Dynamics of affinely deformable bodies from the standpoint of theoretical mechanics and differential geometry
type: Item
instance of: scholarly article
title: Dynamics of affinely deformable bodies from the standpoint of theoretical mechanics and differential geometry
zbMATH Open document ID: 1172.74005
DOI: 10.1016/S0034-4877(09)00003-2
published in: Reports on Mathematical Physics
publication date: 2009-03-25T00:00:00Z
review text: The article presents an overview of the geometrical structure of affinely deformable bodies, an intermediate situation between rigid and deformable bodies. The authors point out the links between various geometrical objects involved in these structures with the principal features of kinematics and dynamics. Two natural structures coexist in the configuration space of an affinely deformable body: a principal homogeneous space under the transitive action of an affine group, and a principal fiber bundle under the nontransitive action of Euclidean displacement group. These structures are connected by means of polar decomposition (extended from linear to affine maps), the former expresses the definition of affine deformability whereas the latter defines the rigid motions. The whole mechanics is developed in a canonical form using Lie groups, differential geometry of principal homogeneous spaces and principal fiber bundles endowed with a dynamic connection.
reviewed by: Juan Monterde
Mathematics Subject Classification ID: 74A99
Mathematics Subject Classification ID: 70E99
Mathematics Subject Classification ID: 70G45
Mathematics Subject Classification ID: 53Z05
zbMATH DE Number: 5532823
zbMATH Keywords: homogeneous spaces
zbMATH Keywords: fiber bundles
zbMATH Keywords: dynamic connection
Wikidata QID: Q115339930
author: A. A. Burov
author: D. P. Chevallier
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5532823