准坐标下非完整力学系统的Lie对称性和守恒量

研究准坐标下非完整系统的Ｌｉｅ对称性，首先，对准坐标下非完整力学系统定义无限小变换生成元，由微分方程在无限小变换下的不变性，建立Ｌｉｅ对称性的确定方程，得到结构方程并求出守恒量；其次，研究上述问题的逆问题；根据已知积分求相应的Ｌｉｅ对称性，举例说明结果的应用。

Lie Symmetries and Conserved Quantities of Nonholonomic Mechanical Systems in Terms of Quasi-coordinates

This paper involves Lie symmetries and conservation laws of nonholnomic systems in terms of quasi-coordinates.We studied two kinds of problems on Lie symmetries and conserved quantities.One is the direct problem of Lie symmetriesfinding out the corresponding conserved quantity according to a given Lie symmetry.We gives the definition of the infiniteshmal generator for the nonholonomic systems in terms of quasi-coordinates.Using the invariance of the ordinary differential equations under the infinitesimal transformations,establishes the determining equations of the Lie symmetries.Obtains the structure equation and conserved quantities.The another kinds of problem is called the inverse problem of Lie symmetriesfind out the corresponding Lie symmetry according to a known conserved quantity.Gives an example to illustrate the application of the result.