变质量单面完整约束系统的Lie对称性与守恒量

Lie Symmetries and Conserved Quantities of Holonomic Systems of Variable Mass with Unilateral Constraints

研究变质量单面完整约束系统的Lie 对称性与守恒量. 首先利用微分方程在无限小群变换下的不变性建立了系统的Lie 对称性的确定方程,给出了结构方程和守恒量;其次研究了系统的Lie 对称性逆问题;最后举例说明结果的应用.

This paper studies Lie symmetries and conserved quantities of holonomic systems of variable mass with unilateral constraints. Firstly,it establishes the determining equations and the restriction equations of the Lie symmetries of the systems and it gives the structure equation and the conserved quantities,which are using the invariance of the ordinary differential equations under the infinitesimal transformations;Secondly,it studies the inverse problem of Lie symmetries of the systems;Finally,it gives an example to illustrate the application of the result.