Higher-order variational calculus on Lie algebroids

Eduardo Martínez

doi:10.3934/jgm.2015.7.81

Article Contents

2015, Volume 7, Issue 1: 81-108. Doi: 10.3934/jgm.2015.7.81

This issue Previous Article On the discretization of nonholonomic dynamics in $\mathbb{R}^n$ Next Article On the control of stability of periodic orbits of completely integrable systems

Higher-order variational calculus on Lie algebroids

Eduardo Martínez^1,

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

Received: July 31, 2014

Revised: December 31, 2014

Published: February 2015

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Abstract

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:

Mathematics Subject Classification: 70H25, 70H30, 70H50, 37J15, 58K05, 70H03, 37K05.

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