Affine Bodies Revisited. Constraints, Symmetry, Analytical Methods and Some Perspectives

TL;DR

This paper revisits the equations of motion for affinely rigid bodies in Euclidean space, emphasizing analytical methods, geometric structures, and invariance properties, while exploring future research directions.

Contribution

It provides a comprehensive analysis of the equations of motion for affinely rigid bodies, highlighting geometric and symmetry aspects, and discusses potential avenues for further development.

Findings

Derived equations of motion for affinely rigid bodies

Analyzed geometric structures and invariance properties

Outlined perspectives for future research

Abstract

The purpose of this publication is to derive and discuss equations of motion of affinely rigid (homogeneously deformable) body moving in Euclidean space of general dimension $n$. Our aim is to present some analytical methods and to discuss geometric structure and invariance properties of the theory. Some perspectives of further developments are also discussed.