# Manchester Geometry Seminar 2008/2009

**Thursday 23 October 2008. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4pm*
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Gauge Equivalence and Conserved Quantities for Lagrangian Systems on Lie Algebroids

Miguel Rodríguez-Olmos (University of Manchester)

`miguel.rodriguez.olmos@gmail.com`

Lie algebroids generalize several geometric objects such as tangent bundles, Lie algebras or Atiyah sequences. It is possible to give a geometric formalism of Lagrangian mechanics on Lie algebroids that specializes to the usual Euler-Lagrange, Euler-Poincaré, or Wong equations for the above particular cases. In this talk we will introduce this formalism and will study the notions of gauge and dynamical equivalence for Lagrangian systems as well as their relationship with Nöther conserved quantities.