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A minimal-variable symplectic integrator on spheres

Robert McLachlan ; Klas Modin (Institutionen för matematiska vetenskaper, matematik) ; Olivier Verdier
(2015)
[Preprint]

We construct a symplectic, globally defined, minimal coordinate, 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-Lifschitz 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.



Denna post skapades 2016-01-11.
CPL Pubid: 230385

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Geometri
Beräkningsmatematik

Chalmers infrastruktur