Almost Poisson integration of rigid body systems
type: Item
instance of: scholarly article
title: Almost Poisson integration of rigid body systems
zbMATH Open document ID: 0782.70001
author: Mark A. Austin
author: P. S. Krishnaprasad
author: Lisheng Wang
published in: Journal of Computational Physics
publication date: 1994-03-13T00:00:00Z
full work available at URL: http://hdl.handle.net/1903/5093
review text: 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.
reviewed by: Michael Sever
Mathematics Subject Classification ID: 70-08
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 404853
zbMATH Keywords: Lie-Poisson systems
zbMATH Keywords: mid-point rule
zbMATH Keywords: Hamiltonian systems
MaRDI profile type: Publication
OpenAlex ID: W2044078245
DOI: 10.1006/JCPH.1993.1128
description: scientific article; zbMATH DE number 404853