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In this article we consider the affinely-rigid body moving in thethree-dimensional physical space and subject to the Kirchhoff-Love constraints,i.e., while it deforms homogeneously in the two-dimensional central plane ofthe body it simultaneously performs one-dimensional oscillations orthogonal tothis central plane. For the polar decomposition we obtain the stationaryellipsoids as special solutions of the general, strongly nonlinear equations ofmotion. It is also shown that these solutions are conceptually different fromthose obtained earlier for the two-polar (singular value) decomposition.

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