Hamiltonian vector field
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 phase space of one particle on , and is the Hamiltonian, then the flow of the Hamiltonian vector field is the time flow of the physical system.
|Title||Hamiltonian vector field|
|Date of creation||2013-03-22 13:14:07|
|Last modified on||2013-03-22 13:14:07|
|Last modified by||rspuzio (6075)|