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A changing-chart symplectic algorithm for rigid bodies and other Hamiltonian systems on manifolds. (English) Zbl 1002.65136
The authors make use of the idea of constructing symplectic integrators for Hamiltonian flows on manifolds by covering the manifold with charts of an atlas, implementing the algorithm in each chart and switching among the charts whenever a coordinate singularity is approached. They use the method in solving two specific problems.

MSC:
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
70E17 Motion of a rigid body with a fixed point
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
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