a chemical transformation: the process was conducted in “an openable rubber molding press,” and it cured the rubber. In discussing the known mathematical formula used by Diehr to calculate the relation between temperature and the rate of a chemical reaction, the Court recited the traditional exceptions of “laws of nature, natural phenomena, and abstract ideas,” 450 U.S. at 185, 101 S.Ct. 1048, and explained that the entirety of the process must be considered, not an individual mathematical step.

The Court characterized the holdings in Benson and Flook as standing for no more than the continued relevance of these “long-established” judicial exclusions, id., and repeated that a practical application of pure science or mathematics may be patentable, citing Mackay Radio & Telegraph Co. v. Radio Corp. of America, 306 U.S. 86, 94, 59 S.Ct. 427, 83 L.Ed. 506 (1939) ( “While a scientific truth, or the mathematical expression of it, is not a patentable invention, a novel and useful structure created with the aid of knowledge and scientific truth may be.”). The Court explained that the presence of a mathematical formula does not preclude patentability when the structure or process is performing a function within the scope of the patent system, stating:

[W]hen a claim containing a mathematical formula implements or applies that formula in a structure or process which, when considered as a whole, is performing a function which the patent laws were designed to protect ( e.g., transforming or reducing an article to a different state or thing), then the claim satisfies the requirements of § 101.

450 U.S. at 192, 101 S.Ct. 1048. This statement's parenthetical “ e.g.” is relied on by the majority for its statement that Diehr requires today's “machine-or-transformation” test. However, this “ e.g.” does not purport to state the only “function which the patent laws were designed to protect.” Id. This “ e.g.” indeed describes the process in Diehr, but it does not exclude all other processes from access to patenting.

It cannot be inferred that the Court intended, by this “ e.g.” parenthetical, to require the far-reaching exclusions now attributed to it. To the contrary, the Court in Diehr was explicit that “an application of a law of nature or mathematical formula” may merit patent protection, 450 U.S. at 187, 101 S.Ct. 1048 (emphasis in original), and that the claimed process must be considered as a whole, id. at 188, 101 S.Ct. 1048. The Court recognized that a process claim may combine steps that were separately known, and that abstract ideas such as mathematical formulae may be combined with other steps to produce a patentable process. Id. at 187, 101 S.Ct. 1048. The steps are not to be “dissect[ed]” into new and old steps; it is the entire process that frames the Section 101 inquiry. Id. at 188, 101 S.Ct. 1048.

The Diehr Court did not hold, as the majority opinion states, that transformation of physical state is a requirement of eligibility set by Section 101 unless the process is performed by a machine. It cannot be inferred that the Court silently imposed such a rule. See maj. op. at 956 (relying on lack of repetition in Diehr of the Benson and Flook disclaimers of requiring machine or transformation, as an implicit rejection of these disclaimers and tacit adoption of the requirement). There was no issue in Diehr of the need for either machine or transformation, for both were undisputedly present in the process of curing rubber. It cannot be said that the Court “enunciated” today's “definitive test” in Diehr.<ref>Many amici curiae pointed out that the Supreme Court did not adopt the test that this court now attributes to it. See, e.g., Br. of Amicus Curiae Am. Intellectual Property Law Ass'n at 18 & n.16; Br. of Amicus Curiae Biotechnology Industry Org. at 17-21; Br. of Amicus Curiae Boston Patent Law Ass'n at 6-8; Br. of Amicus Curiae Business Software Alliance at 13; Br. of Amicus Curiae Federal Circuit Bar Ass'n at 21; Br. of Amicus Curiae Regulatory Datacorp, Inc. at 12-13; Br. of Amicus Curiae Accenture at 16-17; Br. of Amicus Curiae Washington State Patent Law Ass'n at 10-11.</ref>

Subsequent Supreme Court authority reinforced the breadth of Section 101

In J.E.M. Ag Supply, Inc. v. Pioneer Hi-Bred International, Inc., 534 U.S. 124, 122 S.Ct. 593, 151 L.Ed.2d 508 (2001), the Court described Section 101 as a “dynamic provision designed to encompass new and unforeseen inventions,” id. at 135, 122 S.Ct. 593, that case arising in the context of eligibility of newly developed plant varieties for patenting. The Court stated: “As in Chakrabarty, we decline to narrow the reach of § 101 where Congress has given us no indication that it intends this result.” Id. at 145-46, 122 S.Ct. 593. The Court reiterated that “Congress plainly contemplated that the patent laws would be given wide scope,” id. at 130, 122 S.Ct. 593 (quoting Chakrabarty, 447 U.S. at 308, 100 S.Ct. 2204), and that the language of Section 101 is “extremely broad,” id. This is not language of restriction, and it reflects the statutory policy and purpose of inclusion, not exclusion, in Section 101.

The Court's decisions of an earlier age do not support this court's restrictions of Section 101
My colleagues also find support for their restrictions on patent-eligible “process” inventions in the pre-Section 101 decisions O'Reilly v. Morse, 56 U.S. (15 How.) 62, 14 L.Ed. 601 (1853), Cochrane v. Deener, 94 U.S. 780, 24 L.Ed. 139 (1876), and Tilghman v. Proctor, 102 U.S. 707, 26 L.Ed. 279 (1880). Although the Court in Benson and in Flook took care to state that these early decisions do not require the restrictions that the Court was rejecting, this court now places heavy reliance on these early decisions, which this court describes as “consistent with the machine-or-transformation test later articulated in Benson and reaffirmed in Diehr.” Maj. op. at 955. As I have discussed, no such test was “articulated in Benson ” and “reaffirmed in Diehr.”

However, these early cases do show, contrary to the majority opinion, that a “process” has always been a distinct category of patentable invention, and not tied to either apparatus or transformation, as this court now holds. For example, in Tilghman v. Proctor the Court considered a patent on a process for separating fats and oils, and held that the process was not restricted to any particular apparatus. The Court held that a process is an independent category of invention, and stated:

That a patent can be granted for a process, there can be no doubt. The patent law is not confined to new machines and new compositions of matter, but extends to any new and useful art or manufacture.

102 U.S. at 722; see also Corning v. Burden, 56 U.S. (15 How.) 252, 268, 14 L.Ed. 683 (1853) (“It is for the discovery or invention of some practical method or means of producing a beneficial result or effect, that a patent is granted, and not for the result or effect itself.”) The difference between a process and the other categories of patent-eligible subject matter does not deprive process inventions of the independent status accorded by statute, by precedent, and by logic, all of which negate the court's new rule that a process must be tied to a particular machine or must transform physical matter.

The majority also relies on O'Reilly v. Morse, citing the Court's rejection of Morse's Claim 8 for “the use of the motive power of the electro or galvanic current, which I call electromagnetism, however developed, for making or printing intelligible characters, signs or letters at any distances....” The Court explained:

In fine he claims an exclusive right to use a manner and process which he has not described and indeed had not invented, and therefore could not describe when he obtained his patent. The Court is of the opinion that the claim is too broad, and not warranted by law.

56 U.S. (15 How.) at 113. However, the claims that were directed to the communication system that was described by Morse were held patentable, although no machine, transformation, or manufacture was required. See Morse's Claim 5 (“The system of signs, consisting of dots and spaces, and horizontal lines, for numerals, letters, words, or sentences, substantially as herein set forth and illustrated, for telegraphic purposes.”). I cannot discern how the Court's rejection of Morse's Claim 8 on what would now be Section 112 grounds, or the allowance of his other claims, supports this court's ruling today. Indeed, Morse's claim 5, to a system of signs, is no more “tangible” than the systems held patentable in Alappat and State Street Bank, discussed post and now cast into doubt, or the Bilski system here held ineligible for access to patenting.

The majority opinion also relies on Cochrane v. Deener, particularly on certain words quoted in subsequent opinions of the Court. In Cochrane the invention was a method for bolting flour, described as a series of mechanical steps in the processing of flour meal. The question before the Court was whether the patented process would be infringed if the same steps were performed using different machinery. The answer was “that a process may be patentable, irrespective of the particular form of the instrumentalities used.” 94 U.S. at 788. The Court stressed the independence of a process from the tools that perform it:

A process is a mode of treatment of certain materials to produce a given result. It is an act, or series of acts, performed upon the subject-matter to be transformed and reduced to a different state or thing. If new and useful, it is just as patentable as is a piece of machinery. In the language of the patent law, it is an art. The machinery pointed out as suitable to perform the process may or may not be new or patentable; whilst the process itself may be altogether new, and produce an entirely new result. The process requires that certain things should be done with certain substances, and in a certain order; but the tools to be used in doing this may be of secondary consequence.

94 U.S. at 788. The Court did not restrict the kinds of patentable processes; the issue in Cochrane was whether the process must be tied to the machinery that the patentee used to perform it.

This court now cites Cochrane's description of a process as “acts performed upon subject-matter to be transformed and reduced to a different state or thing,” id., this court stating that unless there is transformation there is no patentable process. That is not what this passage means. In earlier opinions this court and its predecessor court stated the correct view of this passage, as has the Supreme Court. The Court of Customs and Patent Appeals observed:

[This Cochrane passage] has sometimes been misconstrued as a ‘rule’ or ‘definition’ requiring that all processes, to be patentable, must operate physically on substances. Such a result misapprehends the nature of the passage quoted as dictum, in its context, and the question being discussed by the author of the opinion. To deduce such a rule from the statement would be contrary to its intendment which was not to limit process patentability but to point out that a process is not limited to the means used in performing it.

In re Prater, 56 C.C.P.A. 1381, 415 F.2d 1393, 1403 (1969). Again in In re Schrader, 22 F.3d 290, 295 n. 12 (Fed.Cir.1994) this court noted that Cochrane did not limit patent eligible subject matter to physical transformation, and that transformation of “intangibles” could qualify for patenting. In AT & T Corp. v. Excel Communications, Inc., 172 F.3d 1352, 1358 (Fed.Cir.1999), this court described physical transformation as “merely one example of how a mathematical algorithm may bring about a useful application.”

The Court saw the Cochrane decision in its proper perspective. Both Flook and Benson rejected the idea that Cochrane imposed the requirement of either specific machinery or the transformation of matter, as discussed ante. See Flook, 437 U.S. at 588 n. 9, 98 S.Ct. 2522; Benson, 409 U.S. at 71, 93 S.Ct. 253. Non-transformative processes were not at issue in either Cochrane or Diehr, and there is no endorsement in Diehr of a “machine-or-transformation” requirement for patentable processes.

These early cases cannot be held now to require exclusion, from the Section 101 definition of “process,” of all processes that deal with data and information, whose only machinery is electrons, photons, or waves, or whose product is not a transformed physical substance.

The English Statute of Monopolies and English common law do not limit “process” in Section 101
I comment on this aspect in view of the proposal in the concurring opinion that this court's new two-prong test for Section 101 process inventions was implicit in United States law starting with the Act of 1790, because of Congress's knowledge of and importation of English common law and the English Statute of Monopolies of 1623. The full history of patent law in England is too ambitious to be achieved within the confines of Bilski's appeal,<ref> Scholarly histories include M. Frumkin, The Origin of Patents, 27 J.P.O.S. 143 (1945); E. Wyndham Hulme, Privy Council Law and Practice of Letters Patent for Invention from the Restoration to 1794, 33 L.Q. Rev. 63 (Part I), 180 (Part II) (1917); Hulme, On the History of Patent Law in the Seventeenth and Eighteenth Centuries, 18 L.Q. Rev. 280 (1902); Hulme, The History of the Patent System Under the Prerogative and at Common Law, 12 L.Q. Rev. 141 (1896); Ramon A. Klitzke, Historical Background of the English Patent Law, 41 J.P.O.S 615 (1959); Christine MacLeod, Inventing the Industrial Revolution: The English Patent System 1660-1800 (1988); Frank D. Prager, Historic Background and Foundation of American Patent Law, 5 Am. J. Legal Hist. 309 (1961); Brad Sherman & Lionel Bently, The Making of Modern Intellectual Property Law: The British Experience, 1760-1911 (1999); Edward C. Walterscheid, The Early Evolution of the United States Patent Law: Antecedents, printed serially at J. Pat. & Trademark Off. Soc'y (“J.P.T.O.S.”) 76:697 (1994) (Part 1); 76:849 (1994) (Part 2); 77:771, 847 (1995) (Part 3); 78:77 (1996) (Part 4); 78:615 (1996) (Part 5, part I); and 78:665 (1996) (Part 5, part II) (hereinafter “ Early Evolution ”); and Edward C. Walterscheid, To Promote the Progress of Useful Arts: American Patent Law and Administration, 1798-1836 (1998).</ref> and the concurring opinion's selective treatment of this history may propagate misunderstanding.

The concurrence places primary reliance on the Statute of Monopolies, which was enacted in response to the monarchy's grant of monopolies “to court favorites in goods or businesses which had long before been enjoyed by the public.” Graham v. John Deere Co., 383 U.S. 1, 5, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966) (citing Peter Meinhardt, Inventions, Patents and Monopoly 30-35 (1946)). The Statute of Monopolies outlawed these “odious monopolies” or favors of the Crown, but, contrary to the concurring opinion, the Statute had nothing whatever to do with narrowing or eliminating categories of inventive subject matter eligible for a British patent. See Prager, Historical Background and Foundation of American Patent Law, 5 Am. J. Legal Hist. at 313 (“The statute [of Monopolies] said nothing about meritorious functions of patents, nothing about patent disclosures, and nothing about patent procedures; it was only directed against patent abuses.”).

Patents for inventions had been granted by the Crown long before 1623. See Hulme, The History of the Patent System Under the Prerogative and at Common Law, 12 L.Q. Rev. at 143 (the first patent grant to the “introducer of a newly-invented process” was in 1440); Klitzke, Historical Background of the English Patent Law, 41 J.P.O.S. at 626-27 (discussing first patents for “invention” in England in the fifteenth century). That practice was unaffected by the terms of the Statute of Monopolies, which rendered “utterly void” all “Monopolies and all Commissions, Grants, Licenses, Charters and Letters Patent” that were directed to “the sole Buying, Selling, Making, Working or Using any Thing within this Realm,” 21 Jac. 1, c.3, § I (Eng.), but which specifically excepted Letters Patent for inventions from that exclusion, id. § VI. The only new limitation on patents for invention was a fourteen-year limit on the term of exclusivity. See Klitzke, Historical Background of the English Patent Law, 41 J.P.O.S. at 649.

The usage “Letters Patent” described one of the forms of document whereby the Crown granted various rights, whether the grant was for an odious monopoly that the Statute of Monopolies eliminated, or for rights to an invention new to England. That usage was not changed by the Statute of Monopolies. Nor were other aspects of the British practice which differed from that enacted in the United States, particularly the aspect whereby a British patent could be granted to a person who imported something that was new to England, whether or not the import was previously known or the importer was the inventor thereof. In England, “[t]he rights of the inventor are derived from those of the importer, and not vice versa as is commonly supposed.” Hulme, The History of the Patent System Under the Prerogative and at Common Law, 12 L.Q.R. at 152; see also MacLeod, Inventing the Industrial Revolution 13 (“The rights of the first inventor were understood to derive from those of the first importer of the invention.”).

