1. Joel will solve problems on 10/13. VK will not be in class.
2. Make sure you "reload" the page on your browser. Otherwise your browser will simply load the version it has in the cache, and you will not see recent changes.
3. Solutions for homeworks 9 and 10 are available on-line.

The course can be divided into four parts.

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. 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.
4. 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.

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Material covered in previous years:

• MEAM 535: Spring 1997 Schedule.
• MEAM 535: Spring 1998 Schedule

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Notes:
 

1. We will discuss homework problems in an informal setting every Thursday starting at 545. This may run late depending on the energy level of the class.
2. All homeworks will be due on Friday on or before 500 pm in Joel Esposito's mail box in Towne 297.

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Homeworks	25%
Midterm Exams	40%
Final Exam	35%

• All homeworks will be graded.  However, only select problems from each homework will be graded.
• MSE students (excluding those continuing on for a Ph.D.) may opt to pursue a project  and take a third midterm exam instead of the final exam.  Students choosing this option will be graded according to the following weighting scheme.

Homeworks	25%
2 Midterm Exams	40%
Final Exam (third midterm)	20%
Project	15%

 

Unless otherwise noted above, all homeworks are due on or before Friday 500 pm in Joel Esposito's mail box in Room 297, Towne Building.
H indicates help session.

• [DG] Principle of Dynamics, Donald T. Greenwood, Prentice Hall, Englewood Cliffs, New Jersey, 1988. ISBN 0-13-709981-9.

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Reference books
• [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.

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Instructors:

 
 
• If you want to see Professor Kumar (VK) or make an appointment click on his schedule
• If you want to see Professor Turteltaub (ST)

Current finger information for VK

Current finger information for ST

Teaching Assistant:

Name: Joel Esposito
Office:
Phone:
Email: jme@seas.upenn.edu
 
 

Teaching Assistant Office Hours:

Tuesdays 10:30-11:30 am   (in Towne Building, Room 350).
Wednesdays 2:00 - 3:00 pm (Help session in GRASP Conference Room).
 

• Mathematical preliminaries
• Rigid body kinematic analysis
• Notes on symbolic manipulation
• postscript file
• pdf file
• Degrees of freedom, constraints, and configuration space
• Lagrange-d'Alembert equations and Lagrange's equations of motion
• Stability of dynamical systems
• Calculus of variations, variational principles and vibrations of continuous systems.
• postscript file
• pdf file

• Powerpoint slides for lecture on 9/10/98

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Homework Due Dates:

See schedule and assignments.

Homework Assignments:

See schedule.
 
 

HW 1
HW 2
HW 3
HW 4
HW 5
HW 6
HW 7
HW 8
HW 9
HW 10

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Homework Solutions:

HW 9 (pdf)
HW 10 (pdf) If you cannot print more than 5 pages at once on a CETS printer, use the two PostScript files below (each one is 5 pages long):
HW 10 part 1(ps)
HW 10 part 2(ps)

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Exam Dates:

 

Midterm 1	Oct 22
Midterm 2	Nov 24
Final /Midterm 3	TBD

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Projects:

1. Lecture notes on kinematics (1-2 students)

We will develop a set of lecture notes (you will be the first author) based on the discussions in the first three weeks. The notes will be based on Kane's notation (as covered in class). It will start with the material covered in class and have related material that may be appropriate for self reading. The notes will include solved examples. I want them in a format that can be handed out to students in class next year.

2. Symbolic methods in rigid body dynamics (1-2 students)

We will develop a Maple package for the symbolic analysis of rigid body dynamics. The approach will be based on M. Lesser's package, Sophia (see Reference [ML]). The notation used is very similar to Kane's notation.

3. If your research involves modeling the dynamics of a mechanical system, I can try to assign you a project that is relevant to your research. See me to discuss this option.

4. There is a fascinating example of a nonholonomic locomotion system in the paper:

P.S. Krishnaprasad and D.P. Tsakiris, "Oscillations, SE(2)-Snakes and Motion Control", 34rd IEEE Conference on Decision and Control, New Orleans, Louisiana, December 13-15, 1995. See the on-line postscript file.

It would be very interesting to develop the dynamic equations of the system (the authors in the paper use a different approach) and develop a simulator that would help us try to evaluate different control strategies.

5. There is a great deal of interest in micro electromechanical systems (MEMS).  See http://www.mdl.sandia.gov/micromachine/index.html for work going on in Sandia National Laboratories. An interesting research project will be to derive the dynamics of the torque convertor http://www.mdl.sandia.gov/micromachine/3million.html and see how these dynamics are different from the dynamics of the more conventional "macro" systems. A related issue is the numerical methods required for simulation. A gentle warning! This project is somewhat open ended. One mission will be to obtain CAD models of the all the components of the torque converter and build the dynamic models from the CAD models. It is advisable to get an early start on this project.

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SEAS

University of Pennsylvania Library System

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Created: December 29, 1997
Last Update: January 10, 1998
© 1998 By: Vijay Kumar

All rights reserved; 1998 University of Pennsylvania