2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109982It is shown that the Euler-Lagrange equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of reduction and the relation with Lagrange multiplier method are also studied.Small changes. Corrected typosMathematical PhysicsDifferential GeometryOptimization and Control49S05;22A22text