Numerical Integration of Lie-Poisson Systems while Preserving Coadjoint Orbits and Energy

In this paper we apply geometric integrators of the RKMK type to the problem of integrating Lie-Poisson systems numerically. By using the coadjoint action of the Lie group G on the dual Lie algebra$\mathprak{g}^\ast$to advance the numerical flow, we devise methods of arbitrary order that automatical...

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