Towards a Hamilton-Jacobi Theory for Nonholonomic Mechanical Systems

TL;DR

This paper develops a Hamilton-Jacobi theoretical framework specifically for nonholonomic mechanical systems, with a focus on caplygin systems, enhancing the understanding of their dynamics.

Contribution

It introduces a Hamilton-Jacobi theory tailored for nonholonomic systems, extending classical methods to a broader class of mechanical models.

Findings

Established a Hamilton-Jacobi formulation for caplygin systems

Applied the theory to various nonholonomic systems

Provided insights into the integrability of these systems

Abstract

In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical systems. The results are applied to a large class of nonholonomic mechanical systems, the so-called \v{C}aplygin systems.