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Lecture Notes:

Lecture 1 - Derivation of Hamilton's principle from quantum physics.  Variational calculus.

Lecture 2 - Lagrangian and Hamiltonian equations of motion from Hamilton's principle.

Lecture 3 - Translation of Hamilton to Lagrange.  Conserved quantities.

Lecture 4 - Central Force problems.

Lecture 5 - CFs continued, Virial Theorem, Kepler.

Lecture 5 - supplementary material - plots

Lecture 6 - Rigid Body motion, pt I

Lecture 7 - Rigid Body motion, pt II

Lecture 8 - The symmetric Top

Lecture 8 -supplementary material - Mathematica notebook integrating the eqns. of motion; plots

Lecture 9 - Symplectic structure & Canonical Transformations, pt I

Lecture 10 - Symplectic structure & Canonical Transformations, pt II

Lecture 11 - Canonical Invariants, Hamilton-Jacobi equation

Lecture 12 - Action-Angle variables

Lecture 13 - Perturbations to Integrable systems

Lecture 14 - Hamilton-Jacobi theory in optics (J. Dressel, guest lecturer).

Lecture 15 - The fate of resonant tori; maps and local stability

Lecture 16 - 1D maps - chaos, Lyapunov exponents, the period doubling route to chaos.  See here for Wolfram's nice Logistic map application.

Lecture 17 - more on maps

Lecture 18 - 2D maps - analysis of the baker's map

Homework: