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摘要: 研究了Lagrange系统的Lie对称性摄动与新型的非Noether绝热不变量. 列出了未受扰Lagrange系统的Lie对称性导致的Lutzky型精确不变量;基于力学系统的高阶绝热不变量的定义,研究在小扰动作用下Lagrange系统Lie对称性的摄动,得到了系统的一类Lutzky形式的绝热不变量.举例说明方法和结果的应用.
Abstract: The perturbation of Lie symmetries and new non-Noether adiabatic invariants for the Lagrangian system are studied. The exact invariants of Lutzky type arising f rom the Lie symmetries of Lagrangian system without perturbation are given. Base d on the definition of high-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for Lagrangian system under the action of smal l disturbances is investigated, and a type of Lutzky adiabatic invariants of the system are obtained. An example is given to illustrate the application of the m ethod and results.