Perturbation to symmetries and adiabatic invariant of Birkhoffian systems with unilateral constraints
单面约束Birkhoff系统对称性的摄动与绝热不变量

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.