On the control of stability of periodic orbits of completely integrable systems
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On the discretization of nonholonomic dynamics in $\mathbb{R}^n$
March 2015, 7(1): 81-108. doi: 10.3934/jgm.2015.7.81
Higher-order variational calculus on Lie algebroids
Eduardo Martínez 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.
Keywords: Lagrangian mechanics, Lie algebroids, higher order mechanics., Variational calculus.
Mathematics Subject Classification: 70H25, 70H30, 70H50, 37J15, 58K05, 70H03, 37K0.
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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Eduardo Martínez