# 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 Mon, Aug 29 NO CLASSES. Hurricate Irene clean-up. 1. Wed, Aug 31 G 1.1-1.3; FW 1.1-1.3; LL 1 0. Introduction. Class info. Newton's laws. Mechanics of a particle. Conservation laws: momentum, energy, angular momentum. Mechanics of a system of particles. Conservation laws. Center of mass frame. 2. Fri, Sep 2 G 1.3; 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. Homogeneity and isotropy of time and space. 7. Wed, Sep 14 LL 5-9,JS 3.2.2 Conservation of energy, momentum, and angular momentum. Noether's theorem. Gauge symmetries of the Lagrangian. 8. Fri, Sep 16 LL 10-11 Scaling transformations and mechanical similarity. The virial theorem. 3. 1D motion. Solution of 1D motion in quadratures. 9. Mon, Sep 19 LL 11, 13-15 G 3.1-3.3 HW 3 given. Solution of 1D motion in quadratures. Phase portrait. 4. 2D motion. Central force motion. Reduced mass. Motion in central field. 10. Wed, Sep 21 LL 15, G 3.7 Kepler's problem. Kepler's laws. Conic sections. Time dependence in Kepler problem. 11. Fri, Sep 23 LL 15-16, G 3.8-3.9 Time dependence in Kepler problem. Orbit precession in almost Newtonian potentials. Runge-Lenz vector. 12. Mon, Sep 26 LL 1-15 Midterm 1. (open book). HW 4 given. 13. Wed, Sep 28 LL 16-20 Particle decay. Collision between particles. Total and differential scattering cross sections. Rutherford cross section. Fri, Sep 30 NO CLASSES. Rosh Hashanah. 14. Mon, Oct 3 LL 17, 20 Rutherford cross section. Scattering in laboratory reference frame. Scattering by small angle. 15. Wed, Oct 5 LL 21-22 HW 5 given. 5. Small oscillations. Harmonic oscillator. Forced oscillations. Complex notations. Resonance. 16. Fri, Oct 7 LL 23-24 Resonance. Beatings. Oscillations with many degrees of freedom. Eigenfrequences and normal modes. 17. Mon, Oct 10 LL 24-25 Example on normal modes. Degeneracies. Vibrations of molecules. Damped oscillations (1 degree of freedom). 18. Wed, Oct 12 LL 25-26, 31 G 1.5 JS 3.3 Damped oscillations (many degrees of freedom). Dissipative function. Forced oscillations under friction. 19. Fri, Oct 14 LL 32-33 HW 6 given. 6. Rigid body motion. Angular velocity. Kinetic energy of the rigid body. The inertia tensor and its properties. 20. Mon, Oct 17 LL 33-34 Angular momentum of the rigid body. Symmetric top I. Equations of motion. 21. Wed, Oct 19 LL 35-36 Euler angles. Equations of motion in the moving frame. 22. Fri, Oct 21 LL 36-37 HW 7 given. Euler equations. Symmetric top II. Asymmetric top. 23. Mon, Oct 24 LL 39 Asymmetric top. Motion in an non-inertial frame of reference. Centrifugal and Coriolis forces. 24. Wed, Oct 26 LL 40, JS 5.1, G 8.5 7. Hamiltonian and Hamilton-Jacobi formalism. Hamilton's equations. The Legendre transform. 25. Fri, Oct 28 LL 42, 45 HW 8 given. Example: particle in EM field. Poisson brackets. Examples. 26. Mon, Oct 31 LL 42 Poisson brackets. Variational formulation. 27. Wed, Nov 2 LL 45, 46 Canonical transformations. 28. Fri, Nov 4 LL 45-46 HW 9 given. Invariants of canonical transformations: Poisson bracket, phase volume. Liouville theorem. 29. Mon, Nov 7 LL 47-48 The Hamilton-Jacobi equation. Example. Separation of variables. 30. Wed, Nov 9 LL 48-50, 52 Separation of variables. Adiabatic invariants (example of harmonic oscillator). 31. Fri, Nov 11 LL 50 Action-angle variables for 2d phase space. Adiabatic invariance of action. 32. Mon, Nov 14 LL 50, 52 Action-angle variables, multi-dimensional case. Conditionally periodic motion. Action-angle variables (examples). 33. Wed, Nov 16 LL 16-52 HW 10 given. Midterm 2. (open book). 34. Fri, Nov 18 G 11.1-11.3; JS 6.3 Action-angle variables (example of Kepler problem). 8. Nonlinear dynamics and chaos. Introduction. Periodic motion. Perturbations. 35. Mon, Nov 21 G 12-2,3; Perturbations. Corrections to frequency. Example of the quartic oscillator. Wed, Nov 23 NO CLASSES. Thanksgiving. Fri, Nov 25 NO CLASSES. Thanksgiving. 36. Mon, Nov 28 G 11-4,5,8; KAM. Attractors. Chaotic trajectories. 37. Wed, Nov 30 LL 27,30; G 11-5,6,7,8 Henon-Heiles Hamiltonian. Poincare maps. The logistic equation. 38. Fri, Dec 2 JS 7; LL 27 Duffing oscillator. Parametric resonance. 39. Mon, Dec 5 LL 27, 30; LL7 1-4-5, 7 HW 11 given, not for credit Parametric resonance. Motion in rapidly oscillating field. 9. Elasticity theory. Static indeterminancy. Displacement field. the strain tensor. 40. Wed, Dec 8 LL7 7, 11-12 The stress tensor. Elastic energy. Elastic moduli (Hooke's law). Elastic moduli (Hooke's law). Homogenious deformations. Equilibrium for isotropic bodies. Equilibrium for isotropic bodies. Equilibrium for a plate. 41. Fri, Dec 9 LL7 22 10. Dynamics of continuous systems. Elastic waves. Longitudinal and transversal waves in isotropic elastic medium. General dispersions of elastic media. 42. Mon, Dec 12 Introduction into hydrodynamics. Ideal fluid hydrodynamics. Conservation of mass, momentum and energy. Hamiltonian formulation of hydrodynamics. Final remarks: towards field theory and quantum mechanics. Final Mon, Dec 19 Everything FINAL, P-112, 11:15-1:45. Open book. Notes and textbooks are allowed. 4 problems.