Lie symmetrical perturbation and a new type of non-Noether adiabatic invariants for disturbed generalized Birkhoffian systems
Lie symmetrical perturbation and a new type of non-Noether adiabatic invariants for disturbed generalized Birkhoffian systems
复制标题
DOI：
10.1007/s11071-011-0051-1
复制
发表时间：
2011-05
影响因子：
5.6
通讯作者：
Wenan Jiang;Lin Li;Zhuangjun Li;Shaokai Luo
中科院分区：
文献类型：
--
作者：
Wenan Jiang;Lin Li;Zhuangjun Li;Shaokai Luo
对于具有小扰动作用的广义Birkhoff系统，给出了Lie对称扰动和一类新的非Noether绝热不变量。基于扰动广义Birkhoff系统在群的一般无穷小变换下的不变性，构造了系统的Lie对称扰动的判定方程.基于力学系统高阶绝热不变量的定义，通过对Lie对称扰动的研究，得到了扰动广义Birkhoff系统的一类新的非Noether绝热不变量.然后给出了一类新的非Noether型精确不变量，并在群的特殊无穷小变换下得到了非Noether型绝热不变量和精确不变量.最后通过一个实例说明了方法的应用和结果。
For a generalized Birkhoffian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariants are presented. On the basis of the invariance of disturbed generalized Birkhoffian system under general infinitesimal transformation of group, the determining equation of Lie symmetrical perturbation of the system is constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of non-Noether adiabatic invariants of a disturbed generalized Birkhoffian system is obtained by investigating the Lie symmetrical perturbation. Then, a new type of exact invariants of non-Noether type is given, furthermore adiabatic invariants and exact invariants of non-Noether type are obtained under the special infinitesimal transformation of group. Finally, an example is given to illustrate the application of the method and results.