Year: 2014
Type: article
Abstract: We construct symplectic integrators for Lie–Poisson systems. The integrators are standard symplectic (partitioned) Runge–Kutta methods. Their phase space is a symplectic vector space equipped with a Hamiltonian action with momentum map J whose range is the target Lie–Poisson manifold, and their Hamiltonian is collective, that is, it is the target Hamiltonian pulled back by J . The method yields, for example, a symplectic midpoint rule expressed in 4 variables for arbitrary Hamiltonians on . The method specializes in the case that a sufficiently large symmetry group acts on the fibres of J , and generalizes to the case that the vector space carries a bifoliation. Examples involving many classical groups are presented.
Source: Nonlinearity
Authors: Robert I McLachlan, Klas Modin, Olivier Verdier
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2019060281