有挠空间中的约束系统与分析力学
Constrained Systems and Analytical Mechanics in Spases with Torsion
摘要：
讨论了一个具有非完整约束的系统，其中物理自由度的轨迹在一个具有一般Cartan联络的流形上是自平行的。从非完整约束系统的d 'Alambert-Lagrange原理出发，导出了自平行轨道的变分原理。给出了变分原理的一个几何（与坐标无关）公式。建立了它与耗散系统的Sedov非完整变分原理和非完整参考系中的Poincaré变分原理的关系。本文研究了由于扭转力而引起的Noether定理的一个修正。提出了一种极值包含自平行线的非局部作用量。该作用可以通过添加以特殊方式耦合到原始变量的辅助自由度来局部化。
英文摘要：
A system with anholonomic constraints where the trajectories of physical degrees of freedom are autoparallels on a manifold equipped with a general Cartan connection is discussed. A variational principle for the autoparallel trajectories is derived from the d'Alambert-Lagrange principle for anholonomic constrained systems. A geometrical (coordinate-independent) formulation of the variational principle is given. Its relation to Sedov's anholonomic variational principle for dissipative systems and to Poincaré's variational principle in anholonomic reference frames is established. A modification of Noether's theorem due to the torsion force is studied. A non-local action whose extrema contain the autoparallels is proposed. The action can be made local by adding auxiliary degrees of freedom coupled to the original variables in a special way.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
