| LECTURE |
DATE |
TOPIC (click for lecture "black boards") |
| |
10/05 |
Calculus of variations, Hamilton's principle, generalized coordinates |
|
10/07 |
Solving for the motion, examples, linearization, virial theorem |
| No. 3 |
10/12 |
Noether's theorem, the Hamiltonian, rapidly oscillating fields |
| No. 4 |
10/14 |
Extremization with constraints, Lagrange multipliers, mechanics and constraints |
| No. 5 |
10/19 |
Two body central force problem, almost circular orbits, Kepler's problem |
| No. 6 |
10/21 |
Rigid bodies: inertia tensor, coordinate transforms, Euler's eqns., Euler angles |
| No. 7 |
10/26 |
Method of small oscillations, zero modes, harmonic chain, continuum limit |
| No. 8 |
10/28 |
Review of small oscillations; planar right triangle of masses and springs |
| No. 9 |
11/02 |
Strings: Helmholtz eqn, D'Alembert's method, energy density, reflection at interface |
| No. 10 |
11/04 |
Reflection, transmission, S-matrix for strings, Bernoulli's method for finite strings |
| No. 11 |
11/09 |
Sturm-Liouville equation, eigenfunction properties, variational method |
| No. 12 |
11/11 |
Green's functions for inhomogeneous SLE, continua in higher dimensions |
| No. 13 |
11/16 |
Hamiltonian mechanics, incompressible flow, Poisson brackets, Poincare recurrence |
| No. 14 |
11/18 |
Kac ring model, symplectic structure, canonical transformations |
| No. 15 |
11/23 |
Generating functions for canonical transformations, Hamilton-Jacobi theory |
| No. 16 |
11/25 |
HJE for separable time-independent systems, action-angle variables, invariant tori |
| No. 17 |
11/30 |
CT to action-angle variables, Liouville-Arnol'd theorem, adiabatic invariants, resonances |
| No. 18 |
12/02 |
Canonical perturbation theory, the method of averaging, resonances (again) |
| No. 19 |
12/07 |
Removal of resonances for n=3/2 and n=2 systems, KAM theorem |
| No. 20 |
12/09 |
Maps from resonant tori and time-dependent H(t), Poincare-Birkhoff theorem |
| --- |
--- |
ALL IPAD SCREENS FROM F20 PHYS 200A (242 pp, 42 mb pdf) |
| video |
12/11 |
Dec. 11 discussion |
| video |
12/14 |
Dec. 14 review |