Motion of test bodies with internal degrees of freedom in non-Euclidian spaces

TL;DR

This paper explores the mechanics of bodies with internal degrees of freedom in non-Euclidean spaces, introducing a new analysis method using non-holonomic frames and providing examples of integrable models.

Contribution

It presents a novel approach to analyze objects with internal structure in curved spaces, expanding the understanding of their geometric and mechanical properties.

Findings

Geometric peculiarities of non-Euclidean mechanics are detailed.

A new analysis method based on non-holonomic frames is developed.

Examples of integrable models are provided.

Abstract

Discussed is mechanics of objects with internal degrees of freedom in generally non-Euclidean spaces. Geometric peculiarities of the model are investigated detailly. Discussed are also possible mechanical applications, e.g., in dynamics of structured continua, defect theory and in other fields of mechanics of deformable bodies. Elaborated is a new method of analysis based on non-holonomic frames. We compare our results and methods with those of other authors working in nonlinear dynamics (many of them refer to our papers [20], [21], [49], [50]). Simple examples of completely integerable models are presented.