Collective symplectic integrators
Journal article, 2014

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 $\mathfrak{so}(3)^*$ . 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.


Robert McLachlan

Massey University

Klas Modin

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Olivier Verdier

University of Bergen


0951-7715 (ISSN)

Vol. 27 6 1525-1542

Subject Categories

Computational Mathematics



Basic sciences



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