# Manchester Geometry Seminar 2008/2009

**Thursday 19 March 2009.** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4pm*
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Symmetries and Noether Conservation Laws for Lagrangian Systems on Lie Algebroids

Miguel Rodríguez-Olmos (University of Manchester)

`miguel.rodriguez.olmos@gmail.com`

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.