相空间中单面完整约束系统的Lie对称性研究

目的 研究具有单面约束的完整系统在相空间中的Ｌｉｅ对称性与守恒量。方法 利用常微分方程在无限变换下的不变性，建立系统Ｌｉｅ对称性的确定方程和限制方程。结果与结论得到结构方程与守恒量形式，给出了Ｌｉｅ对称逆问题的解，并举例说明结果的应用。

Lie Symmetries of Holonomic Systems with Unilateral Constraints in Phase Space

Aim To study the Lie symmetries and the conserved quantities of holonomic systems with unilateral constraints in phase space. Methods The invariance of ordinary differential equations under the infinitesimal transformations was used to establish the determining equations and the restriction equations of the Lie symmetries of systems. Results and Conclusion The structure equations and the form of conserved quantities were obtained, and the solution of the inverse problem was presented. Two examples were given to illustrate the application of the results.