This article is about the classical theory. For other uses, see Hamiltonian.
In physics and 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.
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