In contrast, in the United States the patent right has never been predicated upon importation, and has never been limited to “manufactures.” See, e.g., Walterscheid, To Promote the Progress of Useful Arts 93, 137-38, 224; see also Prager, Historic Background and Foundation of American Patent Law, 5 Am. J. Legal Hist. at 309 (“The American Revolution destroyed many of the ancient customs; it brought a sweeping reorientation of patent law, with new forms, new rules, new concepts, and new ideals.”). The differences between the American and English patent law at this nation's founding were marked, and English judicial decisions interpreting the English statute are of limited use in interpreting the United States statute. In all events, no English decision supports this court's new restrictive definition of “process.”

The concurrence proposes that the Statute of Monopolies provides a binding definition of the terms “manufacture,” “machine,” “composition of matter,” and “process” in Section 101 of the U.S. Patent Act. See concurring op. at 968-70. The only one of these terms that appears in the Statute of Monopolies is “manufacture”, a broad term that reflects the usage of the period. Even at the time of this country's founding, the usage was broad, as set forth in Samuel Johnson's Dictionary of the English Language (3d. ed. 1768), which defines “manufacture” as “any thing made by art,” and defines “art” as “the power of doing something not taught by nature and instinct”; “a science”; “a trade”; “artfulness”; “skill”; “dexterity.” Historians explain that England's primary motive for patenting was to promote “[a]cquisition of superior Continental technology” at a time when England lagged behind, see MacLeod, Inventing the Industrial Revolution 11; this cannot be interpreted to mean that England and perforce the United States intended to eliminate “processes” from this incentive system. It is inconceivable that on this background the Framers, and again the enactors of the first United States patent statutes in 1790 and 1793, intended sub silentio to impose the limitations on “process” now created by this court.

Congress' earliest known draft patent bill included the terms “art, manufacture, engine, machine, invention or device, or any improvement upon the same.” Walterscheid, To Promote the Progress of Useful Arts 92. The 1793 Act explicitly stated “any new and useful art,” § 1, 1 Stat. 318 (1793), a usage that was carried forward until “art” was replaced with “process” in 35 U.S.C. § 101 and defined in § 100(b). Historians discuss that Congress' inclusion of any “art” or “process” in the patent system was a deliberate clarification of the English practice. See Walterscheid, To Promote the Progress of Useful Arts 93 (“[The first patent bill] appears to be an obvious attempt to deal legislatively with issues that were beginning to be addressed by the English courts.... [I]t states unequivocally that improvement inventions are patentable and expands the definition of invention or discovery beyond simply ‘manufacture.’ ”); Karl B. Lutz, Patents and Science: A Clarification of the Patent Clause of the U.S. Constitution, 32 J.P.O.S. 83, 86 (1950) ( “By the year 1787 it was being recognized even in Great Britain that the phrase ‘new manufactures' was an unduly limited object for a patent system, since it seems to exclude new processes.... [This question was] resolved in the United States Constitution by broadening the field from ‘new manufactures' to ‘useful arts'....”).

In interpreting a statute, it is the language selected by Congress that occupies center stage: “[O]ur obligation is to take statutes as we find them, guided, if ambiguity appears, by the legislative history and statutory purpose.” Chakrabarty, 447 U.S. at 315, 100 S.Ct. 2204. The Court has “perceive[d] no ambiguity” in Section 101, leaving no need for foreign assistance. Id. The legislative choice to afford the patent system “wide scope,” id. at 308, 100 S.Ct. 2204, including “process” inventions, evolved in the United States independent of later developments of the common law in England.

The concurrence concludes that the Statute of Monopolies foreclosed the future patenting of anything that the concurrence calls a “business method”-the term is not defined-whether or not the method is new, inventive, and useful. But the Statute of Monopolies only foreclosed “odious” monopolies, illustrated by historical reports that Queen Elizabeth had granted monopolies on salt, ale, saltpeter, white soap, dredging machines, playing cards, and rape seed oil, and on processes and services such as Spanish leather-making, mining of various metals and ores, dying and dressing cloth, and iron tempering. See Walterscheid, Early Evolution (Part 2), 76 J.P.T.O.S. at 854 n.14; Klitzke, Historical Background of the English Patent Law, 41 J.P.O.S. at 634-35. These and other grants, many of which were implemented by Letters Patent, were the “odious monopolies” that were rendered illegal. They included several classes of known activity, product and process, and had nothing to do with new “inventions.” The Statute of Monopolies cannot be held to have restricted the kinds of new processes that can today be eligible for patenting in the United States, merely because it outlawed patents on non-novel businesses in England. The presence or absence of “organizing human activity,” a vague term created by the concurrence, has no connection or relevance to Parliament's elimination of monopoly patronage grants for old, established arts. The Statute of Monopolies neither excluded nor included inventions that involve human activity, although the words “the sole working or making in any manner of new manufactures” presuppose human activity. 21 Jac. 1, c.3, § VI (emphases added). We are directed to no authority for the proposition that a new and inventive process involving “human activity” has historically been treated differently from other processes; indeed, most inventions involve human activity.

The concurrence has provided hints of the complexity of the evolution of patent law in England, as in the United States, as the Industrial Revolution took hold. Historians have recognized these complexities. See, e.g., Walterscheid, To Promote the Progress of Useful Arts 5 (“[T]he American patent law almost from its inception departed from its common law counterpart in the interpretation that would be given to the definition of novelty....”); Klitzke, Historical Background of the English Patent Law, 41 J.P.O.S. at 638 (noting that in Elizabethan times, novelty only required a showing that “the industry had not been carried on within the realm within a reasonable period of time”, while today “the proof of a single public sale of an article” or a “printed publication” can negate patentability).

I caution against over-simplification, particularly in view of the uncertainties in English common law at the time of this country's founding. See Boulton v. Bull, 2 H. Bl. 463, 491 (C.P.1795) (Eyre, C.J.) (“Patent rights are no where that I can find accurately discussed in our books.”); MacLeod, Inventing the Industrial Revolution 61 (“It was only from the time when the Privy Council relinquished jurisdiction that a case law on patents began to develop.... But it was a slow process and even the spate of hard-fought patent cases at the end of the eighteenth century did little to establish a solid core of judicial wisdom.”). The English judicial opinions of the eighteenth century were not as limiting on the United States as my colleagues suggest. See Walterscheid, The Nature of the Intellectual Property Clause: A Study in Historical Perspective 355 (2002) (“In the eighteenth century, patentees and those who gave advice concerning patents were certainly of the view that the Statute did not preclude the patenting of general principles of operation.”); see also MacLeod, Inventing the Industrial Revolution 63-64.

It is reported that in the century and a half following enactment of the Statute of Monopolies, the English patent registers were replete with inventions claimed as “processes.” See Walterscheid, Early Evolution (Part 3), 77 J.P.T.O.S. at 856 (“As one of the earliest texts on the patent law stated in 1806: “most of the patents now taken out, are by name, for the method of doing particular things....”). The concurrence agrees; but it is also reported that because patents were not litigated in the common law courts until the Privy Council authorized such suits in 1752, judicial interpretation of various aspects of patent law were essentially absent until about the time this country achieved independence, leading to the variety of views expressed in Boulton v. Bull. The legislators in the new United States cannot now be assigned the straightjacket of law not yet developed in England. Indeed, the first patent granted by President Washington, upon examination by Secretary of State Jefferson, was for a method of “making Pot-ash and Pearl-ash,” a process patent granted during the period that the concurrence states was fraught with English uncertainty about process patents. See The First United States Patent, 36 J.P.O.S. 615, 616-17 (1954).

The concurrence lists some English process patents predating the United States' 1793 Patent Act, and argues that processes not sufficiently “like” these archaic inventions should not now be eligible for patenting. I refer simply to Flook, 437 U.S. at 588 n. 9, 98 S.Ct. 2522, where the Court stated: “As in Benson, we assume that a valid process patent may issue even if it does not meet one of the qualifications of our earlier precedents.” Similarly, the Chakrabarty Court stated: “[A] statute is not to be confined to the particular applications ... contemplated by the legislators. This is especially true in the field of patent law.” Chakrabarty, 447 U.S. at 315-16, 100 S.Ct. 2204 (citing Barr v. United States, 324 U.S. 83, 90, 65 S.Ct. 522, 89 L.Ed. 765 (1945); Browder v. United States, 312 U.S. 335, 339, 61 S.Ct. 599, 85 L.Ed. 862 (1941); Puerto Rico v. Shell Co., 302 U.S. 253, 257, 58 S.Ct. 167, 82 L.Ed. 235 (1937)). The meaning of the statutory term “process” is not limited by particular examples from more than two hundred years ago.

However, I cannot resist pointing to the “business method” patents on Woodcroft's list. See concurring op. at 973 (citing No. 1197 to John Knox (July 21, 1778) (“Plan for assurances on lives of persons from 10 to 80 years of age.”)). Several other process patents on Woodcroft's list appear to involve financial subject matter, and to require primarily human activity. See, e.g., No. 1170 to John Molesworth (Sept. 29, 1777) (“Securing to the purchasers of shares and chances of state-lottery tickets any prize drawn in their favor.”); No. 1159 to William Nicholson (July 14, 1777) (“Securing the property of persons purchasing shares of State-lottery tickets.”), cited in Bennet Woodcroft, Alphabetical Index of Patentees of Inventions 383, 410 (U.S. ed.1969). Other English process patents from the several decades following 1793 can aptly be described as “business methods,” although not performed with the aid of computers. E.g., No. 10,367 to George Robert D'Harcourt (Oct. 29, 1844) (“Ascertaining and checking the number of checks or tickets which have been used and marked, applicable for railway officers.”).

While most patents of an earlier era reflect the dominant mechanical and chemical technologies of that era, modern processes reflect the dramatic advances in telecommunications and computing that have occurred since the time of George III. See USPTO White Paper, Automated Financial or Management Data Processing Methods (Business Methods) 4 (2000), available at http:// www. uspto. gov/ web/ menu/ busmethp/ whitepaper. pdf (hereinafter USPTO White Paper) (“The full arrival of electricity as a component in business data processing system[s] was a watershed event.”). It is apparent that economic, or “business method,” or “human activity” patents were neither explicitly nor implicitly foreclosed from access to the English patent system.

Evolution of process patents in the United States
The United States' history of patenting establishes the same point. The PTO has located various patents predating modern computer usages that can be described as financial or business methods. The USPTO White Paper at 3-4 and appendix A describes the history of financial apparatus and method patents dating back to 1799, including patents on bank notes, bills of credit, bills of exchange, check blanks, detecting and preventing counterfeiting, coin counting, interest calculation tables, and lotteries, all within the first fifty years of the United States patent system. It is a distortion of these patents to describe the processes as “tied to” another statutory category-that is, paper and pencil. Concurring op. at 974-75 & n. 18. Replacement of paper with a computer screen, and pencil with electrons, does not “untie” the process. Fairly considered, the many older financial and business-oriented patents that the PTO and many of the amici have identified are of the same type as the Bilski claims; they were surely not rendered patent-eligible solely because they used “paper” to instantiate the financial strategies and transactions that comprised their contribution.

I do not disagree with the general suggestion that statutes intended to codify the existing common law are to be interpreted in light of then-contemporary practice, including, if relevant, the English cases. See concurring op. at 972-73. However, the court must be scrupulous in assessing the relevance of decisions that were formulated on particularized facts involving the technology of the period. The United States Supreme Court has never held that “process” inventions suffered a second-class status under our statutes, achieving patent eligibility only derivatively through an explicit “tie” to another statutory category. The Court has repeatedly disparaged efforts to read in restrictions not based on statutory language. See Diehr, 450 U.S. at 182, 101 S.Ct. 1048; Chakrabarty, 447 U.S. at 308, 100 S.Ct. 2204. Yet second-class status is today engrafted on “process” inventions. There is plainly no basis for such restriction, which is a direct path to the “gloomy thought” that concerned Senator O.H. Platt in his Remarks in Congress at the Centennial Proceedings of the United States Patent System:

For one, I cannot entertain the gloomy thought that we have come to that century in the world's life in which new and grander achievements are impossible.... Invention is a prolific mother; every inventive triumph stimulates new effort. Man never is and never will be content with success, and the great secrets of nature are as yet largely undiscovered.

Invention and Advancement (1891), reprinted in United States Bicentennial Commemorative Edition of Proceedings and Addresses: Celebration of the Beginning of the Second Century of the American Patent System 75-76 (1990).

In sum, history does not support the retrogression sponsored by the concurrence.

This court now rejects its own CCPA and Federal Circuit precedent
The majority opinion holds that there is a Supreme Court restriction on process patents, “enunciated” in Benson, Flook, and Diehr; and that this restriction was improperly ignored by the Federal Circuit and the Court of Customs and Patent Appeals, leading us into error which we must now correct. Thus this court announces that our prior decisions may no longer be relied upon. Maj. op. at 959-60 & nn. 17, 19. The effect on the patents and businesses that did rely on them is not considered.

The Court's decisions in Benson, Flook, and Diehr all reached the Supreme Court by way of the CCPA, and the CCPA successively implemented the Court's guidance in establishing the Freeman/Walter/Abele test for eligibility under Section 101. The Federal Circuit continued to consider computer-facilitated processes, as in Arrhythmia Research Technology, 958 F.2d at 1059-60, where patent-eligibility was confirmed for a computer-assisted mathematical analysis of electrocardiograph signals that determined the likelihood of recurrence of heart attack. This court now rules that this precedent “should no longer be relied on.” Maj. op. at 959 n. 17.

In In re Alappat, 33 F.3d 1526 (Fed.Cir.1994) ( en banc ) the question was the eligibility for patent of a rasterizer that mathematically transforms data to eliminate aliasing in a digital oscilloscope. The court held that a computer-implemented system that produces a “useful, concrete, and tangible result” is Section 101 subject matter. Id. at 1544. This court now rules that “a ‘useful, concrete and tangible result’ analysis should no longer be relied on.” Maj. op. at 960 n. 19.

The Alappat court stressed the intent, embodied in the language of the statute, that the patent system be broadly available to new and useful inventions:

The use of the expansive term “any” in § 101 represents Congress's intent not to place any restrictions on the subject matter for which a patent may be obtained beyond those specifically recited in § 101 and other parts of Title 35.

33 F.3d at 1542. This court looked to the Supreme Court's guidance in its Section 101 decisions, and explained:

A close analysis of Diehr, Flook, and Benson reveals that the Supreme Court never intended to create an overly broad, fourth category of [mathematical] subject matter excluded from § 101. Rather, at the core of the Court's analysis in each of these cases lies an attempt by the Court to explain a rather straightforward concept, namely, that certain types of mathematical subject matter, standing alone, represent nothing more than abstract ideas until reduced to some type of practical application, and thus that subject matter is not, in and of itself, entitled to patent protection.

