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 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.