Reformulation of classical mechanics on phase space (q, p) via H(q,p,t); canonical equations q̇ = ∂H/∂p, ṗ = −∂H/∂q. Natural setting for canonical quantisation and symplectic geometry.
Hamiltonian mechanics
Related concepts
- Lagrangian mechanics (principle of stationary action)
- Symplectic manifold
- Poisson bracket
- Canonical transformation
- Hamilton–Jacobi equation (classical mechanics)
- Symplectic integrator
- Lagrangian mechanics (principle of stationary action)
- Lagrangian mechanics (principle of stationary action)
- Routhian reduction
- Symplectic 2-form ω
- Hamiltonian density and conjugate momenta
- KAM theorem
- Lindstedt–Poincaré perturbation
- Liouville–Arnold integrability
- Milankovitch cycles
- Hamiltonian vector field
- XXX Heisenberg spin chain: Bethe-ansatz diagonalisation
- Kepler third law: T² = (4π²/GM)·a³ from two-body Hamiltonian