Id. at 1543 (emphasis in original). The court cited the Supreme Court's distinction between abstract ideas and their practical application, and stated of the claimed rasterizer: “This is not a disembodied mathematical concept which may be characterized as an ‘abstract idea,’ but rather a specific machine to produce a useful, concrete, and tangible result.” Id. at 1544.

This principle was applied to a computer-implemented data processing system for managing pooled mutual fund assets in State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (Fed.Cir.1998), and to a method for recording and processing telephone data in AT & T v. Excel. The court explained that processes that include mathematical calculations in a practical application can produce a useful, concrete, and tangible result, which in State Street Bank was “expressed in numbers, such as price, profit, percentage, cost, or loss.” 149 F.3d at 1375. In AT & T v. Excel the court applied State Street Bank and Diehr, and stated that “physical transformation ... is not an invariable requirement, but merely one example of how a mathematical algorithm may bring about a useful application” and thus achieve a useful, concrete, and tangible result. 172 F.3d at 1358. This analysis, too, can no longer be relied on. Maj. op. at 960 n. 19.

The now-discarded criterion of a “useful, concrete, and tangible result” has proved to be of ready and comprehensible applicability in a large variety of processes of the information and digital ages. The court in State Street Bank reinforced the thesis that there is no reason, in statute or policy, to exclude computer-implemented and information-based inventions from access to patentability. The holdings and reasoning of Alappat and State Street Bank guided the inventions of the electronic age into the patent system, while remaining faithful to the Diehr distinction between abstract ideas such as mathematical formulae and their application in a particular process for a specified purpose. And patentability has always required compliance with all of the requirements of the statute, including novelty, non-obviousness, utility, and the provisions of Section 112.

The public has relied on the rulings of this court and of the Supreme Court
The decisions in Alappat and State Street Bank confirmed the patent eligibility of many evolving areas of commerce, as inventors and investors explored new technological capabilities. The public and the economy have experienced extraordinary advances in information-based and computer-managed processes, supported by an enlarging patent base. The PTO reports that in Class 705, the examination classification associated with “business methods” and most likely to receive inventions that may not use machinery or transform physical matter, there were almost 10,000 patent applications filed in FY 2006 alone, and over 40,000 applications filed since FY 98 when State Street Bank was decided. See Wynn W. Coggins, USPTO, Update on Business Methods for the Business Methods Partnership Meeting 6 (2007) (hereinafter “ PTO Report ”), available at http:// www. uspto. gov/ web/ menu/ pbmethod/ partnership. pps. An amicus in the present case reports that over 15,000 patents classified in Class 705 have issued. See Br. of Amicus Curiae Accenture, at 22 n.20.<ref>The PTO recognizes that patents on “business methods” have been eligible subject matter for two centuries. See USPTO White Paper 2 (“Financial patents in the paper-based technologies have been granted continuously for over two hundred years.”).</ref> The industries identified with information-based and data-handling processes, as several amici curiae explain and illustrate, include fields as diverse as banking and finance, insurance, data processing, industrial engineering, and medicine.

Stable law, on which industry can rely, is a foundation of commercial advance into new products and processes. Inventiveness in the computer and information services fields has placed the United States in a position of technological and commercial preeminence. The information technology industry is reported to be “the key factor responsible for reversing the 20-year productivity slow-down from the mid-1970s to the mid-1990s and in driving today's robust productivity growth.” R.D. Atkinson & A.S. McKay, Digital Prosperity: Understanding the Economic Benefits of the Information Technology Revolution 10 (Info. Tech. & Innovation Found.2007), available at http:// www. itif. org/ files/ digital_ prosperity. pdf. By revenue estimates, in 2005 the software and information sectors constituted the fourth largest industry in the United States, with significantly faster growth than the overall U.S. economy. Software & Info. Indus. Ass'n, Software and Information: Driving the Knowledge Economy 7-8 (2008), http:// www. siia. net/ estore/ globecon- 08. pdf. A Congressional Report in 2006 stated:

As recently as 1978, intangible assets, such as intellectual property, accounted for 20 percent of corporate assets with the vast majority of value (80 percent) attributed to tangible assets such as facilities and equipment. By 1997, the trend reversed; 73 percent of corporate assets were intangible and only 27 percent were tangible.

H.R.Rep. No. 109-673 (accompanying a bill concerning judicial resources).

This powerful economic move toward “intangibles” is a challenge to the backward-looking change of this court's ruling today. Until the shift represented by today's decision, statute and precedent have provided stability in the rapidly moving and commercially vibrant fields of the Information Age. Despite the economic importance of these interests, the consequences of our decision have not been considered. I don't know how much human creativity and commercial activity will be devalued by today's change in law; but neither do my colleagues.

The Section 101 interpretation that is now uprooted has the authority of years of reliance, and ought not be disturbed absent the most compelling reasons. “Considerations of stare decisis have special force in the area of statutory interpretation, for here, unlike in the context of constitutional interpretation, the legislative power is implicated, and Congress remains free to alter what [the courts] have done.” Shepard v. United States, 544 U.S. 13, 23, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005) (quoting Patterson v. McLean Credit Union, 491 U.S. 164, 172-73, 109 S.Ct. 2363, 105 L.Ed.2d 132 (1989)); see also Hilton v. S.C. Pub. Railways Comm'n, 502 U.S. 197, 205, 112 S.Ct. 560, 116 L.Ed.2d 560 (1991) (in cases of statutory interpretation the importance of adhering to prior rulings is “most compelling”). Where, as here, Congress has not acted to modify the statute in the many years since Diehr and the decisions of this court, the force of stare decisis is even stronger. See Shepard, 544 U.S. at 23, 125 S.Ct. 1254.

Adherence to settled law, resulting in settled expectations, is of particular importance “in cases involving property and contract rights, where reliance interests are involved.” Payne v. Tennessee, 501 U.S. 808, 828, 111 S.Ct. 2597, 115 L.Ed.2d 720 (1991); see also United States v. Title Ins. & Trust Co., 265 U.S. 472, 486, 44 S.Ct. 621, 68 L.Ed. 1110 (1924) (declining to overrule precedent where prior ruling “has become a rule of property, and to disturb it now would be fraught with many injurious results”). This rationale is given no weight by my colleagues, as this court gratuitously disrupts decades of law underlying our own rulings. The only announced support for today's change appears to be the strained new reading of Supreme Court quotations. But this court has previously read these decades-old opinions differently, without objection by either Congress or the Court. My colleagues do not state a reason for their change of heart. See Benjamin N. Cardozo, The Nature of the Judicial Process 149 (1921) (“[T]he labor of judges would be increased almost to the breaking point if every past decision could be reopened in every case, and one could not lay one's own course of bricks on the secure foundation of the courses laid by others who had gone before him.”).

It is the legislature's role to change the law if the public interest so requires. In Chakrabarty the Court stated: “The choice we are urged to make is a matter of high policy for resolution within the legislative process after the kind of investigation, examination, and study that legislative bodies can provide and courts cannot.” 447 U.S. at 317, 100 S.Ct. 2204; see also Flook, 437 U.S. at 595, 98 S.Ct. 2522 (“Difficult questions of policy concerning the kinds of programs that may be appropriate for patent protection and the form and duration of such protection can be answered by Congress on the basis of current empirical data not equally available to this tribunal.”).

It is, however, the judicial obligation to assure a correct, just, and reliable judicial process, and particularly to respect the principles of stare decisis in an area in which prior and repeated statutory interpretations have been relied upon by others. See, e.g., Shepard, 544 U.S. at 23, 125 S.Ct. 1254 (“[T]he claim to adhere to case law is generally powerful once a decision has settled statutory meaning.”); Hilton, 502 U.S. at 202, 112 S.Ct. 560 (“Adherence to precedent promotes stability, predictability, and respect for judicial authority.”); Payne, 501 U.S. at 827, 111 S.Ct. 2597 (“ Stare decisis is the preferred course because it promotes the evenhanded, predictable, and consistent development of legal principles, fosters reliance on judicial decisions, and contributes to the actual and perceived integrity of the judicial process.”). These considerations appear to be abandoned.

Uncertain guidance for the future
Not only past expectations, but future hopes, are disrupted by uncertainty as to application of the new restrictions on patent eligibility. For example, the court states that even if a process is “tied to” a machine or transforms matter, the machine or transformation must impose “meaningful limits” and cannot constitute “insignificant extra-solution activity”. Maj. op. at 961-62. We are advised that transformation must be “central to the purpose of the claimed process,” id., although we are not told what kinds of transformations may qualify, id. at 962-63. These concepts raise new conflicts with precedent.

This court and the Supreme Court have stated that “there is no legally recognizable or protected ‘essential’ element, ‘gist’ or ‘heart’ of the invention in a combination patent.” Allen Eng'g Corp. v. Bartell Industries, Inc., 299 F.3d 1336, 1345 (Fed.Cir.2002) (quoting Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336, 345, 81 S.Ct. 599, 5 L.Ed.2d 592 (1961)). This rule applies with equal force to process patents, see W.L. Gore & Associates, Inc. v. Garlock, Inc., 721 F.2d 1540, 1548 (Fed.Cir.1983) (there is no gist of the invention rule for process patents), and is in accord with the rule that the invention must be considered as a whole, rather than “dissected,” in assessing its patent eligibility under Section 101, see Diehr, 450 U.S. at 188, 101 S.Ct. 1048. It is difficult to predict an adjudicator's view of the “invention as a whole,” now that patent examiners and judges are instructed to weigh the different process components for their “centrality” and the “significance” of their “extra-solution activity” in a Section 101 inquiry.

As for whether machine implementation will impose “meaningful limits in a particular case,” the “meaningfulness” of computer usage in the great variety of technical and informational subject matter that is computer-facilitated is apparently now a flexible parameter of Section 101. Each patent examination center, each trial court, each panel of this court, will have a blank slate on which to uphold or invalidate claims based on whether there are sufficient “meaningful limits”, or whether a transformation is adequately “central,” or the “significance” of process steps. These qualifiers, appended to a novel test which itself is neither suggested nor supported by statutory text, legislative history, or judicial precedent, raise more questions than they answer. These new standards add delay, uncertainty, and cost, but do not add confidence in reliable standards for Section 101.

Other aspects of the changes of law also contribute uncertainty. We aren't told when, or if, software instructions implemented on a general purpose computer are deemed “tied” to a “particular machine,” for if Alappat's guidance that software converts a general purpose computer into a special purpose machine remains applicable, there is no need for the present ruling. For the thousands of inventors who obtained patents under the court's now-discarded criteria, their property rights are now vulnerable.

The court also avoids saying whether the State Street Bank and AT & T v. Excel inventions would pass the new test. The drafting of claims in machine or process form was not determinative in those cases, for “we consider the scope of § 101 to be the same regardless of the form-machine or process-in which a particular claim is drafted.” AT & T v. Excel, 172 F.3d at 1357. From either the machine or the transformation viewpoint, the processing of data representing “price, profit, percentage, cost, or loss” in State Street Bank is not materially different from the processing of the Bilski data representing commodity purchase and sale prices, market transactions, and risk positions; yet Bilski is held to fail our new test, while State Street is left hanging. The uncertainty is illustrated in the contemporaneous decision of In re Comiskey, 499 F.3d 1365, 1378-79 (Fed.Cir.2007), where the court held that “systems that depend for their operation on human intelligence alone” to solve practical problems are not within the scope of Section 101; and In re Nuijten, 500 F.3d 1346, 1353-54 (Fed.Cir.2007), where the court held that claims to a signal with an embedded digital watermark encoded according to a given encoding process were not directed to statutory subject matter under Section 101, although the claims included “physical but transitory forms of signal transmission such as radio broadcasts, electrical signals through a wire, and light pluses through a fiber-optic cable.”

Although this uncertainty may invite some to try their luck in court, the wider effect will be a disincentive to innovation-based commerce. For inventors, investors, competitors, and the public, the most grievous consequence is the effect on inventions not made or not developed because of uncertainty as to patent protection. Only the successes need the patent right.

The Bilski invention has not been examined for patentability
To be patentable, Bilski's invention must be novel and non-obvious, and the specification and claims must meet the requirements of enablement, description, specificity, best mode, etc. See 35 U.S.C. § 101 (“Whoever invents or discovers a new and useful process ... may obtain a patent therefor, subject to the conditions and requirements of this title.”); Diehr, 450 U.S. at 190, 101 S.Ct. 1048 (the question of whether an invention is novel is distinct from whether the subject matter is statutory); State Street Bank, 149 F.3d at 1377 (“Whether the patent's claims are too broad to be patentable is not to be judged under § 101, but rather under §§ 102, 103, and 112.”). I don't know whether Bilski can meet these requirements-but neither does this court, for the claims have not been examined for patentability, and no rejections apart from Section 101 are included in this appeal.

Instead, the court states the “true issue before us” is “whether Applicants are seeking to claim a fundamental principle (such as an abstract idea) or mental process,” maj. op. at 952, and answers “yes.” With respect, that is the wrong question, and the wrong answer. Bilski's patent application describes his process of analyzing the effects of supply and demand on commodity prices and the use of a coupled transaction strategy to hedge against these risks; this is not a fundamental principle or an abstract idea; it is not a mental process or a law of nature. It is a “process,” set out in successive steps, for obtaining and analyzing information and carrying out a series of commercial transactions for the purpose of “managing the consumption risk costs of a commodity sold by a commodity provider at a fixed price.” Claim 1, preamble.

Because the process Bilski describes employs complex mathematical calculations to assess various elements of risk, any practicable embodiment would be conducted with the aid of a machine-a programmed computer-but the court holds that since computer-implementation is not recited in claim 1, for that reason alone the process fails the “machine” part of the court's machine-or-transformation test. Maj. op. at 962. And the court holds that since Bilski's process involves the processing of data concerning commodity prices and supply and demand and other risk factors, the process fails the “transformation” test because no “physical objects or substances” are transformed. Maj. op. at 963-64. The court then concludes that because Bilski's Claim 1 fails the machine-or-transformation test it ipso facto preempts a “fundamental principle” and is thereby barred from the patent system under Section 101: an illogical leap that displays the flaws in the court's analysis.

If a claim is unduly broad, or if it fails to include sufficient specificity, the appropriate ground of rejection is Section 112, for claims must “particularly point out and distinctly claim[ ]” the invention. See In re Vaeck, 947 F.2d 488, 495-96 (Fed.Cir.1991) (affirming rejection under Section 112 where “[t]here is no reasonable correlation between the narrow disclosure in applicant's specification and the broad scope of protection sought in the claims”); In re Foster, 58 C.C.P.A. 1001, 438 F.2d 1011, 1016 (1971) (claims “not commensurate with appellants' own definition of what they are seeking to cover” are rejected under Section 112, rather than Section 101); In re Prater, 415 F.2d at 1403-04 (applying Section 112 to claims that included mental steps). The filing of a broader claim than is supported in the specification does not convert the invention into an abstraction and evict the application from eligibility for examination. A broad first claim in a patent application is routine; it is not the crisis event postulated in the court's opinion.

