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Collective Lie–Poisson integrators on R³
Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand.
Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden.
Department of Mathematics, University of Bergen, Bergen, Norway.ORCID iD: 0000-0003-3699-6244
2014 (English)In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642Article in journal (Refereed) Epub ahead of print
Abstract [en]

We develop Lie–Poisson integrators for general Hamiltonian systems on R³ equipped with the rigid body bracket. The method uses symplectic realisation of RR³ on T*R² and application of symplectic Runge–Kutta schemes. As a side product, we obtain simple symplectic integrators for general Hamiltonian systems on the sphere S².

Place, publisher, year, edition, pages
Oxford University Press, 2014.
Keyword [en]
Lie–Poisson manifold, Poisson integrator, rigid body bracket, collective Hamiltonian, symplectic Runge–Kutta, Hopf fibration, symplectic realization, Clebsch variables, Cayley–Klein parameters
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-79723DOI: 10.1093/imanum/dru013OAI: oai:DiVA.org:umu-79723DiVA: diva2:644132
Available from: 2013-08-29 Created: 2013-08-29 Last updated: 2017-12-06Bibliographically approved

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Publisher's full texthttp://arxiv.org/abs/1307.2387

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