The nonholonomic bracket on contact mechanical systems

In this paper we study contact nonholonomic mechanical sys-tems. We construct a general framework for non-holonomic constraints in contact geometry and, in this framework, we define different nonholonomic brackets using con-venient \linebreak decompositions of the tangent bundle of the phase space. \linebreak Furthermore, we prove that all of them coincide. In particular, one the brackets is a natural extension of that defined by R.J. Eden, but now it is an almost Jacobi bracket since it is not satisfy the Leibniz rule.