The role of examination is to determine the scope of the claims to which the applicant is entitled. See 37 C.F.R. § 1.104(a). The PTO's regulations provide:

On taking up an application for examination or a patent in a reexamination proceeding, the examiner shall make a thorough study thereof and shall make a thorough investigation of the available prior art relating to the subject matter of the claimed invention. The examination shall be complete with respect to both compliance of the application or patent under reexamination with the applicable statutes and rules and to the patentability of the invention as claimed, as well as with respect to matters of form, unless otherwise indicated.

Id. § 1.104(a)(1). The Manual of Patent Examining Procedure (MPEP) similarly instructs the examiners to conduct a “thorough search of the prior art” before evaluating the invention under Section 101. MPEP § 2106(III) (8th ed., rev.7, July.2008) (“Prior to evaluating the claimed invention under 35 U.S.C. § 101, USPTO personnel are expected to conduct a thorough search of the prior art.”). The MPEP also requires examiners to identify all grounds of rejection in the first official PTO action to avoid unnecessary delays in examination. Id. § 2106(II) (“Under the principles of compact prosecution, each claim should be reviewed for compliance with every statutory requirement for patentability in the initial review of the application, even if one or more claims are found to be deficient with respect to some statutory requirement.”). I note that this requirement does not appear to have been here met.

Several amici curiae referred to the difficulties that the PTO has reported in examining patents in areas where the practice has been to preserve secrecy, for published prior art is sparse. The Federal Trade Commission recognized that the problem of “questionable” patents stems mostly from “the difficulty patent examiners can have in considering all the relevant prior art in the field and staying informed about the rapid advance of computer science.” FTC, To Promote Innovation: The Proper Balance of Competition & Patent Law and Policy at ch. 3, pp. 44 (Oct.2003), available at http:// www. ftc. gov/ os/ 2003/ 10/ innovationrpt. pdf. However, this problem seems to be remedied, for the PTO reported in 2007 that for Class 705, “[t]he cases the examiners are now working on have noticeably narrower claims” than the cases filed in or before FY 2000. PTO Report at 9. The PTO reports that its search fields have been enlarged, staff added, and supervision augmented. FTC Report at ch. 1, p. 30. (“Since the PTO introduced [these changes] the allowance rate for business method patents has decreased, and the PTO believes that this decreased allowance rate indicates improved PTO searches for prior art.”). If this court's purpose now is to improve the quality of issued patents by eliminating access to patenting for large classes of past, present, and future inventions, the remedy would appear to be excessive.

A straightforward, efficient, and ultimately fair approach to the evaluation of “new and useful” processes-quoting Section 101-is to recognize that a process invention that is not clearly a “fundamental truth, law of nature, or abstract idea” is eligible for examination for patentability. I do not suggest that basic scientific discoveries are a proper subject matter of patents (the Court in Chakrabarty mentioned E=mc 2 and the law of gravity), and I do not attempt an all-purpose definition of the boundary between scientific theory and technological application. But it is rare indeed that a question arises at the boundary of basic science; more usual is the situation illustrated by Samuel Morse's telegraph, in which the Court simply held that Morse's general claim was “too broad,” exceeding the scope of his practical application.

Bilski's process for determining risk in commodity transactions does not become an abstraction because it is broadly claimed in his first claim. It may be claimed so broadly that it reads on the prior art, but it is neither a fundamental truth nor an abstraction. Bilski's ten other claims contain further details and limitations, removing them farther from abstraction. Although claim 1 may have been deemed “representative” with respect to Section 101, the differences among the claims may be significant with respect to Sections 102, 103, and 112. Bilski's application, now pending for eleven years, has yet to be examined for patentability.

CONCLUSION
In sum, the text of Section 101, its statutory history, its interpretation by the Supreme Court, and its application by the courts, contravene this court's redefinition of the statutory term “process.” The court's decision affects present and future rights and incentives, and usurps the legislative role. The judicial role is to support stability and predictability in the law, with fidelity to statute and precedent, and respect for the principles of stare decisis.

Patents provide an incentive to invest in and work in new directions. In United States v. Line Material Co., 333 U.S. 287, 332, 68 S.Ct. 550, 92 L.Ed. 701 (1948), Justice Burton, joined by Chief Justice Vinson and Justice Frankfurter, remarked that “the frontiers of science have expanded until civilization now depends largely upon discoveries on those frontiers to meet the infinite needs of the future. The United States, thus far, has taken a leading part in making those discoveries and in putting them to use.” This remains true today. It is antithetical to this incentive to restrict eligibility for patenting to what has been done in the past, and to foreclose what might be done in the future.

===Footnotes===
<references/>

In Re Bilski, Dky concurring opinion

2015-04-02T17:44:13Z

Bill:

DYK, Circuit Judge, with whom LINN, Circuit Judge, joins, concurring.

While I fully join the majority opinion, I write separately to respond to the claim in the two dissents that the majority's opinion is not grounded in the statute, but rather “usurps the legislative role.”<ref>The dissents fault the majority for “ventur[ing] away from the statute,” Rader, J., dissenting op. at 1013, and “usurp[ing] the legislative role,” Newman, J., dissenting op. at 997.</ref> In fact, the unpatentability of processes not involving manufactures, machines, or compositions of matter has been firmly embedded in the statute since the time of the Patent Act of 1793, ch. 11, 1 Stat. 318 (1793). It is our dissenting colleagues who would legislate by expanding patentable subject matter far beyond what is allowed by the statute.

I

Section 101 now provides:

Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.

35 U.S.C. § 101 (emphases added).

The current version of § 101 can be traced back to the Patent Act of 1793. In relevant part, the 1793 Act stated that a patent may be granted to any person or persons who:

shall allege that he or they have invented any new and useful art, machine, manufacture or composition of matter, or any new and useful improvement on any art, machine, manufacture or composition of matter....

1 Stat. 318, 319 § 1 (1793) (emphases added). The criteria for patentability established by the 1793 Act remained essentially unchanged until 1952, when Congress amended § 101 by replacing the word “art” with “process” and providing in § 100(b) a definition of the term “process.” The Supreme Court has made clear that this change did not alter the substantive understanding of the statute; it did not broaden the scope of patentable subject matter.<ref>See Diamond v. Diehr, 450 U.S. 175, 182, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981) (“[A] process has historically enjoyed patent protection because it was considered a form of ‘art’ as that term was used in the 1793 Act.”); Diamond v. Chakrabarty, 447 U.S. 303, 309, 100 S.Ct. 2204, 65 L.Ed.2d 144 (1980). Rather, the 1952 Act simply affirmed the prior judicial understanding, as set forth in Corning v. Burden, 56 U.S. (15 How.) 252, 14 L.Ed. 683 (1853), that Congress in 1793 had provided for the patentability of a “process” under the term “art.” Diehr, 450 U.S. at 182, 101 S.Ct. 1048.</ref> Thus, our interpretation of § 101 must begin with a consideration of what the drafters of the early patent statutes understood the patentability standard to require in 1793. See Diehr, 450 U.S. at 182-83, 101 S.Ct. 1048 (looking to the 1793 Act).

A

The patentability criteria of the 1793 Act were to a significant extent the same in the 1790 Act.<ref>In relevant part, the 1790 Act permitted patents upon “any useful art, manufacture, engine, machine, or device, or any improvement therein not before known or used.” Ch. 11, § 1, 1 Stat. 109, 110 (1790).</ref> The 1790 “statute was largely based on and incorporated” features of the English system and reveals a sophisticated knowledge of the English patent law and practice.<ref>Edward C. Walterscheid, To Promote the Progress of Useful Arts: American Patent Law & Administration, 1798-1836 109 (1998) (hereinafter To Promote the Progress ); see also Edward C. Walterscheid, The Early Evolution of the United States Patent Law: Antecedents (Part 1), 76 J. Pat. & Trademark Off. Soc'y 697, 698 (1994) (“[T]he English common law relating to patents was what was best known in the infant United States.”).</ref> This is reflected in Senate committee report<ref>Senate Committee Report Accompanying Proposed Amendments to H.R. 41, reprinted in Proceedings in Congress During the Years 1789 & 1790 Relating to the First Patent & Copyright Laws, 22 J. Pat. Off. Soc'y 352, 363 (1940).</ref> for the bill that became the 1790 Act, which expressly noted the drafters' reliance on the English practice:

The Bill depending before the House of Representatives for the Promotion of useful Arts is framed according to the Course of Practice in the English Patent Office except in two Instances-
22 J. Pat. Off. Soc'y at 363 (emphasis added).<ref>Neither of those two instances related to patentable subject matter or was adopted in the enacted statute. The first proposed departure from the English practice was a novelty provision protecting the inventor against those who derived their knowledge of the invention from the true inventor; the second was in a requirement that patentees make a “Public Advertisement” of their invention. Such a requirement was thought necessary “in so extensive a Country as the United States.” Senate Report, reprinted in 22 J. Pat. Off. Soc'y at 363-64.

The American statute ultimately differed in some other respects. For example, Congress rejected the English rule that the invention need only be novel in England. The American statute required novelty against the whole world and did not permit “patents of importation.” See To Promote the Progress, supra n. 4 at 95-97, 137-38. </ref> Likewise, the legislative history of the 1793 Patent Act reflects the same keen understanding of English patent practice. During a debate in the House over the creation of a Patent Office, for example, the Representative who introduced the bill noted that its principles were “an imitation of the Patent System of Great Britain.” 3 Annals of Congress 855 (1793).<ref>Even the opposing view-urging departure from the English practice in particular respects-recognized that the English practice provided considerable guidance. See 3 Annals of Congress at 855-56 (“[Great Britain] had afforded, it was true, much experience on the subject; but regulations adopted there would not exactly comport in all respects either with the situation of this country, or with the rights of the citizen here. The minds of some members had taken a wrong direction, he conceived, from the view in which they had taken up the subject under its analogy with the doctrine of patents in England.”); see also To Promote the Progress, supra n. 4 at 216-17.</ref>

Later, Justice Story, writing for the Supreme Court, recognized the profound influence of the English practice on these early patent laws, which in many respects codified the common law:

It is obvious to the careful inquirer, that many of the provisions of our patent act are derived from the principles and practice which have prevailed in the construction of that of England .... The language of [the patent clause of the Statute of Monopolies] is not, as we shall presently see, identical with ours; but the construction of it adopted by the English courts, and the principles and practice which have long regulated the grants of their patents, as they must have been known and are tacitly referred to in some of the provisions of our own statute, afford materials to illustrate it.

Pennock v. Dialogue, 27 U.S. 1, 18, 2 Pet. 1, 7 L.Ed. 327 (1829) (emphases added); see also Graham v. John Deere Co., 383 U.S. 1, 5, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966) (noting that first patent statute was written against the “backdrop” of English monopoly practices); Sears, Roebuck & Co. v. Stiffel Co., 376 U.S. 225, 230 n. 6, 84 S.Ct. 784, 11 L.Ed.2d 661 (1964) (“Much American patent law derives from English patent law.”).

While Congress departed from the English practice in certain limited respects, in many respects Congress simply adopted the English practice without change. Both the 1790 and the 1793 Acts, for example, adopted the same 14-year patent term as in England. Both also required inventors to file a written specification-a requirement recognized by the English common law courts in the mid-eighteenth century.<ref>See Christine MacLeod, Inventing the Industrial Revolution: The English Patent System, 1660-1800 48-49 (2002); To Promote the Progress, supra n. 4 at 400, 404.</ref> In addition, as discussed below, the categories of patentable subject matter closely tracked the English approach, and in certain respects reflected a deliberate choice between competing views prevalent in England at the time.

B

The English practice in 1793, imported into the American statutes, explicitly recognized a limit on patentable subject matter. As the Supreme Court recounted in Graham v. John Deere, the English concern about limiting the allowable scope of patents arose from an aversion to the odious Crown practice of granting patents on particular types of businesses to court favorites. 383 U.S. 1, 5, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966); see also MacLeod, supra n. 8 at 15 (“But most offensive of all was the granting of monopoly powers in established industries, as a form of patronage, to courtiers whom the crown could not otherwise afford to reward.”). Parliament responded to the Crown's abuses in 1623 by passing the Statute of Monopolies, prohibiting the Crown from granting these despised industry-type monopolies. Not all monopolies were prohibited, however: the Statute expressly exempted invention-type patent monopolies. Section 6 of the Statute exempted from its prohibitions “letters patent and grants of privilege for the term of fourteen years or under, hereafter to be made, of the sole working or making of any manner of new manufactures within this realm, to the true and first inventor and inventors of such manufactures....” 21 Jac. 1. c.3, s.6 (emphases added).

Each of the five categories of patentable subject matter recognized by the 1793 Patent Act-(1) “manufacture,” (2) “machine,” (3) “composition of matter,” (4) “any new and useful improvement,” and (5) “art”- was drawn either from the Statute of Monopolies and the common law refinement of its interpretation or resolved competing views being debated in England at the time. See To Promote the Progress, supra n. 4 at 239.

“ Manufacture.” At the most basic level, the 1793 Act, like the Statute of Monopolies, expressly provided for the patentability of “manufactures.” This language was not accidental, but rather reflected a conscious adoption of that term as it was used in the English practice. Id. (“It is clear that the Congress sought to incorporate into the U.S. statutory scheme in 1793 at least as much of the common law interpretation of ‘new manufactures' as was understood at the time.”).

“ Machine.” Likewise, the category of “machines” in the 1793 Act had long been understood to be within the term “manufactures” as used in the English statute. See id.; see, e.g., Morris v. Bramson, 1 Carp. P.C. 30, 31 (K.B.1776) (sustaining a patent “for an engine or machine on which is fixed a set of working needles ... for the making of eyelet-holes”) (emphasis added); MacLeod, supra n. 8 at 101 (noting, among numerous other early machine patents, seven patents on “machinery to raise coal and ores” before 1750).

