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

TL;DR

This paper analyzes the classical dynamics of affinely-rigid bodies under Kirchhoff-Love constraints, deriving special solutions like stationary ellipsoids and highlighting differences from previous approaches.

Contribution

It introduces a new analysis of affinely-rigid bodies with Kirchhoff-Love constraints, deriving stationary solutions and contrasting polar and two-polar decompositions.

Findings

Stationary ellipsoids as solutions to nonlinear equations

Differences between polar and two-polar decomposition solutions

Insights into the dynamics of constrained affinely-rigid bodies

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.