单面约束Birkhoff系统对称性的摄动与绝热不变量

研究了具有单面约束的Birkhoff系统在小扰动作用下对称性的摄动与不变量之间的关系.首先,建立了系统的运动微分方程,给出了系统的精确不变量;其次,基于力学系统的高阶绝热不变量的概念,得到了系统的绝热不变量存在的条件及其形式;最后,举例说明结果的应用 关键词： 分析力学 单面约束 Birkhoff系统 对称性 摄动 绝热不变量

Perturbation to symmetries and adiabatic invariant of Birkhoffian systems with unilateral constraints

The relation between the invariant and the perturbation to symmetries of Birkhoffian systems with unilateral constraints under the action of small disturbance is studied. First, the differential equations of motion of the systems are established, and the exact invariant of the systems is obtained. Next, based on the concept of high order adiabatic invariant of mechanical systems, the form of the adiabatic invariant and the conditions for their existence are given; and finally, an example is given to illustrate the application of the results.