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arXiv · 1405.1698

Variational integrators for perturbed non-canonical Hamiltonian systems

J. W. Burby·C. L. Ellison·H. Qin
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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.

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J. W. Burby, C. L. Ellison, H. Qin. 2014-05-07. Variational integrators for perturbed non-canonical Hamiltonian systems. https://arxiv.org/abs/1405.1698

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