Hamilton–Jacobi theory for nonholonomic and forced hybrid mechanical systems

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 utilized to describe the dynamics of a mechanical system with impacts. Based on the approach by Clark [Invariant measures, geometry and control of hybrid and nonholonomic dynamical systems, Ph.D thesis, University of Mirchigan (2020)], 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.