On the regular reduction of the \(n\)-dimensional problem of \(N+1\) bodies to Euler-Poincaré equations on the Lie algebra \(sp(2N)\)
type: Item
instance of: scholarly article
title: On the regular reduction of the \(n\)-dimensional problem of \(N+1\) bodies to Euler-Poincaré equations on the Lie algebra \(sp(2N)\)
zbMATH Open document ID: 1011.70011
published in: Regular and Chaotic Dynamics
publication date: 2003-02-24T00:00:00Z
full work available at URL: https://eudml.org/doc/158500
review text: The title reduction is performed by the passage to the complete set of invariants of the action of linear group of rotations and reflections on the phase space \(T^\ast {\mathbb{R}}^n\otimes {\mathbb{R}}^N\). In contrast to known reductions, the reduction proposed is homeomorphic. For \(N+1=3\), \(n=3,2\), the orbits of the coadjoint representation of group \(Sp(4)\) on which real motions take place, have the homotopy type of the projective space \({\mathbb{R}}P^3\), the sphere \(S^3\), and the homogeneous space \((S^2 \times S^1)/{\mathbb{Z}}_2\).
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 70G65
zbMATH DE Number: 1873412
zbMATH Keywords: \(n\)-body problem
zbMATH Keywords: linear group
zbMATH Keywords: symplectic leaves
zbMATH Keywords: Euler-Poincare equation
zbMATH Keywords: Lie group
zbMATH Keywords: rotations
zbMATH Keywords: reflections
zbMATH Keywords: phase space
zbMATH Keywords: coadjoint representation
zbMATH Keywords: homotopy
zbMATH Keywords: projective space
zbMATH Keywords: sphere
zbMATH Keywords: homogeneous space
author: S. T. Sadètov
reviewed by: I. A. Taimanov
MaRDI profile type: Publication
DOI: 10.1070/RD2002V007N03ABEH000216
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description: scientific article; zbMATH DE number 1873412