Lagrange系统Lie点变换下的共形不变性与守恒量  

Conformal invariance and conserved quantity of Lagrange systems under Lie point transformation

作　　者：蔡建乐[1] 梅凤翔[2] 

机构地区：[1]杭州师范大学理学院,杭州310018 [2]北京理工大学理学院,北京100081

出　　处：《物理学报》2008年第9期5369-5373,共5页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10572021;10772025);高等学校博士学科点专项科研基金(批准号:20040007022)资助的课题~~

摘　　要：研究Lagrange系统Lie点变换下的共形不变性与守恒量,给出Lagrange系统的共形不变性定义和确定方程,讨论系统共形不变性与Lie对称性的关系,得到在无限小单参数点变换群作用下系统共形不变性同时是Lie对称性的充要条件,导出系统相应的守恒量,并给出应用算例.Conformal invariance and conserved quantities of Lagrange system under Lie point transformation are studied. Firstly, the definition of conformal invariance and determining equation for the Lagrange system are provided. Secondly, the relationship between the system＇s eonformal invariance and Lie symmetry are discussed; the necessary and sufficient condition on which the system＇ s conformal invarianee would be Lie symmetry under the infinitesimal one-parameter point transformation group is deduced; and the eonserved quantities of the system are given. Lastly, an illustration example is introduced.

关 键 词：LAGRANGE系统 Lie点变换 共形不变性 守恒量 

分 类 号：O316[理学—一般力学与力学基础] O174.51[理学—力学]