  In this paper we study a Hamiltonization procedure for mechanical systems
with velocity-depending (nonholonomic) constraints. We first rewrite the
nonholonomic equations of motion as Euler-Lagrange equations, with a Lagrangian
that follows from rephrasing the issue in terms of the inverse problem of
Lagrangian mechanics. Second, the Legendre transformation transforms the
Lagrangian in the sought-for Hamiltonian. As an application, we compare some
variational integrators for the new Lagrangians with some known nonholonomic
integrators.
