Year: 2014
Type: preprint
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 $ε$, this type of integrator can take $O(1)$ time steps with arbitrary accuracy in $ε$ 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.
Source: arXiv (Cornell University)
Authors: Burby, J. W., Ellison, C. L., Qin, H.
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2250170074