Some multidimensional integrable cases of nonholonomic rigid body dynamics

TL;DR

This paper explores the dynamics of n-dimensional rigid bodies with constraints, reviewing known integrable cases in three dimensions and extending them to higher dimensions, thus broadening understanding of nonholonomic rigid body systems.

Contribution

It introduces higher-dimensional generalizations of known three-dimensional integrable cases in nonholonomic rigid body dynamics.

Findings

Review of known 3D integrable cases

Extension to higher dimensions

Identification of new integrable cases in n-dimensions

Abstract

In this paper we study the dynamics of the constrained $n$--dimensional rigid body (the Suslov problem). We give a review of known integrable cases in three dimensions and present their higher dimensional generalizations.