Resumen
Two approaches for the study of mechanical systems with non-holonomic constraints are presented: d'Alembertian mechanics and variational (vakonomic) mechanics. The first one is equivalent to the d'Alembert principle and the second comes from a variational principle. In order to develop the two approaches, d'Alembertian and vakonomic trajectories are introduced. A generalized version of the classical Liouville theorem for the conservation of volume is proved in the context of d'Alembertian mechanics. A characterization for the notions of regular and singular curves is presented. The flow corresponding to the regular vakonomic trajectories is Hamiltonian.