Physics 507: THEORETICAL MECHANICS (Winter 2008)

M W F,  10 - 11 AM @ Randall 4404

Instructor: Alexei V. Tkachenko ( alexei@umich.edu ) 

Office: West Hall 273; phone: (734)763-4154; office hours: Tuesday Thursday (1-2 PM)

Syllabus  (click the topic to see  lecture handouts, or download the  Complete set of notes )

• Lagrangian Mechanics

Generalized coordinates - Hamilton Principle - Lagrange Equation - Symmetries & Conservation Laws

• Classical Integrable Problems

1D motion - Mechanical analogies in physics -  Two-body problem - Motion in central field & Kepler's problem - Virial theorem - Scattering

• Mechanics of Rigid Body

Rotational motion - Angular momentum - Inertia tensor -  Euler Equations - Precession - Heavy Spinning Top

• Oscillations

Small oscillations: normal mode problem - Damping, Forced oscillations and Resonance

• Hamiltonian Mechanics

Canonical Variables & Hamiltonian - Hamilton Equations - Phase Space - Poisson Brackets - Liouville Theorem   - Canonical Transformations - Action-angle variables

• Non-integrable systems, Introduction to Chaos

KAM theorem -  Lyapunov exponent - Poincare Maps - Stable and chaotic trajectories

Homework and Exam Information

Final Score = 50% * Homework + 20% * Midterm Exam + 30% * Final Exam


Homework 1 + solutions  due on Monday, January 21

Homework 2 + solutions  due on Friday, February 1

Homework 3 + solutions  due on Wednesday, February 13

Homework 4 + solutions  due on Friday, February 22

Homework 5 + solutions  due on Wednesday, March 19

Homework 6 + solutions  due on Friday, March 28

Homework 7 + solutions  due on Wednesday, April 9

Homework 8 + solutions  due on Wednesday, April 16

Midterm Exam + solutions  Monday March 10,  5:30-7:30 PM. Room Dennison 268 (open books, notes, etc).

Textbooks

Required: 

and/or

Recommended: