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