Hamilton-Jacobi theory for nonholonomic and forced hybrid mechanical systems

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.

arXiv comment31 pages, accepted for publication on Geometric Mechanics

References in corpus (7)

• Geometric Hamilton-Jacobi Theory
• Nonholonomic Hamilton-Jacobi equation and Integrability
• Symmetries and periodic orbits in simple hybrid Routhian systems
• Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities
• A Hamilton-Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds
• Geometric Hamilton-Jacobi theory for systems with external forces
• A new perspective on nonholonomic brackets and Hamilton-Jacobi theory