Collective Lie-Poisson integrators on R3
Journal article, 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

Author

Robert McLachlan

Massey University

Klas Modin

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Olivier Verdier

University of Bergen

IMA Journal of Numerical Analysis

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

Vol. 35 2 546-560

Subject Categories

Computational Mathematics

Geometry

Roots

Basic sciences

DOI

10.1093/imanum/dru013

More information

Latest update

3/27/2018