Force free conformal motions of the sphere.
type: Item
instance of: scholarly article
title: Force free conformal motions of the sphere.
zbMATH Open document ID: 1036.53026
DOI: 10.1016/S0926-2245(02)00061-X
author: Marcos Salvai
published in: Differential Geometry and its Applications
publication date: 2002-08-14T00:00:00Z
review text: The author studies force free motion of a nonrigid body on the \(n\)-sphere, equipped with its standard metric. Nonrigidness is described by the fact that two configurations differ by the action of an element of the conformal group \(G\) of the sphere. Following the methods described by \textit{V. I. Arnold} in ``Mathematical Methods of Classical Mechanics'', Springer, New York (1978; Zbl 0386.70001), the author associates to a distribution of mass on the sphere a Riemanniann metric on \(G\) in such a way that geodesics on \(G\) induce force free motions of the mass. He then gives properties of this metric. In particular \(G\) is not complete with respect to it.
reviewed by: Jean-François Quint
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 22E99
Mathematics Subject Classification ID: 70E15
Mathematics Subject Classification ID: 70G45
zbMATH DE Number: 1780876
zbMATH Keywords: force free motion
zbMATH Keywords: distribution of mass
zbMATH Keywords: conformal group
zbMATH Keywords: \(n\)-sphere
MaRDI profile type: Publication
Wikidata QID: Q115338220
cites work: Q4692311
cites work: Q3310101
cites work: Q4018677
cites work: Dynamical invariants of rigid motions on the hyperbolic plane
cites work: On the dynamics of a rigid body in the hyperbolic space
cites work: Q3956040
cites work: SOME REMARKS ON THE MOTION OF A RIGID BODY IN A SPACE OF CONSTANT CURVATURE WITHOUT EXTERNAL FORCES1
full work available at URL: s0926-2245(02)00061-x
OpenAlex ID: W2012632894
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description: scientific article; zbMATH DE number 1780876