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Hamilton's equations

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Symplectic geometry

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Idea

The equation of motion as expressed in Hamiltonian mechanics.

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

dH()=ω(γ˙,), \mathbf{d} H(-) = \omega(\dot \gamma,-) \,,

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

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.