Collective symplectic integrators
2014 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 27, no 6, 1525-1542 p.Article in journal (Refereed) Published
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 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.
Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2014. Vol. 27, no 6, 1525-1542 p.
symplectic integrators, Lie-Poisson systems, reduction
IdentifiersURN: urn:nbn:se:umu:diva-89403DOI: 10.1088/0951-7715/27/6/1525ISI: 000337159700020OAI: oai:DiVA.org:umu-89403DiVA: diva2:720446