2014/05/07 by J. W. Burby, Burby, J. W., C. L. Ellison +5
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Magnetic confinement fusion research #Mathematical Physics (math-ph) #Numerical methods for differential equations #Quantum chaos and dynamical systems #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1405.1698
28 pages
arxiv created 2014/05/07 · openalex publication_date 2014/05/07 · arxiv updated 2014/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.