arXiv 1310.21312013-10-06math-phmath.DSmath.MP

广义李代数体框架下的力学系统

Mechanical Systems in the Generalized Lie Algebroids Framework

Constantin M. Arcus

备注：: 43 pages International journal of Geometric Methods in Modern Physics, 2013. arXiv admin note: substantial text overlap with arXiv:1108.2844, arXiv:1007.1541, arXiv:1109.1242, arXiv:1101.0960, arXiv:1108.5050

摘要：

给出了使用时调用的\emph{Mechanical systems}、\emph{mechanical} $\left(ρ,η\right) $ \emph{-systems, Lagrange mechanical} $\left(ρ,η\right) $ \emph{-systems}或\emph{Finsler mechanical} $\left(ρ,η\right) $ \emph{-systems}。获得了与机械$\left(ρ,η\right) $系统相关联的规范$\left(ρ,η\right) $ \emph{-}半（喷雾）。在李代数胚的特殊情况下得到了新的重要结果。拉格朗日力学$(ρ,η)$ % -系统是发展新的拉格朗日形式主义所必需的空间。我们得到了正则拉格朗日量$L$和外力$F_{e}$的$(ρ,η)$ -半映射，并导出了Euler-Lagrange型方程.因此，在广义李代数胚的一般框架下给出了Weinstein问题的一个新的解。

英文摘要：

\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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摘要：

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