Examples
Suppose that M is a 2n-dimensional symplectic manifold. Then locally, one may choose canonical coordinates (q1, ..., qn, p1, ..., pn) on M, in which the symplectic form is expressed as
where d denotes the exterior derivative and ∧ denotes the exterior product. Then the Hamiltonian vector field with Hamiltonian H takes the form
where Ω is a 2n by 2n square matrix
and
Suppose that M = R2n is the 2n-dimensional symplectic vector space with (global) canonical coordinates.
- If H = pi then
- if H = qi then
- if then
- if then
Read more about this topic: Hamiltonian Vector Field
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