# | 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. |