M6 · Hamiltonian mechanics
A 17-module path through m6 · hamiltonian mechanics, in study order from foundations to the frontier.
Modules
- Legendre Transformation
- Generalized Momenta
- The Hamiltonian Function
- Hamiltonian as Total Energy
- Hamilton's Canonical Equations
- Equivalence of Lagrangian and Hamiltonian Formulations
- Phase Space
- Phase Portraits and Trajectories
- The Harmonic Oscillator in Phase Space
- Fixed Points and Stability in Phase Space
- The Pendulum Phase Portrait and Separatrix
- Hamiltonian Flow and the Phase Fluid
- Liouville's Theorem
- The Virial Theorem
- Time Evolution of Phase-Space Functions
- Conservation Laws in the Hamiltonian Formalism
- Cyclic Coordinates and Conserved Momenta