“ Composition of Matter.” Although the 1790 statute did not explicitly include “compositions of matter,” this was remedied in the 1793 statute. At the time, “compositions of matter” were already understood to be a type of manufacture patentable under the English statute. See To Promote the Progress, supra n. 4, at 224 n. 4. One example is found in Liardet v. Johnson, 1 Carp. P.C. 35 (K.B.1778), a case involving a patent on a “composition” of stucco (a composition of matter). Lord Mansfield's jury instructions noted that by the time of that trial he had decided “several cases” involving compositions: “But if ... the specification of the composition gives no proportions, there is an end of his patent.... I have determined, [in] several cases here, the specification must state, where there is a composition, the proportions....” <ref>Edward C. Walterscheid, The Nature of the Intellectual Property Clause: A Study in Historical Perspective 55 (2002) (quoting E. Wyndham Hulme, On the History of the Patent Laws in the Seventeenth and Eighteenth Centuries, 18 L.Q. Rev. 280, 285 (1902)).</ref>

“ Any new and useful improvement.” The reference to “any new and useful improvement” in the 1793 Act also adopted a consensus recently reached by the English courts. The common law courts had first ruled in Bircot's Case in the early seventeenth century that an improvement to an existing machine could not be the proper subject of a patent under the Statute of Monopolies. See Boulton v. Bull, 2 H. Bl. 463, 488 (C.P.1795). In 1776 that line of cases was overruled in Morris v. Bramson, because such a reading of the statute “would go to repeal almost every patent that was ever granted.”<ref>Morris, 1 Carp. P.C. at 34; see also Boulton, 2 H.Bl. at 489 (“Since [ Morris v. Bramson ], it has been the generally received opinion in Westminster Hall, that a patent for an addition is good.”).</ref>

“ Art.” As the Supreme Court has recognized, a process “was considered a form of ‘art’ as that term was used in the 1793 Act.” Diehr, 450 U.S. at 182, 101 S.Ct. 1048 (citing Corning v. Burden, 56 U.S. at 267-268). The language of the Statute of Monopolies permitted patents on that which could be characterized as the “working or making of any manner of new manufactures within this realm.” 21 Jac. 1. c.3, s.6. While this language plainly applied to tangible “new manufactures” (such as machines or compositions of matter), it also appeared to allow patenting of manufacturing processes as the “ working or making of any manner of new manufactures.” Thus, under the Statute of Monopolies patents could be had on the “working or making of any manner of new manufactures.” Numerous method patents had issued by 1793, including James Watt's famous 1769 patent on a “ [m]ethod of diminishing the consumption of fuel in [steam]-engines.”<ref>Walterscheid, supra n. 9 at 355-56 (emphasis added); see also Boulton, 2 H. Bl. at 494-95 (1795) (noting that many method patents had issued).</ref> However, the English courts in the mid-eighteenth century had not yet resolved whether processes for manufacturing were themselves patentable under the statute, and as discussed below, the issue was being actively litigated in the English courts. In the 1793 Act Congress resolved this question by including the term “art” in the statute, adopting the practice of the English law officers and the views of those in England who favored process patents.

II

The question remains as to what processes were considered to be patentable in England at the time of the 1793 Act. Examination of the relevant sources leads to the conclusion that the method Bilski seeks to claim would not have been considered patentable subject matter as a process under the English statute.

A

First, the language of the Statute of Monopolies-“ working or making of any manner of new manufactures ”-suggests that only processes that related to “manufactures” (including machines or compositions of matter) could be patented.

Second, the English patent practice before and contemporaneous with the 1793 Act confirms the notion that patentable subject matter was limited by the term “manufacture” in the Statute of Monopolies and required a relation to the other categories of patentable subject matter. The organization of human activity was not within its bounds. Rather, the patents registered in England under the Statute of Monopolies before 1793 were limited to articles of manufacture, machines for manufacturing, compositions of matter, and related processes. A complete list of such patents (with a few missing patents from the 17th century) was published in the mid-1800s by Bennet Woodcroft, the first head of the English Patent Office.<ref>Bennet Woodcroft, Alphabetical Index of Patentees of Inventions, from March 2, 1617 (14 James I) to October 1, 1852 (16 Victoriae) (2d ed. 1857).</ref> Representative examples of patented processes at the time include: “Method of making a more easy and perfect division in stocking frame-work manufactures,” No. 1417 to John Webb (1784); “Making and preparing potashes and pearl-ashes of materials not before used for the purpose,” No. 1223 to Richard Shannon (1779); “Making salt from sea-water or brine, by steam,” No. 1006 to Daniel Scott (1772); “Milling raw hides and skins so as to be equally good for leather as if tanned,” No. 893 to George Merchant (1768); “Making salt, and removing the corrosive nature of the same, by a separate preparation of the brine,” No. 416 to George Campbell (1717); and “Making good and merchantable tough iron ... with one-fifth of the expense of charcoal as now used,” No. 113 to Sir Phillibert Vernatt (1637).

Nothing in Woodcroft's list suggests that any of these hundreds of patents was on a method for organizing human activity, save for one aberrational patent discussed below. Rather, the established practice reflects the understanding that only processes related to manufacturing or “manufactures” were within the statute. The English cases before 1793 recognized that the practice followed in issuing patents was directly relevant to the construction of the statute. See, e.g., Morris, 1 Carp. P.C. at 34 (declining to read the statute in such a way that “would go to repeal almost every patent that was ever granted”).

Third, nearly contemporaneous English cases following shortly after the 1793 Act lend further insight into what processes were thought to be patentable under the English practice at the time the statute was enacted. Although the issue of the validity of process patents had not conclusively been settled in the English common law before 1793, the question was brought before the courts in the landmark case of Boulton v. Bull, 2 H. Bl. 463, 465 (C.P.1795), which involved James Watt's patent for a “method of lessening the consumption of steam, and consequently fuel in [steam] engines.”<ref>The Supreme Court has in several opinions noted Boulton v. Bull in connection with its consideration of English patent practice. See, e.g., Markman v. Westview Instruments, Inc., 517 U.S. 370, 381 n. 6, 116 S.Ct. 1384, 134 L.Ed.2d 577 (1996); Evans v. Eaton, 20 U.S. (7 Wheat.) 356, 388 n. 2-3, 5 L.Ed. 472 (1822).</ref> In 1795, the court rendered a split decision, with two judges on each side. Boulton, 2 H. Bl. at 463 (1795). Those who viewed process patents as invalid, as did Justice Buller, urged that a method was merely an unpatentable principle: “A patent must be for some new production from [elements of nature], and not for the elements themselves.” Id. at 485. He thought “it impossible to support a patent for a method only, without having carried it into effect and produced some new substance.” Id. at 486. Justice Health similarly found that the “new invented method for lessening the consumption of steam and fuel in [steam] engines” (i.e., the Watt patent), being neither “machinery” nor a “substance [ ] (such as medicine[ ] ) formed by chemical and other processes,” was not within the Statute of Monopolies. Id. at 481-82. In contrast, Lord Chief Justice Eyres, who believed processes had long been a valid subject of patents, urged that “two-thirds, I believe I might say three-fourths, of all patents granted since the statute [of Monopolies] passed, are for methods of operating and of manufacturing.... ” Id. at 494-95 (emphasis added). He agreed that “[u]ndoubtedly there can be no patent for a mere principle; but for a principle so far embodied and connected with corporeal substances ... I think there may be a patent.” Id. at 495 (emphasis added). Justice Rooke also noted that Watt's method was within the statute because it was connected with machinery: “What method can there be of saving steam or fuel in engines, but by some variation in the construction of them?” Id. at 478. The Justices who believed process patents were valid spoke in terms of manufacturing, machines, and compositions of matter, because the processes they believed fell within the statute were processes that “embodied and connected with corporeal substances.” Id. at 495.

In 1799, on appeal from another case involving the same Watt patent, the validity of such process patents were upheld. Hornblower v. Boulton (K.B.1799), 8 T.R. 95. There, Chief Justice Lord Kenyon stated that “it evidently appears that the patentee claims a monopoly for an engine or machine, composed of material parts, which are to produce the effect described; and that the mode of producing this is so described, as to enable mechanics to produce it.... I have no doubt in saying, that this is a patent for a manufacture, which I understand to be something made by the hands of man.” Id. at 99. Justice Grose agreed, finding that “Mr. Watt had invented a method of lessening the consumption of steam and fuel in [steam] engines”, and this was “not a patent for a mere principle, but for the working and making of a new manufacture within the words and meaning of the statute.” Id. at 101-02. He further noted, however, that “This method ... if not effected or accompanied by a manufacture, I should hardly consider as within the [statute].” Id. at 102-03 (emphasis added). Justice Lawrence similarly found such process patents to be permissible: “Engine and method mean the same thing, and may be the subject of a patent. ‘Method,’ properly speaking, is only placing several things and performing several operations in the most convenient order....” Id. at 106.

There is no suggestion in any of this early consideration of process patents that processes for organizing human activity were or ever had been patentable. Rather, the uniform assumption was that the only processes that were patentable were processes for using or creating manufactures, machines, and compositions of matter.

B

The dissenters here, by implication at least, appear to assume that this consistent English practice should somehow be ignored in interpreting the current statute because of technological change.<ref>See, e.g., Rader, J., dissenting op. at 1011 (“[T]his court ties our patent system to dicta from an industrial age decades removed from the bleeding edge.”); id. (“[T]his court ... links patent eligibility to the age of iron and steel at a time of subatomic particles and terabytes....”); Newman, J., dissenting op. at 1011 (“[T]his court now adopts a redefinition of ‘process' in Section 101 that excludes forms of information-based and software-implemented inventions arising from new technological capabilities....”).</ref> There are several responses to this.

The first of these is that the Supreme Court has made clear that when Congress intends to codify existing law, as was the case with the 1793 statute, the law must be interpreted in light of the practice at the time of codification. In Schmuck v. United States, 489 U.S. 705, 718-19, 109 S.Ct. 1443, 103 L.Ed.2d 734 (1989), for example, the Court considered the proper interpretation of Rule 31(c) of the Federal Rules of Criminal Procedure. The rule, “which ha [d] not been amended since its adoption in 1944,” was a restatement of an 1872 Act “codif[ying] the common law for federal criminal trials.” Because of this fact, the Court found that the “prevailing practice at the time of the Rule's promulgation informs our understanding of its terms.” Id.; see also, e.g., Eldred v. Ashcroft, 537 U.S. 186, 200 n. 5, 123 S.Ct. 769, 154 L.Ed.2d 683 (2003) (considering the English practice at the time of the enactment of the 1790 copyright act); Tome v. United States, 513 U.S. 150, 159-60, 166, 115 S.Ct. 696, 130 L.Ed.2d 574 (1995) (looking to practice and noting that “a majority of common-law courts were performing [a task required by the common law] for well over a century” in interpreting a Federal Rule of Evidence that “was intended to carry over the common-law”); Harper & Row Publishers, Inc. v. Nation Enters., 471 U.S. 539, 549-554, 105 S.Ct. 2218, 85 L.Ed.2d 588 (1985) (relying on the history and practice of copyright fair-use when statutory provision reflected the “intent of Congress to codify the common-law doctrine”); Sprague v. Ticonic Nat'l Bank, 307 U.S. 161, 164-65, 59 S.Ct. 777, 83 L.Ed. 1184 (1939) (considering the English practice “which theretofore had been evolved in the English Court of Chancery” at the time of the 1789 Judiciary Act in determining availability of costs under equity jurisdiction).

Second, the Supreme Court language upon which the dissents rely<ref>See, e.g., Newman, J., dissenting op. at 981 (“ ‘[C]ourts should not read into the patent laws limitations and conditions which the legislature has not expressed.’ ” (quoting Diehr, 450 U.S. at 182, 101 S.Ct. 1048)); Rader, J., dissenting op. at 1012 (same).</ref> offers no warrant for rewriting the 1793 Act. To be sure, Congress intended the courts to have some latitude in interpreting § 101 to cover emerging technologies, Chakrabarty, 447 U.S. at 316, 100 S.Ct. 2204, and the categorical terms chosen are sufficiently broad to encompass a wide range of new technologies. But there is no evidence that Congress intended to confer upon the courts latitude to extend the categories of patentable subject matter in a significant way. To the contrary, the Supreme Court made clear that “Congress has performed its constitutional role in defining patentable subject matter in § 101; we perform ours in construing the language Congress has employed. In so doing, our obligation is to take statutes as we find them, guided, if ambiguity appears, by the legislative history and statutory purpose.” Id. at 315, 100 S.Ct. 2204. In Benson, the Court rejected the argument that its decision would “freeze process patents to old technologies, leaving no room for the revelations of the new, onrushing technology.” Gottschalk v. Benson, 409 U.S. 63, 71, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972). Instead, the Court explained that it “may be that the patent laws should be extended to cover [such onrushing technology], a policy matter to which we are not competent to speak” but that “considered action by the Congress is needed.” Id. at 72-73, 93 S.Ct. 253.

Third, we are not dealing here with a type of subject matter unknown in 1793. One commentator has noted:

The absence of business method patents cannot be explained by an absence of entrepreneurial creativity in Great Britain during the century before the American Revolution. On the contrary, 1720 is widely hailed as the beginning of a new era in English public finance and the beginning of major innovations in business organization.

Malla Pollack, The Multiple Unconstitutionality of Business Method Patents, 28 Rutgers Computer & Tech. L.J. 61, 96 (2002) (footnotes omitted).<ref>Similarly, another commentator states: “it might be wondered why none of the many ingenious schemes of insurance has ever been protected by patenting it.” D.F. Renn, John Knox's Plan for Insuring Lives: A Patent of Invention in 1778, 101 J. Inst. Actuaries 285 (1974), available at http:// www. actuaries. org. uk/ _data/assets/pdf_file/0006/25278/0285-0289.pdf (last visited Oct. 3, 2008).</ref> In the hundreds of patents in Woodcroft's exhaustive list of English patents granted from 1612 to 1793, there appears to be only a single patent akin to the type of method Bilski seeks to claim. That sole exception was a patent granted to John Knox in 1778 on a “Plan for assurances on lives of persons from 10 to 80 years of age.”<ref>Woodcroft, supra n. 12 at 324.</ref> Later commentators have viewed this single patent as clearly contrary to the Statute of Monopolies:

Such protection of an idea should be impossible.... It is difficult to understand how Knox's plan for insuring lives could be regarded as ‘a new manner of manufacture’; perhaps the Law Officer was in a very good humour that day, or perhaps he had forgotten the wording of the statute; most likely he was concerned only with the promised ‘very considerable Consumption of [Revenue] Stamps' which, Knox declared, would ‘contribute to the increase of the Public Revenues.’
Renn, supra n. 16 at 285. There is no indication that Knox's patent was ever enforced or its validity tested, or that this example led to other patents or efforts to patent similar activities. But the existence of the Knox patent suggests that as of 1793 the potential advantage of patenting such activities was well-understood.
In short, the need to accommodate technological change in no way suggests that the judiciary is charged with rewriting the statute to include methods for organizing human activity that do not involve manufactures, machines, or compositions of matter.

C

Since the 1793 statute was reenacted in 1952, it is finally important also to inquire whether between 1793 and 1952 the U.S. Patent Office and the courts in this country had departed from the English practice and allowed patents such as those sought by Bilski. In fact, the U.S. Patent Office operating under the 1793 Act hewed closely to the original understanding of the statute. As in the English practice of the time, there is no evidence that patents were granted under the 1793 Act on methods of organizing human activity not involving manufactures, machines or the creation of compositions of matter. The amicus briefs have addressed the early American practice, and some of them claim that human activity patents were allowed in the early period. To the contrary, the patents cited in the briefs are plainly distinguishable.

