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The purpose of this paper is describe Lagrangian Mechanics for constrainedsystems on Lie algebroids, a natural framework which covers a wide range ofsituations (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 constrainedmechanics). Several examples illustrate the interest of these developments.

Singular lagrangian systems and variational constrained mechanics on Lie algebroids