To the top

Page Manager: Webmaster
Last update: 9/11/2012 3:13 PM

Tell a friend about this page
Print version

Collective symplectic int… - University of Gothenburg, Sweden Till startsida
Sitemap
To content Read more about how we use cookies on gu.se

Collective symplectic integrators

Journal article
Authors Robert McLachlan
Klas Modin
Olivier Verdier
Published in Nonlinearity
Volume 27
Issue 6
Pages 1525-1542
ISSN 0951-7715
Publication year 2014
Published at Department of Mathematical Sciences, Mathematics
Pages 1525-1542
Language en
Links arxiv.org/abs/1308.6620
dx.doi.org/10.1088/0951-7715/27/6/1...
Subject categories Geometry, Numerical analysis

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

Page Manager: Webmaster|Last update: 9/11/2012
Share:

The University of Gothenburg uses cookies to provide you with the best possible user experience. By continuing on this website, you approve of our use of cookies.  What are cookies?