Variational calculus on Lie algebroids

TL;DR

This paper develops a variational calculus framework on Lie algebroids, deriving Euler-Lagrange equations as critical points of an action functional, and explores reduction and Lagrange multiplier methods.

Contribution

It introduces a variational calculus approach on Lie algebroids, connecting Euler-Lagrange equations with reduction techniques and Lagrange multipliers.

Findings

Euler-Lagrange equations derived from action functional on Lie algebroids

Reduction theory for Lie algebroid systems studied

Relation with Lagrange multiplier method established

Abstract

It is shown that the Euler-Lagrange equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of reduction and the relation with Lagrange multiplier method are also studied.