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Lagrangian mechanics on Lie algebroids. (English) Zbl 1002.70013
Summary: We give a geometric description of Lagrangian mechanics on Lie algebroids in a way parallel to the usual formalism of Lagrangian mechanics on the tangent bundle of a manifold. The dynamical system defined by a Lagrangian is shown to be symplectic in a generalized sense.

MSC:
70H03 Lagrange’s equations
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70G60 Dynamical systems methods for problems in mechanics
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