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
symplectic realization
rigid body bracket
Lie-Poisson manifold
collective Hamiltonian
symplectic Runge-Kutta
Poisson integrator
Hopf fibration
Cayley-Klein parameters
Författare
Robert McLachlan
Massey University
Klas Modin
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Matematik
Olivier Verdier
Universitetet i Bergen
IMA Journal of Numerical Analysis
0272-4979 (ISSN) 1464-3642 (eISSN)
Vol. 35 2 546-560Ämneskategorier (SSIF 2011)
Beräkningsmatematik
Geometri
Fundament
Grundläggande vetenskaper
DOI
10.1093/imanum/dru013