A minimal-variable symplectic integrator on spheres
Artikel i vetenskaplig tidskrift, 2017

© 2017 American Mathematical Society. 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.

Författare

Robert McLachlan

Massey University

Klas Modin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Olivier Verdier

Hogskolen i Bergen

Mathematics of Computation

0025-5718 (ISSN) 1088-6842 (eISSN)

Vol. 86 2325-2344

Ämneskategorier

Matematik

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

Styrkeområden

Livsvetenskaper och teknik

DOI

10.1090/mcom/3153