# Hamiltonian system

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Hamiltonian system

In classical mechanics, a Hamiltonian system is a physical system in which forces are velocity 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

ee also

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

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