  In this article we develop a theory of contact systems with nonholonomic
constraints. We obtain the dynamics from Herglotz's variational principle, by
restricting the variations so that they satisfy the nonholonomic constraints.
We prove that the nonholonomic dynamics can be obtained as a projection of the
unconstrained Hamiltonian vector field. Finally, we construct the nonholonomic
bracket, which is an almost Jacobi bracket on the space of observables and
provides the nonholonomic dynamics.
