In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundness of the approach.
This work has been partially supported by MEC (Spain) Grants MTM 2004-7832, BFM2003-
01319 and BFM2003-02532.
Peer reviewed