The earliest claimed human activity patent cited in the briefs issued in 1840, entitled “Improvement in the Mathematical Operation of Drawing Lottery-Schemes.” Br. of Amicus Curiae Regulatory Datacorp 23 n.54. But that patent is fundamentally unlike the Bilski claim, since it does not claim a method of organizing human activity not involving manufactures, machines or the creation of compositions of matter. See U.S. Patent No. 1700 (issued July 18, 1840). Rather, it is directed to a scheme of combining different combinations of numbers onto a large number of physical lottery tickets (i.e., a method for manufacturing lottery tickets). Id. col.1. The other early-issued patents cited in the amicus briefs are similarly distinguishable.<ref>See, e.g., Complemental Accident Insurance Policy, U.S. Patent No. 389,818 (issued Sept. 18, 1888) (claiming a “complemental insurance policy” as an apparatus consisting of two separate cards secured together); Insurance System, U.S. Patent No. 853,852 (issued May 14, 1907) (claiming a “two-part insurance policy” as “an article of manufacture”).</ref>

A number of the amici also refer to the discussion and the patents cited in “A USPTO White Paper” (the “White Paper”) to establish the historical foundation of business method patents. See, e.g., Br. of Amicus Curiae Accenture 14-15 n. 11. As Judge Mayer notes, dissenting op. at 1001-02 n. 4, the White Paper does not show this proposition. As the White Paper itself recognizes, the early financial patents it discusses were largely mechanical products and methods related to financial paper, not methods for organizing human activity. White Paper at 2. Thus, while the White Paper shows that inventions in the business realm of finance and management historically enjoyed patent protection, it does little to establish that business methods directed to the organization of human activity not involving manufactures, machines or the creation of compositions of matter were similarly patentable.

Likewise, Supreme Court decisions before the 1952 Patent Act assumed that the only processes that were patentable were those involving other types of patentable subject matter. In later cases the Supreme Court has recognized that these cases set forth the standard for process patents in the pre-1952 period. Diehr, 450 U.S. at 182-84, 101 S.Ct. 1048; Gottschalk, 409 U.S. at 69-70, 93 S.Ct. 253. The leading case is Corning v. Burden, 56 U.S. 252, 15 How. 252, 14 L.Ed. 683 (1853). There, the Supreme Court discussed the patentability of processes:

A process, eo nomine, is not made the subject of a patent in our act of Congress. It is included under the general term ‘useful art.’ An art may require one or more processes or machines in order to produce a certain result or manufacture. The term machine includes every mechanical device or combination of mechanical powers and devices to perform some function and produce a certain effect or result. But where the result or effect is produced by chemical action, by the operation or application of some element or power of nature, or of one substance to another, such modes, methods, or operations, are called ‘processes.’ A new process is usually the result of discovery; a machine, of invention. The arts of tanning, dyeing, making water-proof cloth, vulcanizing India rubber, smelting ores, and numerous others are usually carried on by processes, as distinguished from machines.... It is for the discovery or invention of some practicable method or means of producing a beneficial result or effect that a patent is granted, and not for the result or effect itself. It is when the term process is used to represent the means or method of producing a result that it is patentable, and it will include all methods or means which are not effected by mechanism or mechanical combinations.

Id. at 267-68 (emphases added). In Cochrane v. Deener, the Court clarified its understanding of a patentable “process”:

That a process may be patentable, irrespective of the particular form of the instrumentalities used, cannot be disputed.... A process is a mode of treatment of certain materials to produce a given result. It is an act, or a series of acts, performed upon the subject-matter to be transformed and reduced to a different state or thing. If new and useful, it is just as patentable as is a piece of machinery. In the language of the patent law, it is an art. The machinery pointed out as suitable to perform the process may or may not be new or patentable; whilst the process itself may be altogether new, and produce an entirely new result. The process requires that certain things should be done with certain substances, and in a certain order; but the tools to be used in doing this may be of secondary consequence.

94 U.S. 780, 787-88, 24 L.Ed. 139 (1876) (emphases added). Finally, in Tilghman v. Proctor, 102 U.S. 707, 722, 26 L.Ed. 279 (1880), the Court noted:

That a patent can be granted for a process there can be no doubt. The patent law is not confined to new machines and new compositions of matter, but extends to any new and useful art or manufacture. A manufacturing process is clearly an art, within the meaning of the law.

(Emphasis added). The Court's definition of a patentable process was well-accepted and consistently applied by the courts of appeals. See, e.g., P.E. Sharpless Co. v. Crawford Farms, 287 F. 655, 658-59 (2nd Cir.1923); Chicago Sugar-Refining Co. v. Charles Pope Glucose Co., 84 F. 977, 982 (7th Cir.1898).

Finally, nothing in the legislative history of the 1952 Act suggests that Congress intended to enlarge the category of patentable subject matter to include patents such as the method Bilski attempts to claim. As discussed above, the only change made by the 1952 Act was in replacing the word “art” with the word “process.” The Supreme Court has already concluded that this change did not alter the substantive understanding of the statute. See Diehr, 450 U.S. at 182, 101 S.Ct. 1048 (“[A] process has historically enjoyed patent protection because it was considered a form of ‘art’ as that term was used in the 1793 Act.”).

The House Report accompanying the 1952 bill includes the now-famous reference to “anything under the sun made by man”:

A person may have “invented” a machine or a manufacture, which may include anything under the sun made by man, but it is not necessarily patentable under section 101 unless the conditions of the title are fulfilled.

H.R.1923 at 7. Although this passage has been used by our court in past cases to justify a broad interpretation of patentable subject matter, I agree with Judge Mayer that, when read in context, the statement undercuts the notion that Congress intended to expand the scope of § 101. See Mayer, J., dissenting op. at 1000. It refers to things “made by man,” not to methods of organizing human activity. In this respect, the language is reminiscent of the 1799 use of the phrase “something made by the hands of man” by Chief Justice Lord Kenyon as a limitation on patentable subject matter under the Statute of Monopolies. The idea that an invention must be “made by man” was used to distinguish “a philosophical principle only, neither organized or capable of being organized” from a patentable manufacture. Hornblower, 8 T.R. at 98. Lord Kenyon held that the patent before him was not based on a mere principle, but was rather “a patent for a manufacture, which I understand to be something made by the hands of man.” Id. at 98 (emphases added); accord American Fruit Growers v. Brogdex Co., 283 U.S. 1, 11, 51 S.Ct. 328, 75 L.Ed. 801 (1931) (giving “anything made for use from raw or prepared materials” as one definition of “manufacture”).

In short, the history of § 101 fully supports the majority's holding that Bilski's claim does not recite patentable subject matter. Our decision does not reflect “legislative” work, but rather careful and respectful adherence to the Congressional purpose.

===Footnotes===
<references/>

In Re Bilski, Dky concurring opinion

2015-04-02T17:42:42Z

Bill:

AME 40590 Intellectual Property for Engineers

2015-04-02T15:47:16Z

Bill: /* ALPHABETICAL LISTING OF CASES */

Cases to add:
* Damages:
** MINTZ V. DIETZ & WATSON, INC. (CAFC, May 2012)
** Monsanto Co. v. McFarling, 488 F.3d 973, 978-79 (Fed. Cir. 2007)
** Georgia-Pacific Corp. v. US Plywood Corp., 318 F. Supp. 1116 (SDNY 1970), modified, 446 F. 2d 295 (2d Cir. 1971)
** The Boeing Company v. The United States, 86 Fed. Cl. 303 (April 2, 2009)
** Mahurkar v. CR Bard, Inc. 79 F. 3d 1572, 1580 (Fed. Cir. 1996), adopting Panduit Corp. v. Stahlin Bros. Fibre Works, Inc.,575 F.2d 1152 (6th Cir. 1978)
** Depuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 567 F.3d 1314 (Fed. Cir. 2009)

* Software patents:
** In re Alappat, 33 F.3d 1526, 1545 (Fed. Cir. 1994).
** CyberSource Corporation v. Retail Decisions, Inc., Slip Op. at 19 (2011)
** Ultramercial, LLC v. Hulu, LLC (Fed. Cir. 2011)

=ALPHABETICAL LISTING OF CASES=

*[[A. & P. Tea Co. v. Supermarket Corp., 340 U.S. 147 (1950)]]
*[[Abbott Laboratories v. Geneva Pharmaceuticals, Inc., 182 F.3d 1315 (1999)]]
*[[Alza Corp. v. Mylan Laboratories, 464 F.3d 1286, (2006)]]
*[[Anderson's Black Rock, Inc. v. Pavement Co., 396 U.S. 57 (1969)]]
*[[Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336 (1961)]]
*[[Arrhythmia Research Technology, Inc. v. Corazonix Corp., 958 F.2d 1053 (1992)]]
*[[Asgrow Seed Co. v. Winterboer, 513 U.S. 179 (1994)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. (2013)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. CAFC (2012)]]
*[[Atlas Powder v. E.I. du Pont de Nemours, 750 F2d 1569 (1984)]]
*[[Bilski v. Kappos, 130 S.Ct. 3218 (2010)]]
*[[Bobbs-Merrill Co. v. Straus, 210 U.S. 339 (1908)]]
*[[Bonito Boats. v. Thunder Craft, 489 U.S. 141 (1989)]]
*[[Bowman v. Monsanto, 133 S.Ct. 1761 (2013)]]
*[[CCS Fitness, Inc. v. Brunswick Corporation, 288 F.3d 1359 (2002)]]
*[[Chester v. Miller, 906 F.2d 1574 (1990)]]
*[[D.L. Auld Co. v. Chroma Graphics Corp., 714 F.2d 1144 (1983)]]
*[[Diamond v. Chakrabarty, 100 S.Ct. 2204 (1980)]]
*[[Diamond v. Diehr, 450 U.S. 175 (1981)]]
*[[Egbert v. Lippmann, 104 U.S. 333 (1881)]]
*[[Electric Storage Battery Co. v. Shimadzu, 307 U.S. 5 (1939)]]
*[[Elizabeth v. American Nicholson Pavement Company, 97 U.S. 126 (1877)]]
*[[Filmtec Corp. v. Allied-Signal Inc., 939 F.2d 1568 (1991)]]
*[[Funk Bros. Seed Co. v. Kalo Inoculant Co. 333 U.S. 127 (1948)]]
*[[Gottschalk v. Benson, 409 U.S. 63 (1972)]]
*[[Gould v. Hellwarth, 472 F2d 1383 (1973)]]
*[[Graham v. John Deere, 383 U.S. 1 (1966)]]
*[[Graver Tank & Mfg. Co. v. Linde Air Products Co. 339 US 605 (1950)]]
*[[H.H. Robertson, Co. v. United Steel Deck, Inc., 820 F.2d 384 (1987)]]
*[[Hotchkiss v. Greenwood, 52 U.S. 11 (1850) ]]
*[[Hybritech v. Monoclonal Antiboties, 802 F.2d 1375 (1986)]]
*[[i4i Ltd. Partnership v. Microsoft Corp., 598 F.3d 831 (2010)]]
*[[In Re Bilski]]
**[[In Re Bilski, Dky concurring opinion]]
**[[In Re Bilski, Newman dissenting opinion]]
**[[In Re Bilski, Mayer dissenting opinion]]
**[[In Re Bilski, Rader dissenting opinion]]
*[[In re Brana, 51 F.3d 1560 (1995)]]
*[[In re Carlson, 983 F.2d 1032 (1992)]]
*[[In re Hall, 781 F.2d 897 (1986)]]
*[[In re Kahn, CAFC 04-1616 (2006)]]
*[[In Re Rouffet]]
*[[J.E.M. Ag Supply, Inc. v. Pioneer Hi-Bred International, Inc., 534 U.S. 124 (2001)]]
*[[Juicy Whip v. Orange Bang, 185 F.3d 1364 (1999)]]
*[[KSR International Co. v. Teleflex, Inc., 550 U.S. 398 (2007)]]
*[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]
*[[Lorenz v. Colgate-Palmolive-Peet Co., 167 F.2d 423 (1948)]]
*[[Lough v. Brunswick Corp., 86 F.3d 1113 (1996)]]
*[[Lyon v. Bausch & Lomb, 224 F.2d 530 (1955)]]
*[[Metabolit Laboratories, Inc. and Competitive Technologies, Inc. v. Laboratory Corporation of America Holdings, 370 F.3d 1354 (2004)]]
*[[Metallizing Engineering Co., Inc. v. Kenyon Bearing & Auto Parts Co., Inc., 153 F.2d 516 (1946)]]
*[[Microsoft Corp v. At&T Corp.]]
*[[Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (1978)]]
*[[Perkin-Elmer Corporation v. Computervision Corporation, 732 F2d 888 (1984)]]
*[[Pfaff vs. Wells Electronics, 525 U.S. 55 (1998)]]
*[[Philips Electric Co. v. Thermal Industries, Inc., 450 F.2d 1164 (1971)]]
*[[Quanta Computer, Inc. v. LG Electronics, Inc., 553 U.S. 617 (2008)]]
*[[Reiner v. I. Leon Co., 285 F.2d 501 (1960)]]
*[[South Corp. v. US]]
*[[South Corp. v. US 690 F.2d 1368 (1982)]]
*[[State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (1998)]]
*[[Traffix Devices, Inc. vs. Marketing Displays, Inc.]]
*[[TurboCare Div. of Demag Delaval Turbomachinery Corp. v. General Elec. Co., 264 F.3d 1111 (2001)]]
*[[UMC Electronics Co. v. U.S., 816 F.2d 647 (1987)]]
*[[US v. Adams, 383 U.S. 39 (1966)]]
*[[U.S. v. Univis Lens Co., 316 U.S. 241 (1942)]]
*[[Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530]]
*[[Vas-Cath Inc. v. Mahurkar, 935 F.2d 1555 (1991)]]
*[[Warner-Jenkinson Company v. Hilton Davis Chemical Co., 520 US 17 (1997)]]
**[[Warner-Jenkinson v. Hilton Davis Petitioner Brief]]
**[[Warner-Jenkinson v. Hilton Davis Respondent Brief]]
*[[Winner International Royalty Co. v. Wang, 202 F.3d 1340 (2000)]]
*[[W.L. Gore & Associates, Inc. v. Garlock, Inc., 721 F.2d 1540 (1983)]]

=[[INTRODUCTION]]=
This is a summary. Click on the title for the full chapter: [[INTRODUCTION]]

Outline:
*The main purpose for obtaining a patent is ''economic''.
*It grants the exclusive right to ''make, use or sell'' the invention for a limited period of time.
*The governing law is Title 35 of the United States Code (35 USC).
*The governing regulations are from Title 37 of the Code of Federal Regulations (37 CFR).
*The law is federal, so patent cases are resolved in the federal court system:
**district courts;
**circuit courts;
**the Court of Appeals for the Federal Circuit (CAFC), a special appeals court for patent cases; and,
**the Supreme Court.
*The US Patent and Trademark Office (PTO) processes patent applications.
*Patents last for 20 years from the date the application is filed with the PTO.
*Patents have the attributes of personal property.
*The foundation of the federal government's authority to create a patent system is in the Constitution. The purposes is explicitly economic, "to promote the progress of science and useful arts..."
*Other forms of intellectual property
**copyright;
**trademarks; and,
**trade secrets.

