MEAM 535: Dynamics
Fall 2000

Announcements

Instructors

Professor Vijay Kumar
Office: 111 Towne
Phone: 898-8241
Email: kumar@cis.upenn.edu
Web site: http://www.cis.upenn.edu/~kumar

Professor John L. Bassani
Office: Towne 231
Phone: 898-5632
Email: bassani@lrsm.upenn.edu
Web site: http://www.seas.upenn.edu/meam/faculty/bassani.html

Mr. Calin Belta
Office: GRASP Lab
Phone: 898-0355
Email: calin@seas.upenn.edu

Office Hours

Professor Kumar,   kumar@cis.upenn.edu

Office hours are scheduled on a weekly basis and are available here. If you want to see me at another  time, please make an appointment by e-mailing me or by contacting Ms. Janet Chin (phone: 215.898.5771, email address: jschin@seas.upenn.edu).

Professor Bassani,   bassani@sol1.lrsm.upenn.edu

Regular office hours will be Fridays from 2-3 (unless unavoidable conflicts arise) or other times by e-mailing me (always best) or contacting Ms. Delores Magobet (phone: 215.898-2770, email address magobet@seas.upenn.edu).

Bulk Pack (can be purchased from the Copy Center in Towne Building, Room 143)

[BP]  MEAM 535 Fall 2000,  V. Kumar and J. L. Bassani

Textbook  (can be purchased from the bookstore).
 

[FBH]  Methods of Applied Mathematics, Francis B. Hildebrand, Prentice-Hall, 1965/Dover Publications 1992.

Additional handouts will be provided as we go along.

• [DG] Principle of Dynamics, Donald T. Greenwood, Prentice Hall, Englewood Cliffs, New Jersey, 1988. ISBN 0-13-709981-9.
• [KL] Dynamics: Theory and Applications, T. R. Kane and D. A. Levinson, McGraw Hill, New York, 1985. ISBN 0-07-037846-0.
• [RR] Analytical Dynamics of Discrete Systems, R. M. Rosenberg, Plenum Press, New York, 1977. ISBN 0-306-31014-7.
• [ML] The Analysis of Complex Nonlinear Mechanical Systems: A Computer Algebra Assisted Approach, M. Lesser, World Scientific Series on Nonlinear Science, 1995. ISBN 981-02-2209-2.
• [HG] Classical Mechanics, H. Goldstein, Addison-Wesley, Reading, 1989.

 

• A Treatise on the Analytical Dynamics of Particles & Rigid Bodies" by E. T. Whittaker.
• A Treatise on Analytical Dynamics by L. A. Pars.
• Calculus of Variations with Applications to Physics and Engineering, Robert Weinstock, McGraw-Hill, 1952/Dover 1974.
• Variational Principles of Mechanics by C. Lanczos, Dover.
• Principles of Mechanics by J. L. Synge and B. A. Griffith
• Analytical Dynamics of Discrete Systems R. M. Rosenberg, Plenum Press, New York, 1977. ISBN 0-306-31014-7.
• Rational Mechanics by C. W. Kilmister and J. E. Reeve
• Analytical Dynamics by Haim Baruh, WCB/McGraw-Hill, Boston, ISBN 0-07-365977-0.

1. Lesser, Chapter 1
2. Goldstein, Chapter 1

1. Goldstein, Chapter  2
2. Morris, K. A. and Taylor, K. J. A variational calculus approach to modeling of flexible manipulators, SIAM Review, Vol. 38, No. 2, June 1996

1. Preliminaries – V. Kumar
2. Kinematics – V. Kumar
3. Constraints and Degrees of Freedom – V. Kumar
4. Rosenberg, Sections 4.5-4.6

1. Basics of rigid body dynamics, Sections 7.2-7.8, Greenwood
2. Equations of motion, Sections 8.1-8.3, Greenwood

1. Lagrange’s equations and D’Alembert’s principle – V. Kumar
2. Sections 6.4-6.5, Greenwood

1. Stability of Dynamic Systems – V. Kumar and G. K. Ananthasuresh
2. Vidyasagar, Lyapunov Stability

1. Numerical Integration  – V. Kumar
2. Numerical Solutions to Differential Equations – J. Bassani
3. Problems – J. Bassani

• Dynamics: Theory and Applications, T. R. Kane and D. A. Levinson, McGraw Hill, New York, 1985.
• The Analysis of Complex Nonlinear Mechanical Systems: A Computer Algebra Assisted Approach, M. Lesser, World Scientific Series on Nonlinear Science, 1995.
• Classical Mechanics, H. Goldstein, Addison-Wesley, Reading, 1989.
• Principle of Dynamics, Donald T. Greenwood, Prentice Hall, Englewood Cliffs, New Jersey, 1988.
• Analytical Dynamics of Discrete Systems, R. M. Rosenberg, Plenum Press, New York, 1977.
• Nonlinear Systems Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1978.

Course Description

1. Variational calculus: the mathematics and the methods of variational calculus and their application to solving minimization problems and deriving equations of motion.
2. Rigid body kinematics: the description of the motion of systems of rigid bodies.
3. Rigid body kinetics: the study of  the forces that cause motion and the relationship between the forces and the motion. This relationship is generally described by equations of motion. The main focus will be on analytical mechanics, a set of principles that allow us to write the equations of motion using analytical methods (as opposed to graphical or numerical methods).
4. Energy methods and integrals of the equations of motion: The description of dynamical systems with simplified models in which the order of differential equations is reduced by exploiting conservation laws.
5. Dynamics of continuous systems: the study of the dynamics of deformable bodies in which distributed models of compliance, inertia, and damping are developed using partial differential equations.
6. Simulation: the basic techniques for numerical integration, solving differential equations, and for visualization of results.

