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.
Keywords: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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