广义经典力学系统对称性的摄动与绝热不变量  

Perturbation to symmetries and adiabatic invariant for systems of generalized classical mechanics

作　　者：张毅[1] 梅凤翔[2] 

机构地区：[1]苏州科技学院土木工程系,苏州215011 [2]北京理工大学应用力学系,北京100081

出　　处：《物理学报》2003年第10期2368-2372,共5页Acta Physica Sinica

基　　金：国家自然科学基金 (批准号 :19972 0 10 );江苏省青蓝工程基金资助的课题~~

摘　　要：在高维增广相空间中研究广义经典力学系统的精确不变量和绝热不变量 .建立了该空间中系统的对称性与不变量的关系 ;基于力学系统受到小干扰力作用的高阶绝热不变量的概念 ,给出了系统的高阶绝热不变量的形式及存在条件 ,并建立了绝热不变量与对称变换之间的对应关系 ;最后 。This paper studies the exact invariants and the adiabatic invariants for systems of generalized classical mechanics in the high-dimensional extended phase space and gives the relations between the invariants and the symmetries of the systems in the space. Based on the concept of high-order adiabatic invariant of mechanical systems with the action of small disturbance, it presents the form of the high-order adiabatic invariant and the conditions for their existence, and establishes the relationship between adiabatic invariant and symmetrical transformation. In the end of this paper, an example is given to illustrate the application of the results.

关 键 词：广义经典力学系统 对称性 摄动 绝热不变量 高维增广相空间 

分 类 号：O316[理学—一般力学与力学基础]