Physics 501: Classical Mechanics

Tentative Syllabus

LL - Landau, Lifshitz, v1
FW - Fetter, Walecka
G - Goldstein
LL6 - Landau, Lifshitz, v6
LL7 - Landau, Lifshitz, v7
JS - Jose, Saletan

# Date Read Topic
1. Mon, Aug 29 G 1.1-1.3; FW 1.1-1.3 0. Introduction. Class info. Newton's laws. Mechanics of a particle. Conservation laws: momentum, energy, angular momentum.
2. Wed, Aug 31 G 1.2-1.3; FW 1.2-1.3; LL 1 Mechanics of a system of particles. Conservation laws. Center of mass frame.
3. Fri, Sep 2 LL 2 HW 1 given. Constraints. Generalized coordinates. 1. Lagrangian formalism. Variational calculus. Euler equations. Example: shape of soap film.
Mon, Sep 5 NO CLASSES. Labor Day.
4. Wed, Sep 7 LL 2 Variational calculus. Euler equations. Example: shape of soap film. Lagrange multipliers. Example: maximal area with given perimeter. Hamilton's principle (the principle of least action). Example of a single particle.
5. Fri, Sep 9 LL 3-5 Symmetries of space and time. Galilean invariance. Lagrangian of an isolated particle. Lagrangian of a system of particles.
6. Mon, Sep 12 LL 5-7 HW 2 given. Lagrangian of a system of particles. Examples. 2. Conservation laws. Conservation of energy.
7. Wed, Sep 14 LL 5-9 Homogeneity and isotropy of time and space. Conservation of energy, momentum, and angular momentum.
8. Fri, Sep 16 JS 3.2.2, LL 10 Noether's theorem. Gauge symmetries of the Lagrangian. Scaling transformations and mechanical similarity.
9. Mon, Sep 19 LL 10-11 HW 3 given. The virial theorem. 3. 1D motion. Solution of 1D motion in quadratures. Phase portrait.
10. Wed, Sep 21 LL 13-15 4. 2D motion. Central force motion. Reduced mass. Motion in central field. Kepler's problem. Kepler's laws.
11. Fri, Sep 23 LL 15-16 Conic sections. Time dependence in Kepler problem. Orbit precession in almost Newtonian potentials. Particle decay.
Mon, Sep 26 NO CLASSES. Prepare for the exam.
12. Wed, Sep 28 LL 1-15 Midterm 1. (open book).
13. Fri, Sep 30 LL 16-20 HW 4 given. Collision between particles. Total and differential scattering cross sections. Rutherford cross section.
Mon, Oct 3 NO CLASSES. Rosh Hashanah.
Wed, Oct 5 NO CLASSES. Rosh Hashanah.
14. Fri, Oct 7 LL 17, 20, 21 Scattering in laboratory reference frame. Scattering by small angle. 5. Small oscillations. Harmonic oscillator.
15. Mon, Oct 10 LL 21-22 Harmonic oscillator. Forced oscillations. Complex notations. Resonance. Beatings.
16. Wed, Oct 12 LL 23-24 HW 5 given. Oscillations with many degrees of freedom. Eigenfrequences and normal modes.
17. Fri, Oct 14 LL 24-25 Example on normal modes. Degeneracies. Vibrations of molecules. Damped oscillations (1 degree of freedom).
18. Mon, Oct 17 LL 25-26, 31 Damped oscillations (many degrees of freedom). Dissipative function. Forced oscillations under friction. 6. Rigid body motion. Angular velocity.
19. Wed, Oct 19 LL 32-33 HW 6 given. Kinetic energy of the rigid body. The inertia tensor and its properties.
20. Fri, Oct 21 LL 33-34 Angular momentum of the rigid body. Symmetric top I. Equations of motion.
21. Mon, Oct 24 LL 35-36 Euler angles. Equations of motion in the moving frame.
22. Wed, Oct 26 LL 36-37 HW 7 given. Euler equations. Symmetric top II. Asymmetric top.
23. Fri, Oct 28 LL 39, 40 Motion in an non-inertial frame of reference. Centrifugal and Coriolis forces. 7. Hamiltonian and Hamilton-Jacobi formalism. Hamilton's equations.
24. Mon, Oct 31 LL 40, JS 5.1, G 8.5 Hamilton's equations. The Legendre transform. Variational formulation.
25. Wed, Nov 2 LL 42, 45 HW 8 given. Poisson brackets. Examples. Canonical transformations.
26. Fri, Nov 4 LL 45 Canonical transformations.
27. Mon, Nov 7 LL 46 Invariants of canonical transformations: Poisson bracket, phase volume. Liouville therem.
28. Wed, Nov 9 LL 47-48 The Hamilton-Jacobi equation. Example. Separation of variables.
29. Fri, Nov 11 LL 48-49 Separation of variables. Adiabatic invariants (example of harmonic oscillator).
30. Mon, Nov 14 LL 50, 52 Adiabatic invariants. Action-angle variables. Conditionally periodic motion.
31. Wed, Nov 16 G Action-angle variables (examples). 8. Nonlinear dynamics and chaos. Introduction.
32. Fri, Nov 18 LL 16-49 Midterm 2. (open book).
33. Mon, Nov 21 G 11.1-11.3; JS 6.3 HW 9 given. Periodic motion. Perturbations.
34. Wed, Nov 23 G 11-4,5,7; LL 27-30 KAM. Attractors. Chaotic trajectories.
Fri, Nov 25 NO CLASSES. Thanksgiving.
35. Mon, Nov 28 G 11.8 Poincare maps. The logistic equation.
36. Wed, Nov 30 LL 27,30 HW 10 given. Parametric resonance.
37. Fri, Dec 2 LL7 1-2 9. Elasticity theory. Displacement field. the strain tensor. The stress tensor.
38. Mon, Dec 5 LL7 2-4 The stress tensor. Elastic energy. Elastic moduli (Hooke's law).
39. Wed, Dec 7 LL7 4-5, 7 Elastic moduli (Hooke's law). Homogenious deformations. Equilibrium for isotropic bodies.
40. Fri, Dec 9 LL7 7, 11-12 Equilibrium for isotropic bodies. Equilibrium for a plate.
41. Mon, Dec 12 LL7 22 10. Dynamics of continuous systems. Elastic waves. 11. Final remarks: towards field theory and quantum mechanics.
42. Mon, Dec 19 Room P-112 Solving problems in classical mechanics.
Final Wed, Dec 21 8:00-10:30 AM FINAL, P-112. Open book. Notes and textbooks are allowed. 4 problems.