Hamilton-Jacobi theory for nonholonomic and forced hybrid mechanical systems

TL;DR

This paper develops a geometric Hamilton-Jacobi framework for hybrid mechanical systems with impacts, combining continuous and discrete dynamics, and applies it to analyze specific examples.

Contribution

It introduces a Hamilton-Jacobi theory tailored for forced and nonholonomic hybrid systems, extending classical methods to systems with impacts.

Findings

Derived Hamilton-Jacobi equations for hybrid systems

Provided geometric framework for nonholonomic impacts

Analyzed examples demonstrating the theory's application

Abstract

A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical system with impacts. Based on the approach by Clark, we develop a geometric Hamilton-Jacobi theory for forced and nonholonomic hybrid dynamical systems. We state the corresponding Hamilton-Jacobi equations for these classes of systems and apply our results to analyze some examples.