A Survey of Lagrangian Mechanics and Control on Lie algebroids and   groupoids
  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. 
Jorge Cortes, Manuel de Leon, Juan C. Marrero, D. Martin de Diego and   Eduardo Martinez