The Hess-Appelrot system and its nonholonomic analogs

TL;DR

This paper investigates the Hess-Appelrot system and its nonholonomic analogs, focusing on the existence of invariant measures with singular densities in the Suslov problem and Chaplygin's generalization.

Contribution

It analyzes the existence of invariant measures with singular densities in nonholonomic systems, extending understanding of their phase space properties.

Findings

Existence of invariant measures with singular densities identified

Analysis of singularities at specific phase space points

Insights into nonholonomic Suslov problem and Chaplygin's generalization

Abstract

This paper is concerned with the nonholonomic Suslov problem and its generalization proposed by Chaplygin. The issue of the existence of an invariant measure with singular density (having singularities at some points of phase space) is discussed.