  The purpose of this paper is describe Lagrangian Mechanics for constrained
systems on Lie algebroids, a natural framework which covers a wide range of
situations (systems on Lie groups, quotients by the action of a Lie group,
standard tangent bundles...). In particular, we are interested in two cases:
singular Lagrangian systems and vakonomic mechanics (variational constrained
mechanics). Several examples illustrate the interest of these developments.
