# American Institute of Mathematical Sciences

March  2015, 7(1): 81-108. doi: 10.3934/jgm.2015.7.81

## Higher-order variational calculus on Lie algebroids

 1 IUMA and Department of Applied Mathematics, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain

Received  August 2014 Revised  January 2015 Published  March 2015

The equations for the critical points of the action functional defined by a Lagrangian depending on higher-order derivatives of admissible curves on a Lie algebroid are found. The relation with Euler-Poincaré and Lagrange Poincaré type equations is studied. Reduction and reconstruction results for such systems are established.
Citation: Eduardo Martínez. Higher-order variational calculus on Lie algebroids. Journal of Geometric Mechanics, 2015, 7 (1) : 81-108. doi: 10.3934/jgm.2015.7.81
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