Notes
for Physics 601 (Prof. Agashe): Fall 2018
1.
Equation
of motion for free particle in rotating frame using Lagrangian
formulation.
3. Conservation
of momentum (linear and angular) and energy using NoetherŐs
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 (including on Expressing
unit vector along z-axis in space
frame in terms of body frame unit
vectors)
9. Dynamics of rigid body [including additional one for how to go to principal axes and on the last step involved in parallel axes theorem, which was also used in showing factorization of translation of and rotation about COM, i.e., sum over (masses of particles in body) x (their coordinate relative to COM) vanishes]
11. Free, symmetric top (3 ways)
12.
Heavy,
symmetric top: general discussion
13.
Heavy,
symmetric top: specific cases
14.
Lorentz
force from Hamiltonian
15.
Angular
momentum Poisson brackets
16.
Solving
simple harmonic oscillator using canonical transformation
18.
Action-angle
variables: general formula
19.
Solving
for frequency of simple harmonic oscillator by action-angle variable
20.
Summary
of Hamilton-Jacobi method
21.
Solving
for complete motion of simple harmonic oscillator using Hamilton-Jacobi method
22.
Action
variable is adiabatic invariant
23.
Action-angle
variables from generating function (H-J-like equation)