Austin, Mark A.; Krishnaprasad, P. S.; Wang, Li-Sheng Almost Poisson integration of rigid body systems. (English) Zbl 0782.70001 J. Comput. Phys. 107, No. 1, 105-117 (1993). 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) Cited in 29 Documents MSC: 70-08 Computational methods for problems pertaining to mechanics of particles and systems 65L05 Numerical methods for initial value problems involving ordinary differential equations 65K10 Numerical optimization and variational techniques Keywords:Lie-Poisson systems; mid-point rule; Hamiltonian systems PDFBibTeX XMLCite \textit{M. A. Austin} et al., J. Comput. Phys. 107, No. 1, 105--117 (1993; Zbl 0782.70001) Full Text: DOI Link