# nLab Hamilton's equations

Contents

### Context

#### Symplectic geometry

symplectic geometry

higher symplectic geometry

# Contents

## Idea

The equation of motion as expressed in Hamiltonian mechanics.

Given a phase space represented by a symplectic manifold $(X,\omega)$, and given a Hamiltonian function $H \colon X \longrightarrow \mathbb{R}$ the solutions to the equations of motion are trajectories $\gamma \colon \mathbb{R} \longrightarrow X$ which satisfy

$\mathbf{d} H(-) = \omega(\dot \gamma,-) \,,$

hence which are flow lines of the flow induced by the Hamiltonian vector field associated with $H$.

## References

Last revised on September 12, 2018 at 10:51:35. See the history of this page for a list of all contributions to it.