On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints

Details On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints

2010-04-08

arxiv.org/abs/1004.1248v1

SIGMA 6 (2010), 031, 12 pages

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2010.031

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.

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