MEAM 535: Dynamics
Fall 2001

Announcements

• The final exam will be ready for download at 500 pm on 12/14/01. Click here to download the doc file.
• Turn in completed final exam to Calin Belta by 500 pm on 12/18/01. Address all questions to calin@seas.upenn.edu  or kumar@cis.upenn.edu.

Instructors

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

Mr. Calin Belta
Office: GRASP Lab, Room 332C
Phone: 898-0355
Email: calin@seas.upenn.edu
Web site: http://www.seas.upenn.edu/~calin

Office Hours

Vijay 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. Emily Hoover (phone: 215.898.5771, email address: ehoover@seas.upenn.edu).

Calin Belta :  Tue 4:30 - 6:00 and Wed 5:00 - 6:30,  Room 332C, GRASP Lab

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

[BP]  MEAM 535 Fall 2000,  V. Kumar. University of Pennsylvania.

Textbook  (can be purchased from the bookstore).

[HB]  Analytical Dynamics, Haim Baruh, WCB/McGraw-Hill, Boston, ISBN 0-07-365977-0. 1999.

• [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.

 

• Dynamics: The Geometry of Behavior, R. H. Abraham and C. D. Shaw, Addison Wesley, 1992.
• 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
• Methods of Applied Mathematics, Francis B. Hildebrand, Prentice-Hall, 1965/Dover Publications 1992.

Lesser, Chapter 1
Goldstein, Chapter 1
Abraham and Shaw, Chapters 1 and 2

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

D. Stability of Dynamical Systems

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

F. Homework Problems

Sources of material for the bulkpack include

• 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.
• Dynamics: The Geometry of Behavior, R. H. Abraham and C. D. Shaw, Addison Wesley, 1992.

Course Description

1. Rigid body kinematics: the description of the motion of systems of rigid bodies.
2. 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).
3. Dynamical systems: The study of systems governed by ordinary differential equations including the trajectory of the system, stability, and periodicity.
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. 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
• MEAM 535: Fall 1999 Schedule
• MEAM 535: Fall 2000 Schedule

Time and Location

Tentative Schedule

Schedule

Notes:

• *  denotes make up classes on Monday 600 pm in Towne 315.
• 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 in-class, 1.5 hour midterm.
• There will be one take-home, 2 hour final exam.

Problem for HW 1

Derive the equations for a simple pendulum (massless rod, bob with mass m, and length l), and consider the case when g/l =1. Construct
the phase portrait for the system. Identify critical points and classify them. Solve the problem using Mathematica, Maple or Matlab.

Problem for HW 2

Thought Problem for HW2

Place a book on a table. Define x and y axes along the edges of the book so that they are fixed to the plane of the table. Now consider (finite) rotations about the x and y axes - they will rotate the book out of the plane. Find a sequence of rotations about the x and y axes that return the book to the plane but will rotate the book about the z (vertical) axis.
 

Problems for HW 7

Note:
In problem 29, part (a) consists of deriving expressions for the velocity partials given in the table from the previous homework. Part (b) involves getting expressions for the generalized forces. Note that you must not assume rolling!

• Problem with friction
• Hemisphere

Problems for HW 8

In Problem 29, assume the disk rolls on the plane

• Write down the two nonholonomic constraints in terms of the speeds u1, u2, u3, u4, and u5.
• Considering the independent speeds to be u1, u2, and u3, find the non holonomic velocity partials for the velocities of P and C*.
• Find the non holonomic active generalized forces.

Projects

• Dynamics of continuous systems with applications to robotics or computer graphics;
• Potential field based navigation methods for autonomous agents (vehicles, synthetic figures in animations, robots)
• Multibody dynamics: Dynamics of closed chain systems
• Electronic throttle control, cruise control and the dynamics of automatic transmission vehicles
• Dynamics of biological networks: Modeling, analysis and simulation of biomolecular inter and intra cellular networks.

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

Introduction (pdf file, 53Kb)
Dynamics: the Geometry of Behavior (pdf file, 734Kb)
Kinematics (pdf file)
Kinematics 2 (pdf file)
Constraints (pdf file)

PDF files for all slides are available here
 

Software Tutorials

• Matlab

HELP

• Course administration/questions about the course or homework, or general assistance
• kumar@cis.upenn.edu
• Homework and assistance with the course
• calin@grasp.cis.upenn.edu
• Web site problems/comments (meam535@seas.upenn.edu)

• MEAM Seminars
• GRASP Seminars
• Physics Seminars

Links to Research Laboratories

Other Useful Links

• Penn Online Directory
• Penn Libraries Homepage