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.
symplectic realization
Lie-Poisson manifold
rigid body bracket
Cayley-Klein parameters
Hopf fibration
symplectic Runge-Kutta
Clebsch variables
Poisson integrator
collective Hamiltonian
Author
Robert McLachlan
Massey University
Klas Modin
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Olivier Verdier
Universitetet i Bergen
IMA Journal of Numerical Analysis
0272-4979 (ISSN) 1464-3642 (eISSN)
Vol. 35 2 546-560Subject Categories (SSIF 2011)
Computational Mathematics
Geometry
Roots
Basic sciences
DOI
10.1093/imanum/dru013