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arXiv · 1310.2131

Mechanical Systems in the Generalized Lie Algebroids Framework

Constantin M. Arcus
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Abstract

\emph{Mechanical systems} called by use, \emph{mechanical}$\left(ρ,η\right) $\emph{-systems, Lagrange mechanical}$\left(ρ,η\right) $\emph{-systems} or \emph{Finsler mechanical}$\left(ρ,η\right) $\emph{-systems} are presented. The canonical $\left(ρ,η\right) $\emph{-}semi(spray) associated to a mechanical $\left(ρ,η\right) $-system is obtained. New and important results are obtained in the particular case of Lie algebroids. The Lagrange mechanical $(ρ,η)$% -systems are the spaces necessary to develop a new Lagrangian formalism. We obtain the $(ρ,η)$-semispray associated to a regular Lagrangian $L$ and external force $F_{e}$ and we derive the equations of Euler-Lagrange type. So, a new solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is presented.

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Constantin M. Arcus. 2013-10-06. Mechanical Systems in the Generalized Lie Algebroids Framework. https://arxiv.org/abs/1310.2131

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