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A minimal-variable symplectic integrator on spheres

Journal article
Authors Robert McLachlan
Klas Modin
Olivier Verdier
Published in Mathematics of Computation
Volume 86
Pages 2325-2344
ISSN 0025-5718
Publication year 2017
Published at Department of Mathematical Sciences
Pages 2325-2344
Language en
Links https://doi.org/10.1090/mcom/3153
Subject categories Computational Mathematics

Abstract

We construct a symplectic, globally defined, minimal-variable, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems, include the reduced free rigid body, the motion of point vortices on a sphere, and the classical Heisenberg spin chain, a spatial discretisation of the Landau-Lifshitz equation. The existence of such an integrator is remarkable, as the sphere is neither a vector space, nor a cotangent bundle, has no global coordinate chart, and its symplectic form is not even exact. Moreover, the formulation of the integrator is very simple, and resembles the geodesic midpoint method, although the latter is not symplectic.

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