Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 031, 12 pages      arXiv:1004.1248      https://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 Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints

Vasyl Kovalchuk
Institute of Fundamental Technological Research, Polish Academy of Sciences, 5B Pawinskiego Str., 02-106 Warsaw, Poland

Received November 13, 2009, in final form March 31, 2010; Published online April 08, 2010

Abstract
In this article we consider the affinely-rigid body moving in the three-dimensional physical space and subject to the Kirchhoff-Love constraints, i.e., while it deforms homogeneously in the two-dimensional central plane of the body it simultaneously performs one-dimensional 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 two-polar (singular value) decomposition.

Key words: affinely-rigid bodies with degenerate dimension; Kirchhoff-Love constraints; polar decomposition; Green deformation tensor; deformation invariants; stationary ellipsoids as special solutions.

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