We give a wide class of Lie-Poisson systems for which explicit, Lie-Poisson integrators, preserving all Casimirs, can be constructed. The integrators are extremely simple and have widespread applicability. Examples are the free rigid body, a moment truncation, and a new, fast algorithm for the sine-bracket truncation of the 2D Euler equations.
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Robert I. McLachlan (1993) studied this question.
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