Hamiltonian vector field
Let be a symplectic manifold, and be the isomorphism from the tangentbundle
to the cotangent bundle
and let is a smooth function.Then is the Hamiltonian vector field of . The vector field is symplectic (http://planetmath.org/SymplecticVectorField),and a symplectic vector field is http://planetmath.org/node/6410Hamiltonian if and only if the 1-form is exact.
If is the cotangent bundle of a manifold , which is naturally identified with the phasespace of one particle on , and is the Hamiltonian, then the flow of the Hamiltonianvector field is the time flow of the physical system.