1.  Introduction, course arrangements, etc.

2. Introductory statics problems: the catenary and the ideal arch.

3. Calculus of Variations: catenary revisited as curve of least energy, soap film between rings.

    The Euler –Lagrange minimization equation and its first integral.

    Minimization for constrained systems: Lagrange multipliers.

The Brachistochrone: the downhill curve of least time.

4. Fermat’s Principle of Least Time in wave propagation: wave optics and geometric optics.

5. More minimization: The laws of dynamics and Hamilton’s Principle of Least Action.

6.  Generalized momenta and forces:  conservation laws and Noether’s Theorem.

7. Mechanical similarity and the Virial Theorem.

8. Hamilton’s equations:  Configuration space, State space, Phase space. The Canonical Form of Hamilton’s equations. Poisson Brackets and the link to quantum mechanics, the Jacobi Identity.

9. Action as function of endpoints: Maupertuis’ Principle: connection to time-independent Schrodinger equation.

10. Canonical transformations: a way to simplify the equations of motion.

11. Liouville’s Theorem. 

12. Adiabatic Invariants and their quantum mechanical equivalents.

13. Action Angle Variables: simplifying the equations of motion.

14. Motion in one dimension and motion in a central field in three dimensions.

15: Mathematical review: ellipses, parabolas, hyperbolas.

16: Keplerian orbits standard derivation, Hamilton’s derivation, the Runge-Lenz vector, the hodograph.

17: Bertrand’s Theorem: for what potentials can an orbit be closed?

18: Elastic Scattering, Rutherford’s Formula, CM and Lab Frames.

19: Small Oscillations: normal modes, superposition, coupled pendulums. Forced oscillations.

20: Dynamics of a one-dimensional crystal.  Eigenstates and eigenvalues of a circulant matrix. The Discrete Fourier Transform.

21: Parametric resonance.

22: Motion in a rapidly oscillating field: the ponderomotive force. The upside-down driven pendulum.

23: Anharmonic oscillations, nonquadratic potential, resonance in nonlinear oscillations.

24: Motion of a rigid body.  The inertia tensor: introduction to tensors, examples of inertia tensors.

25: Analyzing rolling motion:  cone on plane, hoops, etc.

26: Rigid body in free flight.

27: Euler’s angles: motion of free top, motion of top with fixed base and gravity.

28: Euler’s equations: free top revisited, asymmetrical case.

29: Motion in a noninertial frame of reference. The Coriolis effect. Gyrocompasses.

30: Motion of a sphere rolling on a rotating inclined plane. 

Graduate Level Classical Mechanics.  Text: Landau and Lifshitz..