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Collective Lie-Poisson integrators on R3

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Authors Klas Modin
Publication year 2013
Published at Department of Mathematical Sciences, Mathematics
Language en
Links arxiv.org/abs/1307.2387
Subject categories Geometry, Numerical analysis

Abstract

We develop Lie--Poisson integrators for general Hamiltonian systems on $\R^{3}$ equipped with the rigid body bracket. The method uses symplectic realisation of $\R^{3}$ on $T^{*}\R^{2}$ and application of symplectic Runge--Kutta schemes. As a side product, we obtain simple symplectic integrators for general Hamiltonian systems on the sphere $S^{2}$.

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