Symplectic geometry is the branch of differential geometry which studies the properties of manifolds endowed with a symplectic structure, i.e., a closed and nondegenerate two-form. Two, not mutually exclusive, classes of examples of these manifolds are cotangent bundles and coadjoint orbits. Symplectic manifolds appear in classical mechanics as the phase spaces of classical dynamical systems. For example, if N is the configuration space of a mechanical system, its cotangent bundle \(T^\ast N\) plays the role of its phase space.