Variational integrators for perturbed non-canonical Hamiltonian systems

Abstract

Finite-dimensional non-canonical Hamiltonian systems arise naturally from Hamilton's principle in phase space. We present a method for deriving variational integrators that can be applied to perturbed non-canonical Hamiltonian systems on manifolds based on discretizing this phase-space variational principle. Relative to the perturbation parameter $\epsilon$, this type of integrator can take $O(1)$ time steps with arbitrary accuracy in $\epsilon$ by leveraging the unperturbed dynamics. Moreover, these integrators are coordinate independent in the sense that their time-advance rules transform correctly when passing from one phase space coordinate system to another.

arXiv comment28 pages

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