Hamiltonian system

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.

Examples

• Dynamical billiards
• Planetary systems
• Canonical general relativity

See also

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

Further Reading

• Treschev, D., & Zubelevich, O. (2010). Introduction to the perturbation theory of Hamiltonian systems. Heidelberg: Springer
• Audin, M., & Babbitt, D. G. (2008). Hamiltonian systems and their integrability. Providence, R.I: American Mathematical Society.
• Zaslavsky, G. M. (2007). The physics of chaos in Hamiltonian systems. London: Imperial College Press.
• Dickey, L. A. (2003). Soliton equations and Hamiltonian systems. Advanced series in mathematical physics, v. 26. River Edge, NJ: World Scientific.
• Almeida, A. M. (1992). Hamiltonian systems: Chaos and quantization. Cambridge monographs on mathematical physics. Cambridge [u.a.: Cambridge Univ. Press.]