具有单面完整约束的有多余坐标 力学系统的Lie对称性与守恒量

Lie Symmetries and Conserved Quantities of Mechanical Systems of Remainder Coordinates with Unilateral Holonomic Constraints

研究具有单面完整约束的有多余坐标力学系统的Ｌｉｅ对称性与守恒量。利用常微分方程在无限小变换下的不变性，建立了系统Ｌｉｅ对称性的确定方程、限制方程和附加限制方程，得到了结构方程与守恒量的形式；并研究了上述问题的逆问题，即根据系统的已知积分来求相应的Ｌｉｅ对称性。文末举例说明结果的应用。

This paper studies the Lie symmetries and the conserved quantities of unilateral holonomic mechanical systems with remainder coordinates. Using the invariance of ordinary differential equations under the infinitesimal transformations, the author establishes the determining equations, restriction equations, additional restriction equations of the Lie symmetries of the systems and obtains the structure equations and the form of conserved quantities. Meanwhile, the paper discusses the inverse problem of the above, i.e., finding the corresponding Lie symmetry according to a given integral of the systems. In the end of the paper, an example is given to illustrate the application of the results.