  We introduce a method which allows one to recover the equations of motion of
a class of nonholonomic systems by finding instead an unconstrained Hamiltonian
system on the full phase space, and to restrict the resulting canonical
equations to an appropriate submanifold of phase space. We focus first on the
Lagrangian picture of the method and deduce the corresponding Hamiltonian from
the Legendre transformation. We illustrate the method with several examples and
we discuss its relationship to the Pontryagin maximum principle.
