Notes for Physics 601 (Prof. Agashe): Fall 2017

1. Equation of motion for free particle in rotating frame using Lagrangian formulation.

2. Lagrange multiplier method for simple pendulum (solving for constraint force as a function of coordinate).

3. Conservation of momentum (linear and angular) and energy using Noether’s theorem

4. Solving coupled system for small oscillations.

5. Summary of central force/Kepler problem

6. Relating impact parameter to angle of scattering in central force

7. Relating scattering angle in COM frame to lab frame

8. Kinematics of rigid body

9. Dynamics of rigid body (including additional ones for principal and parallel axes)

10.Free, symmetric top

11.Heavy, symmetric top: general discussion

12.Heavy, symmetric top: specific cases

13. Lorentz force from Hamiltonian

14. Angular momentum Poisson brackets

15. Solving simple harmonic oscillator using canonical

transformation

16. Action-angle variables: general idea

17. Solving for frequency of simple harmonic oscillator by action-angle variable

18. Solving for complete motion of simple harmonic oscillator using Hamilton-Jacobi method

19. Action-angle variables from generating function (H-J-like equation)