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Collective Lie-Poisson integrators on $\mathbf{R}^{3}$ (1307.2387v2)
Published 9 Jul 2013 in math.NA, math-ph, math.MP, and math.SG
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 $T{*}\mathbf{R}{2}$ and application of symplectic Runge-Kutta schemes. As a side product, we obtain simple symplectic integrators for general Hamiltonian systems on the sphere $S{2}$.