MEAM 535 is a graduate level course in rigid body dynamics and dynamical systems. This course is open to all engineering graduate students. If you are an undergraduate student, you must talk to the instructor before registering for the course. A more detailed description of the course is available here.

Announcements

Instructors

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

Dr. Herbert Tanner
Office: GRASP Lab, Room 311C
Phone: 898 - 8741
Email: tanner@grasp.cis.upenn.edu
Web site: http://www.cis.upenn.edu/~tanner/

Teaching Assistant

Fan Zhang (Michael)

Office: GRASP Lab, Room 325C

Phone:

Email: zhangf@grasp.cis.upenn.edu

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).

Herbert Tanner,

Fan Zhang, Mon 4:30 – 6:00 and Wed 4:30 – 6:00, GRASP Lab Room 325C

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Texts

Bulk Pack

[BP] MEAM 535 Fall 2001 V. Kumar. University of Pennsylvania.

An electronic version of the bulk pack is available here. You have to be registered in the course to get access to this website.

There is no prescribed text for this class. Several suggested references are provided here.

References

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

Other references

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.

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Bulk Pack - Table of Contents

A. Introduction

Lesser, Chapter 1
Goldstein, Chapter 1
Abraham and Shaw, Chapters 1 and 2
Review: Particle Dynamics

B. Rigid Body Kinematics

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

C. Rigid Body Dynamics and Analytical Mechanics

Basics: Dynamics of a System of Particles
Mass Distribution and Inertia Tensor
Principle of Virtual Work
Lagrange’s equations and D’Alembert’s principle - V. Kumar

D. Stability of Dynamical Systems

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

E. Simulation
Basics of Numerical Integration - V. Kumar

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.

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E-Bulk Pack

NB: You must be registered for the course before accessing these notes.

Course Information

Course Description

MEAM 535 deals with advanced concepts in dynamics. The course will emphasize the tools of analytical mechanics with the main goal of developing mathematical models that describe the dynamics of systems of rigid bodies and continuous systems. The course will also address the formulation of equations of motion for complicated mechanical systems and methods for solving these equations. In particular, the course will include:

Rigid body kinematics: the description of the motion of systems of rigid bodies.
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).
Dynamical systems: The study of systems governed by ordinary differential equations including the trajectory of the system, stability, and periodicity.
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.
Simulation: the basic techniques for numerical integration, solving differential equations, and for visualization of results.

The course will include applications to multibody systems, and in particular, robots and spatial mechanisms. See tentative schedule for a list of topics covered. Also see the websites for material covered in previous years.

Students are expected to have a basic background in physics and must be familiar with Newton's laws and their application to particles in two and three dimensions. We will assume that everybody is familiar with matrices and determinants, and has had a basic course in ordinary differential equations (equivalent of MEAM 240 and 241 at Penn). Students must also know how to manipulate, multiply and differentiate vectors.

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Time and Location

Tuesdays and Thursdays 3:00pm-4:30pm
Towne 315. (See http://www.upenn.edu/fm/map.html to locate Towne Building)

Tentative Schedule


Week	Date	Topic	Work	Remarks
1	5-Sep	Introduction (history, connection to geometry)
2	10-Sep	Rigid body kinematics, angular velocity
	12-Sep	Differentiation of vectors	HW 1
3	17-Sep	Differentiation (cont'd), frame dependence
	19-Sep	Velocity and acceleration	HW 2	HT
4	24-Sep	Holonomic and nonholonomic constraints
	26-Sep	Configuration space, constraints	HW 3
	30-Sep	Review Session 1
5	1-Oct	Generalized coordinates, partial velocities		HT
	3-Oct	Configuration space, generalized coord., speeds	HW 4
6	8-Oct	Kinetics of particles, momentum, energy
	10-Oct	System of particles	HW 5
	14-Oct	Review Session 2
7	15-Oct	Kinetic energy, angular momentum, inertia dyadic
	17-Oct	Inertia Dyadic, eigen values and eigenvectors	HW 6	HT
8	22-Oct	Principle of virtual work
	24-Oct	Partial velocities, generalized forces	HW 7
	28-Oct	Review Session 3
9	29-Oct	D' Alembert's principle
	31-Oct	Applications to nonholonomic systems	HW 8
10	5-Nov	Constraint forces
	7-Nov	Newton-Euler Equations of Motion	HW 9
11	12-Nov	Lagrange's equations
	14-Nov	Nonholonomic systems	HW 10
	18-Nov	Review Session 4
12	19-Nov	Examples
	21-Nov	Numerical methods and simulation
13	26-Nov	Integrals of motion
	28-Nov	Thanksgiving	HW 11
14	3-Dec	Stability of dynamical systems (cont'd)		HT
	5-Dec	Make-up, problems, etc.	HW 12	HT
	9-Dec	Tentative Date for Final Exam

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Schedule

Material Covered in Class - Weekly Updates
Weekly homework

Week	Date	Topic	Covered material
1	Sep 5	Introduction, history, geometric mechanics.	A.1, A.3 (pages 1-6). Link to applet for phase portraits
2	Sep 20	Potential Fields, transformation and differentiation of vectors, angular velocity.	B.1, B.2 (2.1, 2.3).
2	Sep 12	Velocity and acceleration of points, angular acceleration.	B.2 (2.2.4, 2.4-2.5).
3	Sep 17	Velocity and acceleration analysis (cont'd); Examples.	B.2 (2.4-2.7).
4	Sep 24	Degrees of freedom, constraints.	B.3 (3.1-3.3).
4	Sep 26	Nonholonomic constraints, integrability conditions.	B.3 (3.4), B.4.
5	Oct 1	Generalized speeds, partial velocities.	B.3 (3.5).
5	Oct 3	Particle dynamics (review), Newton's laws, work and energy, linear and angular momentum, conservation laws	A.2 (Sections 1.1-1.3), A.4
6	Oct 8	Review of basic concepts for HW3, Dynamics of Systems of Particles, Example: Rolling Cone (Maple program)	C.1 (4.1-4.5), C.2 (Section 3.1)
6	Oct 10	System of particles: Angular momentum and kinetic energy	C.2 (Section 3.2-3.8)
7	Oct 15	Inertia Dyadic, angular momentum and kinetic energy for a rigid body
7	Oct 17	Properties of the Inertia Dyadic	C.2
8	Oct 22	Principle of Virtual Work for Holonomic Systems	C.3
8	Oct 24	Principle of Virtual Work (cont'd)	C.3
9	Oct 29	Midterm
9	Oct 31	Principle of Virtual Work for Nonholonomic Systems
10	Nov 5	D'Alembert's Principle, Kane's Equations, Newton-Euler Equations	(C.4: 8.1-8.4, 8.8)
10	Nov 7	Kane-Lagrange Equations (Two examples: Spherical and BalancingPendulum)	(C.4: 8.5-8.7)
11	Nov 12	Kane-Lagrange Equations for Nonholonomic Systems
11	Nov 14	Lagrange's Equations for Systems with Constraints
12	Nov 19	Integrals of Motion and Hamilton Equations of Motion	(Goldstein, Chapter 8: pages 339-356)
12	Nov 21	Introduction to the Calculus of Variations

MEAM 535: Dynamics Fall 2002

Send mail to the class (instructors only)

General Information

Announcements

Instructors

Teaching Assistant

Office Hours

Texts

Bulk Pack

References

E-Bulk Pack

Course Information

Course Description

Time and Location

Tentative Schedule

MEAM 535: Dynamics
Fall 2002

`Send mail to the class` (instructors only)