摘要
本文在增广相空间中研究力学系统的对称性与不变量．基于增广相空间中的Ｈａｍｉｌｔｏｎ作用泛函在无穷小变换群的作用下的不变性，我们给出了力学系统相应的不变量，相应的结论被推广到非保守和非完整力学系统．我们还得到了有关结论的逆命题．文章最后，我们讨论了著名的Ｅｍｄｅｎ方程及Ｈａｍｅｌ－Ａｐｐｅｌｌ问题的不变量．
The symmetry and invariant for dynamical system in the extended plase space are researched in this paper. We get the dynamical invariants corresponding to the Hamilton's action is inwariantal under the infinitesimal transformations,and extend these to nonholonomic and nonconservative system. We have those the converse proposition. Finally, We discuss the famous Emdent's equation and the Hamel-Appell problem.
基金
国家自然科学基金
青年基金
