Collective Lie-Poisson integrators on ${\mathbf{R}}^3$

Abstract

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

15 pages, 3 figures

References in corpus (1)

• Geometric Generalisations of SHAKE and RATTLE

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• Collective symplectic integrators
• Geometry of discrete-time spin systems
• Clebsch Canonization of Lie-Poisson Systems
• Collective Heavy Top Dynamics
• Collective Symplectic Integrators on $S_2^N\times T^{\ast }{\mathbb{R}}^M$