In classical mechanics, a Hamiltonian system is a physical system in which forces are momentum invariant. Hamiltonian systems are studied in Hamiltonian mechanics.

In mathematics, a Hamiltonian system is a system of differential equations which can be written in the form of Hamilton's equations. Hamiltonian systems are usually formulated in terms of Hamiltonian vector fields on a symplectic manifold or Poisson manifold. Hamiltonian systems are a special case of dynamical systems.

Examples

• Dynamical billiards
• Planetary systems

See also

• Action-angle coordinates
• Liouville's theorem
• Integrable system