Graduate-leaning notes on canonical transformations, generating functions, the Hamilton-Jacobi equation, and action-angle variables.

For students who already know Hamilton’s equations and need the next layer for GR or advanced CM.

• Four generating-function types with examples
• Hamilton-Jacobi for separable systems
• Action-angle variables and frequencies
• Adiabatic invariants
• Completely worked harmonic oscillator and Kepler cases