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Variational calculus on Lie algebroids

Eduardo Martínez (2008)

ESAIM: Control, Optimisation and Calculus of Variations

It is shown that the Lagrange's 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 Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.

Vector form brackets in Lie algebroids

Albert Nijenhuis (1996)

Archivum Mathematicum

A brief exposition of Lie algebroids, followed by a discussion of vector forms and their brackets in this context - and a formula for these brackets in “deformed” Lie algebroids.

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