=[[NONOBVIOUSNESS]]=
This is a summary. Click on the title for the full chapter: [[NONOBVIOUSNESS]]

Outline:

*This is perhaps the most difficult factual patent issue. In addition to meeting the novelty requirements of 35 USC 102, 35 USC 103 requires that the claimed invention as a whole must have been nonobvious "at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains."
*There is a lot of historical confusion regarding this standard. Basically, it is a notion of something being meeting some type of sufficient inventive standard or nontriviality.
*To determine this, there are three fundamental lines of inquiry:
**the scope and content of the prior art;
**the differences between the prior art and claims at issue; and,
**the level of ordinary skill in the art.
*Secondary considerations include:
**a long-felt but unsatisfied need met by the invention;
**appreciation by those versed in the art that the need existed;
**substantial attempts to meet this need;
**commercial success of the invention;
**replacement in the industry by the claimed invention;
**acquiescence by the industry;
**''teaching away'' by those skilled in the art;
**unexpectedness of the results; and,
**disbelief or incredulity on the part of industry with respect to the new invention.

=[[INFRINGEMENT]]=
This is a summary. Click on the title for the full chapter: [[INFRINGEMENT]]

=[[THE PATENT DOCUMENT]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT DOCUMENT]]

Outline:
*A patent has several parts:
**specification: describes the invention;
**claims: delineates the ownership rights;
**drawings: not required, but if they are included then any element included in the claims must be shown in the drawings; and,
**other miscellaneous parts.
*Interpreting claims: claims are said to ''read on'' another device.
*The doctrine of equivalence, prevents something from being patented that only has minor alterations from the prior art.
*The date of the invention
**''reduction to practice'';
**''diligence'' requirement.
*The ''file wrapper''.

=[[NOVELTY]]=
This is a summary. Click on the title for the full chapter: [[NOVELTY]]

Outline:
*Specified in 35 USC 102.
*Fundamentally: an invention must be ''new''.
*Section 102 basically defines in a technical way what it means to not be new:
**Events prior to invention
***known or used by others in the US
***patented or in a printed publication in another country
**Events one year before filing the patent application
***patented or in a printed publication anywhere (''in this or a foreign country'')
***in public use or on sale in the US
**Other bars
*The applicant must be the inventor (not the employer)

Outline:
*Literal Infringement
*The Doctrine of Equivalents

=[[UTILITY]]=
This is a summary. Click on the title for the full chapter: [[UTILITY]]

=[[PATENTABLE SUBJECT MATTER]]=
This is a summary. Click on the title for the full chapter: [[PATENTABLE SUBJECT MATTER]]

Can computer programs, algorithms, laws of nature, life forms, plants, ''etc.'' be patented. In particular, are the following patentable:

* Plants
* Algorithms and Computer Programs
* Scientific Facts?

In a recent case
* State Street (1998)
the CAFC substantially broadened the subject matter of section 101 to include such things as methods of doing business, etc.

=[[FOREIGN AND DOMESTIC PRIORITY]]=
This is a summary. Click on the title for the full chapter: [[FOREIGN AND DOMESTIC PRIORITY]]

Outline:
*Priority in general
*Foreign priority
*International applications
*Domestic priority
*Provisional applications

=[[THE PATENT APPLICATION]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT APPLICATION]]

Outline:
*The Disclosure
*The Claims
*Other Sections
*New Matter
*The Examination Process

=[[INVENTOR ELIGIBILITY]]=
This is a summary. Click on the title for the full chapter: [[INVENTOR ELIGIBILITY]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972): full text]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981): (full text)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005): (full text)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]

[[METABOLITE LABORATORIES, INC. and Competitive Technologies, Inc. v. LABORATORY CORPORATION OF AMERICA HOLDINGS (doing business as LabCorp): the CAFC case (full text)]]

=[[ANTICIPATION]]=
This is a summary. Click on the title for the full chapter: [[ANTICIPATION]]

=[[PRIOR ART]]=
This is a summary. Click on the title for the full chapter: [[PRIOR ART]]

[[Pfaff v. Wells Electronics: full text]]

[[Perkin-Elmer Corporation v. Computervision Corporation (full text)]]

[[Perkin-Elmer Corporation v. Computervision Corporation]]

AME 40590 Intellectual Property for Engineers

2015-04-02T15:46:56Z

Bill: /* ALPHABETICAL LISTING OF CASES */

Cases to add:
* Damages:
** MINTZ V. DIETZ & WATSON, INC. (CAFC, May 2012)
** Monsanto Co. v. McFarling, 488 F.3d 973, 978-79 (Fed. Cir. 2007)
** Georgia-Pacific Corp. v. US Plywood Corp., 318 F. Supp. 1116 (SDNY 1970), modified, 446 F. 2d 295 (2d Cir. 1971)
** The Boeing Company v. The United States, 86 Fed. Cl. 303 (April 2, 2009)
** Mahurkar v. CR Bard, Inc. 79 F. 3d 1572, 1580 (Fed. Cir. 1996), adopting Panduit Corp. v. Stahlin Bros. Fibre Works, Inc.,575 F.2d 1152 (6th Cir. 1978)
** Depuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 567 F.3d 1314 (Fed. Cir. 2009)

* Software patents:
** In re Alappat, 33 F.3d 1526, 1545 (Fed. Cir. 1994).
** CyberSource Corporation v. Retail Decisions, Inc., Slip Op. at 19 (2011)
** Ultramercial, LLC v. Hulu, LLC (Fed. Cir. 2011)

=ALPHABETICAL LISTING OF CASES=

*[[A. & P. Tea Co. v. Supermarket Corp., 340 U.S. 147 (1950)]]
*[[Abbott Laboratories v. Geneva Pharmaceuticals, Inc., 182 F.3d 1315 (1999)]]
*[[Alza Corp. v. Mylan Laboratories, 464 F.3d 1286, (2006)]]
*[[Anderson's Black Rock, Inc. v. Pavement Co., 396 U.S. 57 (1969)]]
*[[Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336 (1961)]]
*[[Arrhythmia Research Technology, Inc. v. Corazonix Corp., 958 F.2d 1053 (1992)]]
*[[Asgrow Seed Co. v. Winterboer, 513 U.S. 179 (1994)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. (2013)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. CAFC (2012)]]
*[[Atlas Powder v. E.I. du Pont de Nemours, 750 F2d 1569 (1984)]]
*[[Bilski v. Kappos, 130 S.Ct. 3218 (2010)]]
*[[Bobbs-Merrill Co. v. Straus, 210 U.S. 339 (1908)]]
*[[Bonito Boats. v. Thunder Craft, 489 U.S. 141 (1989)]]
*[[Bowman v. Monsanto, 133 S.Ct. 1761 (2013)]]
*[[CCS Fitness, Inc. v. Brunswick Corporation, 288 F.3d 1359 (2002)]]
*[[Chester v. Miller, 906 F.2d 1574 (1990)]]
*[[D.L. Auld Co. v. Chroma Graphics Corp., 714 F.2d 1144 (1983)]]
*[[Diamond v. Chakrabarty, 100 S.Ct. 2204 (1980)]]
*[[Diamond v. Diehr, 450 U.S. 175 (1981)]]
*[[Egbert v. Lippmann, 104 U.S. 333 (1881)]]
*[[Electric Storage Battery Co. v. Shimadzu, 307 U.S. 5 (1939)]]
*[[Elizabeth v. American Nicholson Pavement Company, 97 U.S. 126 (1877)]]
*[[Filmtec Corp. v. Allied-Signal Inc., 939 F.2d 1568 (1991)]]
*[[Funk Bros. Seed Co. v. Kalo Inoculant Co. 333 U.S. 127 (1948)]]
*[[Gottschalk v. Benson, 409 U.S. 63 (1972)]]
*[[Gould v. Hellwarth, 472 F2d 1383 (1973)]]
*[[Graham v. John Deere, 383 U.S. 1 (1966)]]
*[[Graver Tank & Mfg. Co. v. Linde Air Products Co. 339 US 605 (1950)]]
*[[H.H. Robertson, Co. v. United Steel Deck, Inc., 820 F.2d 384 (1987)]]
*[[Hotchkiss v. Greenwood, 52 U.S. 11 (1850) ]]
*[[Hybritech v. Monoclonal Antiboties, 802 F.2d 1375 (1986)]]
*[[i4i Ltd. Partnership v. Microsoft Corp., 598 F.3d 831 (2010)]]
*[[In Re Bilski]]
**[[In Re Bilski, Dky concurring opinion]]
**[[In Re Bilski, Newman dissenting opinion]]
**[[In Re Bilski, Mayer dissenting opinion]]
**[[In Re Bilski, Rader dissenting opinion]]
*[[In re Brana, 51 F.3d 1560 (1995)]]
*[[In re Carlson, 983 F.2d 1032 (1992)]]
*[[In re Hall, 781 F.2d 897 (1986)]]
*[[In re Kahn, CAFC 04-1616 (2006)]]
*[[In Re Rouffet]]
*[[J.E.M. Ag Supply, Inc. v. Pioneer Hi-Bred International, Inc., 534 U.S. 124 (2001)]]
*[[Juicy Whip v. Orange Bang, 185 F.3d 1364 (1999)]]
*[[KSR International Co. v. Teleflex, Inc., 550 U.S. 398 (2007)]]
*[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]
*[[Lorenz v. Colgate-Palmolive-Peet Co., 167 F.2d 423 (1948)]]
*[[Lough v. Brunswick Corp., 86 F.3d 1113 (1996)]]
*[[Lyon v. Bausch & Lomb, 224 F.2d 530 (1955)]]
*[[Metabolit Laboratories, Inc. and Competitive Technologies, Inc. v. Laboratory Corporation of America Holdings, 370 F.3d 1354 (2004)]]
*[[Metallizing Engineering Co., Inc. v. Kenyon Bearing & Auto Parts Co., Inc., 153 F.2d 516 (1946)]]
*[[Microsoft Corp v. At&T Corp.]]
*[[Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (1978)]]
*[[Perkin-Elmer Corporation v. Computervision Corporation, 732 F2d 888 (1984)]]
*[[Pfaff vs. Wells Electronics, 525 U.S. 55 (1998)]]
*[[Philips Electric Co. v. Thermal Industries, Inc., 450 F.2d 1164 (1971)]]
*[[Quanta Computer, Inc. v. LG Electronics, Inc., 553 U.S. 617 (2008)]]
*[[Reiner v. I. Leon Co., 285 F.2d 501 (1960)]]
*[[South Corp. v. US]]
*[[South Corp. v. US 690 F.2d 1368 (1982)]]
*[[State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (1998)]]
*[[Traffix Devices, Inc. vs. Marketing Displays, Inc.]]
*[[TurboCare Div. of Demag Delaval Turbomachinery Corp. v. General Elec. Co., 264 F.3d 1111 (2001)]]
*[[UMC Electronics Co. v. U.S., 816 F.2d 647 (1987)]]
*[[US v. Adams, 383 U.S. 39 (1966)]]
*[[US v. Adams (full text)]]
*[[U.S. v. Univis Lens Co., 316 U.S. 241 (1942)]]
*[[Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530]]
*[[Vas-Cath Inc. v. Mahurkar, 935 F.2d 1555 (1991)]]
*[[Warner-Jenkinson Company v. Hilton Davis Chemical Co., 520 US 17 (1997)]]
**[[Warner-Jenkinson v. Hilton Davis Petitioner Brief]]
**[[Warner-Jenkinson v. Hilton Davis Respondent Brief]]
*[[Winner International Royalty Co. v. Wang, 202 F.3d 1340 (2000)]]
*[[W.L. Gore & Associates, Inc. v. Garlock, Inc., 721 F.2d 1540 (1983)]]

=[[INTRODUCTION]]=
This is a summary. Click on the title for the full chapter: [[INTRODUCTION]]

Outline:
*The main purpose for obtaining a patent is ''economic''.
*It grants the exclusive right to ''make, use or sell'' the invention for a limited period of time.
*The governing law is Title 35 of the United States Code (35 USC).
*The governing regulations are from Title 37 of the Code of Federal Regulations (37 CFR).
*The law is federal, so patent cases are resolved in the federal court system:
**district courts;
**circuit courts;
**the Court of Appeals for the Federal Circuit (CAFC), a special appeals court for patent cases; and,
**the Supreme Court.
*The US Patent and Trademark Office (PTO) processes patent applications.
*Patents last for 20 years from the date the application is filed with the PTO.
*Patents have the attributes of personal property.
*The foundation of the federal government's authority to create a patent system is in the Constitution. The purposes is explicitly economic, "to promote the progress of science and useful arts..."
*Other forms of intellectual property
**copyright;
**trademarks; and,
**trade secrets.

=[[NONOBVIOUSNESS]]=
This is a summary. Click on the title for the full chapter: [[NONOBVIOUSNESS]]

Outline:

*This is perhaps the most difficult factual patent issue. In addition to meeting the novelty requirements of 35 USC 102, 35 USC 103 requires that the claimed invention as a whole must have been nonobvious "at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains."
*There is a lot of historical confusion regarding this standard. Basically, it is a notion of something being meeting some type of sufficient inventive standard or nontriviality.
*To determine this, there are three fundamental lines of inquiry:
**the scope and content of the prior art;
**the differences between the prior art and claims at issue; and,
**the level of ordinary skill in the art.
*Secondary considerations include:
**a long-felt but unsatisfied need met by the invention;
**appreciation by those versed in the art that the need existed;
**substantial attempts to meet this need;
**commercial success of the invention;
**replacement in the industry by the claimed invention;
**acquiescence by the industry;
**''teaching away'' by those skilled in the art;
**unexpectedness of the results; and,
**disbelief or incredulity on the part of industry with respect to the new invention.

=[[INFRINGEMENT]]=
This is a summary. Click on the title for the full chapter: [[INFRINGEMENT]]

=[[THE PATENT DOCUMENT]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT DOCUMENT]]

Outline:
*A patent has several parts:
**specification: describes the invention;
**claims: delineates the ownership rights;
**drawings: not required, but if they are included then any element included in the claims must be shown in the drawings; and,
**other miscellaneous parts.
*Interpreting claims: claims are said to ''read on'' another device.
*The doctrine of equivalence, prevents something from being patented that only has minor alterations from the prior art.
*The date of the invention
**''reduction to practice'';
**''diligence'' requirement.
*The ''file wrapper''.

=[[NOVELTY]]=
This is a summary. Click on the title for the full chapter: [[NOVELTY]]

Outline:
*Specified in 35 USC 102.
*Fundamentally: an invention must be ''new''.
*Section 102 basically defines in a technical way what it means to not be new:
**Events prior to invention
***known or used by others in the US
***patented or in a printed publication in another country
**Events one year before filing the patent application
***patented or in a printed publication anywhere (''in this or a foreign country'')
***in public use or on sale in the US
**Other bars
*The applicant must be the inventor (not the employer)

Outline:
*Literal Infringement
*The Doctrine of Equivalents

=[[UTILITY]]=
This is a summary. Click on the title for the full chapter: [[UTILITY]]

=[[PATENTABLE SUBJECT MATTER]]=
This is a summary. Click on the title for the full chapter: [[PATENTABLE SUBJECT MATTER]]

Can computer programs, algorithms, laws of nature, life forms, plants, ''etc.'' be patented. In particular, are the following patentable:

* Plants
* Algorithms and Computer Programs
* Scientific Facts?

