Editing Symplectic manifold (section)

{{Short description|Type of manifold in differential geometry}}
{{Use American English|date = March 2019}}

In [[differential geometry]], a subject of [[mathematics]], a '''symplectic manifold''' is a [[Differentiable manifold#Definition|smooth manifold]], <math> M </math>, equipped with a [[Closed and exact differential forms|closed]] [[nondegenerate form|nondegenerate]] [[Differential form|differential 2-form]] <math> \omega </math>, called the symplectic form. The study of symplectic manifolds is called [[symplectic geometry]] or symplectic topology. Symplectic manifolds arise naturally in abstract formulations of [[classical mechanics]] and [[analytical mechanics]] as the [[cotangent bundle]]s of manifolds. For example, in the [[Hamiltonian mechanics|Hamiltonian formulation]] of classical mechanics, which provides one of the major motivations for the field, the set of all possible configurations of a system is modeled as a manifold, and this manifold's cotangent bundle describes the [[phase space]] of the system.