Miguel Rodríguez-Olmos (University of Manchester)
In a previous seminar, I introduced the Lagrangian formalism for mechanics on Lie algebroids, and show how it generalizes the usual Lagrangian formalisms on tangent bundles, Lie algebras, or Atiyah sequences. In this seminar I will explain how one can introduce several equivalence relations among Lagrangian functions and how one can associate conserved Nöther quantities to one-parameter families of equivalent Lagrangians. If time allows I will also show how additional conserved quantities can be found which are not of Nöther type, related to the bi-Hamiltonian structure of the section generating the dynamics. This is a joint work with J.F. Cariñena.