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**Almost Poisson integration of rigid body systems.**
*(English)*
Zbl 0782.70001

The authors discuss the numerical integration of Lie-Poisson systems using the mid-point rule. Such systems result from the reduction of Hamiltonian systems with symmetry by Lie group actions. They also present examples of reconstruction rules for the full dynamics. A primary motivation is to preserve in the integration process various conserved quantities of the original dynamics. A main result of this paper is an \(O(h^ 3)\) error estimate for the Lie-Poisson structure, where \(h\) is the integration step size. The authors note that Lie-Poisson systems appear naturally in many areas of physical science and engineering, including theoretical mechanics of fluids and plasmas, satellite dynamics, and polarization dynamics. They consider a progressively complicated series of examples related to rigid body systems. They also consider a dissipative example associated to a Lie-Poisson system. The behavior of the mid-point rule and an associated reconstruction rule is numerically explored.

Reviewer: Michael Sever (Jerusalem)