相空间中非完整可控力学系统的对称性摄动与绝热不变量

研究相空间中非完整可控力学系统的对称性摄动与绝热不变量. 列出相空间中未受扰非完整可控力学系统的形式不变性导致的Noether守恒量. 基于力学系统高阶绝热不变量的定义，研究小扰动作用下相空间中非完整可控力学系统的形式不变性摄动与绝热不变量，给出了精确不变量与绝热不变量存在的条件与形式，并举例说明结果的应用.

Perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical system in phase place

This paper studies the perturbation to symmetries and the adiabatic invariant for nonholonomic controllable mechanical system in the phase space. The exact invariants introduced by the form invariance of the nonholonomic controllable mechanical system in phase space without perturbation are given. Based on the definition of high-order adiabatic invariants of the mechanical system, the perturbation to symmetries and the adiabatic invariant for nonholonomic controllable mechanical system in phase space under the action of small disturbance is investigated, then the form of high-order adiabatic invariants and the conditions for their existence are presented. An example is finally given to illustrate the application of the results.