• MEAM 535: Spring 1997 Schedule
• MEAM 535: Spring 1998 Schedule
• MEAM 535: Fall 1998 Schedule  (this might be the most relevant for this year's organization)
• MEAM 535: Fall 1999 Schedule

Time and Location

Tentative Schedule

Schedule

Week	Date	Material	Reading	Work due & notes
1	Sep 7	Intro to MEAM 535 and Brachistochrone Problem (on web site in Power Point Introduction).	Chap. 1 in ML, Chap. 1 and Sec. 2.1 and 2.2 in HG, and Sec. 2.1 and 2.2 in FBH	HW 1 - Sept. 15: probs. #1, 2, 5, 6, 7, 8 in Chap. 2 of FBH
2	Sep 12, 14	Calculus of variations - Euler Equations; Examples - Brachistochrone Problem; Natural Boundary Conditions; Calculus of Variations with several dependent variables.	2.2 in HG, Sec. 2.2, 2.3, 2.5 in FBH; class notes pp. 12-14 (JLB); Sec. 2.4 in FBH	HW 2 - Sept. 22: variant of brachistochrone; vibrating string; and problems 16, 56, and 57 in FBH (see pdf file for HW 2)
3	Sept 19, 21	Hamilton's principle; Particle dynamics: D'Alembert's and Hamilton's principles; Energy conservation.  Cartesian tensor notation: summation convention; derivatives of scalars and vectors with respect to vectors.	Chap. 1 in HG;  Sec. 2.10 and 2.11 in FBH; Sec. E on Analytical Mechanics in the bulk pack	HW 3 - Oct. 3: Numerical integration of N spring-mass system (see pdf file for HW3)
4	Sept 26, 28	Numerical Integration of ODEs; introduction to MATLAB and project; Constraints and Lagrange Multipliers; isoperimetric constraints	Sec. G on Simulation in bulk pack; in-class demonstration of MATLAB; class notes pp. 24-28 (JLB) plus examples on pp. 53-57 of Weinstock; Sec. 2.1 and 2.7 in FBH; Sec. 1-3 and 2-4 in HG; Sec. C-3 in bulk pack	note: see Calin Belta for questions using MATLAB, plus session in the Towne computer lab on Sept. 29 at 1pm
5	Oct 3, 5	Finite and Differential Constraints; holonomic and nonholonomic constraints. Notation for rigid body kinematics, definition of angular velocity.	class notes pp. 29-34 (JLB); 2.7 in FBH; Sec. C-1, C-3 in bulk pack.	note: the xerox copies of JLBs lecture notes, pp. 12-14 and 24-34 cover variational methods for several dependent variables and related material on constraints.
6	Oct 10, 12	Differentiation of vectors, dependence on reference frames, velocity and acceleration analysis.	Sec C-1, C-2, C-3.	HW 4 (Oct 12)
7	Oct 17, 19	Holonomic and nonholonomic constraints revisited. Generalized coordinates and speeds. Examples	Sec C-3 complete. Handouts (handwritten notes).	HW 5 (Oct 19), The midterm (HW 6) will be handed out on Oct 19, due on Oct 23.
8	Oct 24, 26	Partial velocities. Kinetics of particles, momentum, energy.	Section C.3, transparencies (copies handed out in class)	Midterm 1 (due Oct 23, 500 pm)
9	Oct 31, Nov 2	Systems of particles, kinetic energy, angular momentum, inertia dyadic, dyadics, Riemann-Stieltjes integral.	Transparencies (copies handed out in class). Section D.1 (Greenwood, 7.2-7.8)
10	Nov 7, 9	From systems of particles to rigid bodies, Newton-Euler equations of motion.	Section D.1, D.2.	HW 6 (Nov 7)
11	Nov 14, 16	Principle of virtual work and D'Alembert's principle	Section E.2	In class midterm, open notes, bulkpack (11/16), covering material from 10/5-1/14.
12	Nov 21	Virtual work, examples	Section E.1
13	Nov 28, 30	Lagrange's equations for nonholonomic systems, constraint forces	Section E.1	HW 7 (Nov. 28)
14	Dec 5, 7	Dynamics of flexible systems - Flexible Manipulators	Section B.2	HW 8 (Dec. 5)

Note:   See http://www.upenn.edu/registrar/roster/tfinals.html for final exam schedule.

Assignments/Homeworks

• Homework assignments will be announced on a weekly basis and posted on the web site. Reading assignments, and homework problem sets will be announced  through the web (see Lectures and homeworks). Problem sets will be assigned at least one week before they are due. Only selected problems from each set will be graded. You may consult your colleagues or talk to the instructors before doing the homework problems. Solutions to all problems will be kept in the library. No late homework will be accepted without special permission from one of the instructors.
• There will be one take home, 1.5 hour midterm.
• There will be one in-class, 2 hour final exam.

Grading Policy

Students taking this course generally have diverse backgrounds. This will be taken into account when grading.

Online Grades

Do not know how to use Blackboard see the Student Manual

See the grading policy for the course.

Notes/Handouts

Slides

Power Point Introduction

Software Tutorials

• Matlab

HELP

• Course administration/questions
• kumar@cis.upenn.edu
• bassani@lrsm.upenn.edu
• Web site problems/comments (meam520@seas.upenn.edu)

• MEAM Seminars
• GRASP Seminars
• Physics Seminars

Links to Research Laboratories

• The Robotics Institute at Carnegie Mellon University
• Telerobotics at NASA
• Laboratory for Perceptual Robotics at UMass
• The Automation and Robotics Research Institute, The University of Texas at Arlington

Other Useful Links

• Penn Online Directory
• Penn Libraries Homepage