标题： 广义李代数丛上的拉格朗日力学 显示英文标题

标题： Lagrangian Mechanics on Generalized Lie Algebroids

摘要： 针对广义李代数束框架下的Weinstein问题的解决方案是本文的目标。 我们介绍了被称为机械系统（?; ?）-系统、拉格朗日机械（?; ?）-系统或芬斯勒机械（?; ?）-系统，并发展了它们的几何学。 我们得到了与机械（?; ?）-系统相关的规范（?; ?）-半喷射。 拉格朗日机械（?; ?）-系统是发展拉格朗日形式主义所必需的空间。 我们得到了与正则拉格朗日量L和外力Fe相关的（?; ?）-半喷射，并推导了欧拉-拉格朗日类型的方程。 特别是，利用李代数束的广义切丛，我们得到了Weinstein问题的新解。 显示英文摘要

摘要： A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or Finsler mechanical (?; ?)-systems and we develop their geometries. We obtain the canonical (?; ?)-semi(spray) associated to a mechanical (?; ?)-system. The Lagrange mechanical (?; ?)-systems are the spaces necessary to develop a Lagrangian formalism. We obtain the (?; ?)-semispray associated to a regular Lagrangian L and external force Fe and we derive the equations of Euler-Lagrange type. In particular, using the Lie algebroid generalized tangent bundle of a Lie algebroid, we obtain a new solution for the Weinstein's problem.