Collective Lie-Poisson integrators on R3
Artikel i vetenskaplig tidskrift, 2015

We develop Lie–Poisson integrators for general Hamiltonian systems on ℝ3 equipped with the rigid body bracket. The method uses symplectic realization of ℝ3 on T*ℝ2 and application of symplectic Runge–Kutta schemes. As a consequence, we obtain simple symplectic integrators for general Hamiltonian systems on the sphere S2.

Clebsch variables

collective Hamiltonian

symplectic realization

Poisson integrator

Cayley-Klein parameters

Lie-Poisson manifold

symplectic Runge-Kutta

Hopf fibration

rigid body bracket

Författare

Robert McLachlan

Massey University

Klas Modin

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Olivier Verdier

Universitetet i Bergen

IMA Journal of Numerical Analysis

0272-4979 (ISSN) 1464-3642 (eISSN)

Vol. 35 2 546-560

Ämneskategorier

Beräkningsmatematik

Geometri

Fundament

Grundläggande vetenskaper

DOI

10.1093/imanum/dru013