Kirchhoff-Love约束下仿射刚体的经典动力学
On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints
摘要：
本文考虑在三维物理空间中运动的受Kirchhoff-Love约束的仿射刚体，当它在主体的二维中心平面中均匀变形时，它同时执行与该中心平面正交的一维振荡。对于极分解，我们得到的特殊解决方案的一般，强非线性运动方程的固定椭球。它还表明，这些解决方案是从概念上不同的双极（奇异值）分解较早获得的。
英文摘要：
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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