Hamilton-Jacobi Framework for Nonholonomic Dynamics

We derive generalized Hamilton–Jacobi equations for dynamical systems subject to nonholonomic constraints. The geometric formulation of Hamilton-Jacobi theory for nonholonomic constraints is developed, following the ideas of the authors in previous papers. It is shown that the equations of motion which follow from the principle of d’Alembert are identical to the equationswhich follow from the variational action principle. To illustrate the effectiveness of the proposed framework, we present and analyze two illustrative examples: the motion of a rolling disk on a horizontal plane and the motion of a knife edge on an inclined plane.