Suslov problem with the Klebsh-Tisserand potential

TL;DR

This paper investigates a nonholonomic mechanical system called the Suslov problem with the Klebsh-Tisserand potential, analyzing the topology of its level sets and describing the flow on these manifolds.

Contribution

It provides a detailed topological analysis of the level sets in the Suslov problem with the Klebsh-Tisserand potential, combining explicit construction and Poincaré-Hopf theorem insights.

Findings

Topology of level sets characterized

Flow dynamics on manifolds described

Explicit construction of level sets provided

Abstract

In this paper, we study a nonholonomic mechanical system, namely the Suslov problem with the Klebsh-Tisserand potential. We analyze the topology of the level sets defined by the integrals in two ways: using an explicit construction and as a consequence of the Poincar\'e-Hopf theorem. We describe the flow on such manifolds.