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We develop Hamilton-Jacobi theory for Chaplygin systems, a certain class ofnonholonomic mechanical systems with symmetries, using a technique calledHamiltonization, which transforms nonholonomic systems into Hamiltoniansystems. We give a geometric account of the Hamiltonization, identify necessaryand sufficient conditions for Hamiltonization, and apply the conventionalHamilton-Jacobi theory to the Hamiltonized systems. We show, under a certainsufficient condition for Hamiltonization, that the solutions to theHamilton-Jacobi equation associated with the Hamiltonized system also solve thenonholonomic Hamilton-Jacobi equation associated with the original Chaplyginsystem. The results are illustrated through several examples.

Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization