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
symplectic realization
rigid body bracket
Lie-Poisson manifold
collective Hamiltonian
symplectic Runge-Kutta
Poisson integrator
Hopf fibration
Cayley-Klein parameters
Author
Robert McLachlan
Massey University
Klas Modin
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
Olivier Verdier
University of Bergen
IMA Journal of Numerical Analysis
0272-4979 (ISSN) 1464-3642 (eISSN)
Vol. 35 2 546-560Subject Categories
Computational Mathematics
Geometry
Roots
Basic sciences
DOI
10.1093/imanum/dru013