In a recent case
* State Street (1998)
the CAFC substantially broadened the subject matter of section 101 to include such things as methods of doing business, etc.

=[[FOREIGN AND DOMESTIC PRIORITY]]=
This is a summary. Click on the title for the full chapter: [[FOREIGN AND DOMESTIC PRIORITY]]

Outline:
*Priority in general
*Foreign priority
*International applications
*Domestic priority
*Provisional applications

=[[THE PATENT APPLICATION]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT APPLICATION]]

Outline:
*The Disclosure
*The Claims
*Other Sections
*New Matter
*The Examination Process

=[[INVENTOR ELIGIBILITY]]=
This is a summary. Click on the title for the full chapter: [[INVENTOR ELIGIBILITY]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972): full text]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981): (full text)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005): (full text)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]

[[METABOLITE LABORATORIES, INC. and Competitive Technologies, Inc. v. LABORATORY CORPORATION OF AMERICA HOLDINGS (doing business as LabCorp): the CAFC case (full text)]]

=[[ANTICIPATION]]=
This is a summary. Click on the title for the full chapter: [[ANTICIPATION]]

=[[PRIOR ART]]=
This is a summary. Click on the title for the full chapter: [[PRIOR ART]]

[[Pfaff v. Wells Electronics: full text]]

[[Perkin-Elmer Corporation v. Computervision Corporation (full text)]]

[[Perkin-Elmer Corporation v. Computervision Corporation]]

AME 40590 Intellectual Property for Engineers

2015-04-02T15:46:25Z

Bill: /* ALPHABETICAL LISTING OF CASES */

Cases to add:
* Damages:
** MINTZ V. DIETZ & WATSON, INC. (CAFC, May 2012)
** Monsanto Co. v. McFarling, 488 F.3d 973, 978-79 (Fed. Cir. 2007)
** Georgia-Pacific Corp. v. US Plywood Corp., 318 F. Supp. 1116 (SDNY 1970), modified, 446 F. 2d 295 (2d Cir. 1971)
** The Boeing Company v. The United States, 86 Fed. Cl. 303 (April 2, 2009)
** Mahurkar v. CR Bard, Inc. 79 F. 3d 1572, 1580 (Fed. Cir. 1996), adopting Panduit Corp. v. Stahlin Bros. Fibre Works, Inc.,575 F.2d 1152 (6th Cir. 1978)
** Depuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 567 F.3d 1314 (Fed. Cir. 2009)

* Software patents:
** In re Alappat, 33 F.3d 1526, 1545 (Fed. Cir. 1994).
** CyberSource Corporation v. Retail Decisions, Inc., Slip Op. at 19 (2011)
** Ultramercial, LLC v. Hulu, LLC (Fed. Cir. 2011)

=ALPHABETICAL LISTING OF CASES=

*[[A. & P. Tea Co. v. Supermarket Corp., 340 U.S. 147 (1950)]]
*[[Abbott Laboratories v. Geneva Pharmaceuticals, Inc., 182 F.3d 1315 (1999)]]
*[[Alza Corp. v. Mylan Laboratories, 464 F.3d 1286, (2006)]]
*[[Anderson's Black Rock, Inc. v. Pavement Co., 396 U.S. 57 (1969)]]
*[[Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336 (1961)]]
*[[Arrhythmia Research Technology, Inc. v. Corazonix Corp., 958 F.2d 1053 (1992)]]
*[[Asgrow Seed Co. v. Winterboer, 513 U.S. 179 (1994)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. (2013)]]
*[[Association for Molecular Pathology et al. v. Myriad Genetics, Inc., et al. CAFC (2012)]]
*[[Atlas Powder v. E.I. du Pont de Nemours, 750 F2d 1569 (1984)]]
*[[Bilski v. Kappos, 130 S.Ct. 3218 (2010)]]
*[[Bobbs-Merrill Co. v. Straus, 210 U.S. 339 (1908)]]
*[[Bonito Boats. v. Thunder Craft, 489 U.S. 141 (1989)]]
*[[Bowman v. Monsanto, 133 S.Ct. 1761 (2013)]]
*[[CCS Fitness, Inc. v. Brunswick Corporation, 288 F.3d 1359 (2002)]]
*[[Chester v. Miller, 906 F.2d 1574 (1990)]]
*[[D.L. Auld Co. v. Chroma Graphics Corp., 714 F.2d 1144 (1983)]]
*[[Diamond v. Chakrabarty, 100 S.Ct. 2204 (1980)]]
*[[Diamond v. Diehr, 450 U.S. 175 (1981)]]
*[[Egbert v. Lippmann, 104 U.S. 333 (1881)]]
*[[Electric Storage Battery Co. v. Shimadzu, 307 U.S. 5 (1939)]]
*[[Elizabeth v. American Nicholson Pavement Company, 97 U.S. 126 (1877)]]
*[[Filmtec Corp. v. Allied-Signal Inc., 939 F.2d 1568 (1991)]]
*[[Funk Bros. Seed Co. v. Kalo Inoculant Co. 333 U.S. 127 (1948)]]
*[[Gottschalk v. Benson, 409 U.S. 63 (1972)]]
*[[Gould v. Hellwarth, 472 F2d 1383 (1973)]]
*[[Graham v. John Deere, 383 U.S. 1 (1966)]]
*[[Graver Tank & Mfg. Co. v. Linde Air Products Co. 339 US 605 (1950)]]
*[[H.H. Robertson, Co. v. United Steel Deck, Inc., 820 F.2d 384 (1987)]]
*[[Hotchkiss v. Greenwood, 52 U.S. 11 (1850) ]]
*[[Hybritech v. Monoclonal Antiboties, 802 F.2d 1375 (1986)]]
*[[i4i Ltd. Partnership v. Microsoft Corp., 598 F.3d 831 (2010)]]
*[[In Re Bilski]]
**[[In Re Bilski, Dky concurring opinion]]
**[[In Re Bilski, Newman dissenting opinion]]
**[[In Re Bilski, Mayer dissenting opinion]]
**[[In Re Bilski, Rader dissenting opinion]]
*[[In re Brana, 51 F.3d 1560 (1995)]]
*[[In re Carlson, 983 F.2d 1032 (1992)]]
*[[In re Hall, 781 F.2d 897 (1986)]]
*[[In re Kahn, CAFC 04-1616 (2006)]]
*[[In Re Rouffet]]
*[[J.E.M. Ag Supply, Inc. v. Pioneer Hi-Bred International, Inc., 534 U.S. 124 (2001)]]
*[[Juicy Whip v. Orange Bang, 185 F.3d 1364 (1999)]]
*[[KSR International Co. v. Teleflex, Inc., 550 U.S. 398 (2007)]]
*[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]
*[[Lorenz v. Colgate-Palmolive-Peet Co., 167 F.2d 423 (1948)]]
*[[Lough v. Brunswick Corp., 86 F.3d 1113 (1996)]]
*[[Lyon v. Bausch & Lomb, 224 F.2d 530 (1955)]]
*[[Metabolit Laboratories, Inc. and Competitive Technologies, Inc. v. Laboratory Corporation of America Holdings, 370 F.3d 1354 (2004)]]
*[[Metallizing Engineering Co., Inc. v. Kenyon Bearing & Auto Parts Co., Inc., 153 F.2d 516 (1946)]]
*[[Microsoft Corp v. At&T Corp.]]
*[[Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (1978)]]
*[[Perkin-Elmer Corporation v. Computervision Corporation, 732 F2d 888 (1984)]]
*[[Pfaff vs. Wells Electronics, 525 U.S. 55 (1998)]]
*[[Philips Electric Co. v. Thermal Industries, Inc., 450 F.2d 1164 (1971)]]
*[[Quanta Computer, Inc. v. LG Electronics, Inc., 553 U.S. 617 (2008)]]
*[[Reiner v. I. Leon Co., 285 F.2d 501 (1960)]]
*[[South Corp. v. US]]
*[[South Corp. v. US (full text)]]
*[[South Corp. v. US 690 F.2d 1368 (1982)]]
*[[State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (1998)]]
*[[Traffix Devices, Inc. vs. Marketing Displays, Inc.]]
*[[TurboCare Div. of Demag Delaval Turbomachinery Corp. v. General Elec. Co., 264 F.3d 1111 (2001)]]
*[[UMC Electronics Co. v. U.S., 816 F.2d 647 (1987)]]
*[[US v. Adams, 383 U.S. 39 (1966)]]
*[[US v. Adams (full text)]]
*[[U.S. v. Univis Lens Co., 316 U.S. 241 (1942)]]
*[[Universal Athletic Sales Co. v. American Gym Recreational & Athletic Equipment Corporation, Inc., 546 F.2d 530]]
*[[Vas-Cath Inc. v. Mahurkar, 935 F.2d 1555 (1991)]]
*[[Warner-Jenkinson Company v. Hilton Davis Chemical Co., 520 US 17 (1997)]]
**[[Warner-Jenkinson v. Hilton Davis Petitioner Brief]]
**[[Warner-Jenkinson v. Hilton Davis Respondent Brief]]
*[[Winner International Royalty Co. v. Wang, 202 F.3d 1340 (2000)]]
*[[W.L. Gore & Associates, Inc. v. Garlock, Inc., 721 F.2d 1540 (1983)]]

=[[INTRODUCTION]]=
This is a summary. Click on the title for the full chapter: [[INTRODUCTION]]

Outline:
*The main purpose for obtaining a patent is ''economic''.
*It grants the exclusive right to ''make, use or sell'' the invention for a limited period of time.
*The governing law is Title 35 of the United States Code (35 USC).
*The governing regulations are from Title 37 of the Code of Federal Regulations (37 CFR).
*The law is federal, so patent cases are resolved in the federal court system:
**district courts;
**circuit courts;
**the Court of Appeals for the Federal Circuit (CAFC), a special appeals court for patent cases; and,
**the Supreme Court.
*The US Patent and Trademark Office (PTO) processes patent applications.
*Patents last for 20 years from the date the application is filed with the PTO.
*Patents have the attributes of personal property.
*The foundation of the federal government's authority to create a patent system is in the Constitution. The purposes is explicitly economic, "to promote the progress of science and useful arts..."
*Other forms of intellectual property
**copyright;
**trademarks; and,
**trade secrets.

=[[NONOBVIOUSNESS]]=
This is a summary. Click on the title for the full chapter: [[NONOBVIOUSNESS]]

Outline:

*This is perhaps the most difficult factual patent issue. In addition to meeting the novelty requirements of 35 USC 102, 35 USC 103 requires that the claimed invention as a whole must have been nonobvious "at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains."
*There is a lot of historical confusion regarding this standard. Basically, it is a notion of something being meeting some type of sufficient inventive standard or nontriviality.
*To determine this, there are three fundamental lines of inquiry:
**the scope and content of the prior art;
**the differences between the prior art and claims at issue; and,
**the level of ordinary skill in the art.
*Secondary considerations include:
**a long-felt but unsatisfied need met by the invention;
**appreciation by those versed in the art that the need existed;
**substantial attempts to meet this need;
**commercial success of the invention;
**replacement in the industry by the claimed invention;
**acquiescence by the industry;
**''teaching away'' by those skilled in the art;
**unexpectedness of the results; and,
**disbelief or incredulity on the part of industry with respect to the new invention.

=[[INFRINGEMENT]]=
This is a summary. Click on the title for the full chapter: [[INFRINGEMENT]]

=[[THE PATENT DOCUMENT]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT DOCUMENT]]

Outline:
*A patent has several parts:
**specification: describes the invention;
**claims: delineates the ownership rights;
**drawings: not required, but if they are included then any element included in the claims must be shown in the drawings; and,
**other miscellaneous parts.
*Interpreting claims: claims are said to ''read on'' another device.
*The doctrine of equivalence, prevents something from being patented that only has minor alterations from the prior art.
*The date of the invention
**''reduction to practice'';
**''diligence'' requirement.
*The ''file wrapper''.

=[[NOVELTY]]=
This is a summary. Click on the title for the full chapter: [[NOVELTY]]

Outline:
*Specified in 35 USC 102.
*Fundamentally: an invention must be ''new''.
*Section 102 basically defines in a technical way what it means to not be new:
**Events prior to invention
***known or used by others in the US
***patented or in a printed publication in another country
**Events one year before filing the patent application
***patented or in a printed publication anywhere (''in this or a foreign country'')
***in public use or on sale in the US
**Other bars
*The applicant must be the inventor (not the employer)

Outline:
*Literal Infringement
*The Doctrine of Equivalents

=[[UTILITY]]=
This is a summary. Click on the title for the full chapter: [[UTILITY]]

=[[PATENTABLE SUBJECT MATTER]]=
This is a summary. Click on the title for the full chapter: [[PATENTABLE SUBJECT MATTER]]

Can computer programs, algorithms, laws of nature, life forms, plants, ''etc.'' be patented. In particular, are the following patentable:

* Plants
* Algorithms and Computer Programs
* Scientific Facts?

In a recent case
* State Street (1998)
the CAFC substantially broadened the subject matter of section 101 to include such things as methods of doing business, etc.

=[[FOREIGN AND DOMESTIC PRIORITY]]=
This is a summary. Click on the title for the full chapter: [[FOREIGN AND DOMESTIC PRIORITY]]

Outline:
*Priority in general
*Foreign priority
*International applications
*Domestic priority
*Provisional applications

=[[THE PATENT APPLICATION]]=
This is a summary. Click on the title for the full chapter: [[THE PATENT APPLICATION]]

Outline:
*The Disclosure
*The Claims
*Other Sections
*New Matter
*The Examination Process

=[[INVENTOR ELIGIBILITY]]=
This is a summary. Click on the title for the full chapter: [[INVENTOR ELIGIBILITY]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972): full text]]

[[GOTTSCHALK v. BENSON, 409 U.S. 63 (1972)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981): (full text)]]

[[Diamond v. Diehr, 450 U.S. 175 (1981)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005): (full text)]]

[[Laboratory Corporation of America vs. Metabolite Laboratories, 548 U.S. 124 (2005)]]

[[METABOLITE LABORATORIES, INC. and Competitive Technologies, Inc. v. LABORATORY CORPORATION OF AMERICA HOLDINGS (doing business as LabCorp): the CAFC case (full text)]]

=[[ANTICIPATION]]=
This is a summary. Click on the title for the full chapter: [[ANTICIPATION]]

=[[PRIOR ART]]=
This is a summary. Click on the title for the full chapter: [[PRIOR ART]]

[[Pfaff v. Wells Electronics: full text]]

[[Perkin-Elmer Corporation v. Computervision Corporation (full text)]]

[[Perkin-Elmer Corporation v. Computervision Corporation]]