Editing Hamiltonian mechanics (section)

{{Short description|Formulation of classical mechanics using momenta}}
[[File:WilliamRowanHamilton.jpeg|thumb|Sir William Rowan Hamilton]]
{{Classical mechanics|cTopic=Formulations}}
In [[physics]], '''Hamiltonian mechanics''' is a reformulation of [[Lagrangian mechanics]] that emerged in 1833. Introduced by [[Sir William Rowan Hamilton]],<ref>{{cite book |author=Hamilton, William Rowan, Sir |url=http://worldcat.org/oclc/68159539 |title=On a general method of expressing the paths of light, & of the planets, by the coefficients of a characteristic function. |date=1833 |publisher=Printed by P.D. Hardy |oclc=68159539}}</ref> Hamiltonian mechanics replaces (generalized) velocities <math>\dot q^i</math> used in Lagrangian mechanics with (generalized) ''momenta''. Both theories provide interpretations of [[classical mechanics]] and describe the same physical phenomena.

Hamiltonian mechanics has a close relationship with geometry (notably, [[symplectic geometry]] and [[Poisson structure]]s) and serves as a [[Hamilton–Jacobi equation|link]] between classical and [[quantum mechanics]].