
SIGMA 6 (2010), 031, 12 pages arXiv:1004.1248
http://dx.doi.org/10.3842/SIGMA.2010.031
Contribution to the Proceedings of the Eighth International Conference Symmetry in Nonlinear Mathematical Physics
On Classical Dynamics of AffinelyRigid Bodies Subject to the KirchhoffLove Constraints
Vasyl Kovalchuk
Institute of Fundamental Technological Research, Polish Academy of Sciences,
5^{B} Pawinskiego Str., 02106 Warsaw, Poland
Received November 13, 2009, in final form March 31, 2010; Published online April 08, 2010
Abstract
In this article we consider the affinelyrigid body moving in the threedimensional physical space and subject to the KirchhoffLove constraints, i.e., while it deforms homogeneously in the twodimensional central plane of the body it simultaneously performs onedimensional oscillations orthogonal to this central plane. For the polar decomposition we obtain the stationary ellipsoids as special solutions of the general, strongly nonlinear equations of motion. It is also shown that these solutions are conceptually different from those obtained earlier for the twopolar (singular value) decomposition.
Key words:
affinelyrigid bodies with degenerate dimension; KirchhoffLove constraints; polar decomposition; Green deformation tensor; deformation invariants; stationary ellipsoids as special solutions.
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