Physics 507: Theoretical Mechanics

Winter 2002    335 West Hall MWF 10:00-11:00

Poincare section of chaotic pendulum

Leonard M. Sander
Office: 247 West Hall

Grader: Liantao Wang

Text: H. Goldstein, C. Poole, & J. Safko, Classical Mechanics, Addison Wesley, 2002
Recommended: E. Ott, Chaos in Dynamical Systems, Cambridge University Press, 1993

I will give a treatment of advanced classical dynamics with Langranian and Hamiltonian mechanics, Hamilton-Jacobi theory, perturbation theory, non-linear mechanics (including, if time allows, the KAM theorem) and some rigid-body mechanics.


  1. Review of Newtonian Mechanics (3 lectures)
  2. Lagrangian mechanics and constaints (7 lectures)
  3. Topics in Lagrangian mechanics: central forces; rigid bodies; small oscillations. (9 lectures)
  4. Hamiltonian mechanics. (8 lectures)
  5. Canonical transformations, Hamilton-Jacobi theory, action-angle variables, perturbation theory. (8 lectures)
  6. Non-linear dynamics and chaos; KAM theory. (6lectures)


Solutions to Midterm

Solutions to final


There will be a midterm, a final and 8 or 9 problem sets.

For the later part of the course I will introduce some numerical work to be done on a computer. The students will be required to use Matlab . For those who are not familiar with computer techniques, I will hold a few introductory sessions in a computer classroom.

Getting started with Matlab

Books on Reserve in Physics Library

H. Goldstein, Classical Mechanics, Addison Wesley, 2002

Eugene J. Saletan and Alan H. Cromer, Theoretical mechanics, Wiley 1971

L. D. Landau and E. M. Lifshitz, Mechanics, Pergamon Press, 1976

V. I. Arnold, Mathematical methods of classical mechanics, Springer-Verlag, 1978

Jorge V. Jose and Eugene J. Saletan, Classical Dynamics : A Contemporary Approach, Cambridge 1998

E. Ott, Chaos in Dynamical Systems, Cambridge University Press, 1993