Open Access
VOL. 5 | 2004 Classical and Quantum Collective Dynamics of Deformable Objects: Symmetry and Integrability Problems
Jan J. Sławianowski

Editor(s) Ivaïlo M. Mladenov, Allen C. Hirshfeld

Geom. Integrability & Quantization, 2004: 81-108 (2004) DOI: 10.7546/giq-5-2004-81-108


Discussed is affine model of collective degrees of freedom of multi-particle systems or continuous media. The novelty of our approach is that it is not only kinematics, i.e. geometry of degrees of freedom, that is invariant under affine group, but rather we study affinely-invariant geodetic models of such affine systems. It is shown that the dynamics of bounded elastic vibrations may be encoded in such geodetic models in the very form of the kinetic energy expression. Some special solutions like the relative equilibria are discussed. We start with the general approach to group-theoretical degrees of freedom and then discuss peculiarities of the affine group and certain other groups underlying collective dynamics.


Published: 1 January 2004
First available in Project Euclid: 12 June 2015

zbMATH: 1318.70013
MathSciNet: MR2082296

Digital Object Identifier: 10.7546/giq-5-2004-81-108

Rights: Copyright © 2004 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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