A minimal-variable symplectic integrator on spheres
Journal article, 2017

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.


Robert McLachlan

Massey University

Klas Modin

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Olivier Verdier

Hogskolen i Bergen

Mathematics of Computation

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

Vol. 86 307 2325-2344

Subject Categories


Computational Mathematics


Basic sciences

Areas of Advance

Life Science Engineering (2010-2018)



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2/3/2020 9