Hamiltonization of solids of revolution through reduction

TL;DR

This paper explores how conserved quantities in nonholonomic systems can be used to achieve Hamiltonian descriptions, specifically for solids of revolution rolling without slipping, through geometric reduction techniques.

Contribution

It demonstrates a method to Hamiltonize nonholonomic systems with conserved quantities using gauge transformations and symmetry reduction.

Findings

Derived Poisson brackets for solids of revolution

Connected conserved quantities to Hamiltonian structure

Applied geometric methods to classical rolling problems

Abstract

In this paper we study the relation between conserved quantities of nonholonomic systems and the hamiltonization problem employing the geometric methods of [1,3]. We illustrate the theory with classical examples describing the dynamics of solids of revolution rolling without sliding on a plane. In these cases, using the existence of two conserved quantities we obtain, by means of 'gauge transformations' and symmetry reduction, genuine Poisson brackets describing the reduced dynamics.