Perturbation of symmetries and Hojman adiabatic invariants for Lagrangian system
Lagrange系统对称性的摄动与Hojman型绝热不变量

The perturbation of symmetries and adiabatic invariants for Lagrangian system are studied. The exact invariants introduced by the Lie symmetries of Lagrangian system without perturbation are given. Based on the definition of high-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for Lagrangian system with the action of small disturbance is investigated, and a type of Hojman adiabatic invariants of the system are obtained. An example is given to illustrate the application of the results.