A hybrid system is a system whose dynamics are controlled by a mixture of
both continuous and discrete transitions. The geometric framework for the
Hamilton-Jacobi theory is developed to study this theory for hybrid dynamical
systems, in particular, forced and nonholonomic hybrid systems. We state the
corresponding Hamilton-Jacobi equations for these classes of systems and apply
our results to analyze some examples. We give special attention to the
integrability of nonholonomic hybrid systems via the Hamilton-Jacobi theory.
The major advantage of our result is that it provides us with a method of
integrating the equations of motion just as the unconstrained and unforced
Hamilton-Jacobi theory does.