Dynamics of affinely deformable bodies from the standpoint of theoretical mechanics and differential geometry
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.
scientific article; zbMATH DE number 5532823
scientific article