Fall 2001, Jacobus Verbaarschot

1. Historical Perspective; Laws of Newton and Kepler.
2. Energy, momentum and angular momentum; Covariance of the Newton equations.
3. Action principle.
4. Lagrange equations and constraints.
5. Generalized coordinates.
6. Energy; Equivalence of Lagrangians.
7. Charged particle in an electromagnetic field; gauge transformations.
8. Central force problem.
9. Why do Kepler orbits exist: Bertrand's theorem.
10. Geometry of Phase space.
11. Hamilton's principle.
12. Cyclic coordinates and Noether's theorem.
13. Scattering; Rutherford cross-section.
14. Chaotic Scattering.
15. Small Oscillations: general theory.
16. Coupled oscillators.
17. Hamilton equations of motion.
18. Phase space and Poisson brackets.
19. Hamiltonian dyanmical systems.
20. Canonical transformations
21. Liouville's theorem.
22. Special relativity (if necessary).
23. Midterm.
24. Rotation group.
25. Rigid body motion.
26. Inertia tension; torque and angular momentum.
27. Euler angles, Euler equations.
28. Asymmetric top.
29. Hamilton-Jacobi equations.
30. Integrability and separable problems.
31. Action-angle variables.
32. Motion on tori.
33. Liouville's integrability theorem.
34. Adiabatic invariants.
35. Perturbation theory in classical mechanics.
36. Improved perturbation theory.
37. Poincar\'e map.
38. Logistic map.
39. Poincar\'e-Birkhoff theorem.
40. Chaos in Hamiltonian systems.
41. Kicked rotor.
42. Homoclinic tangle.
43. KAM theorem.

    Jacobus Verbaarschot
    Last revised: August 26, 2001.