Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems  

作　　者：张明江 方建会 路凯 张克军 李燕 

机构地区：[1]College of Physics Science and Technology,China University of Petroleum

出　　处：《Chinese Physics B》2009年第11期4650-4656,共7页中国物理B（英文版）

基　　金：Project supported by the Graduate Students Innovative Foundation of China University of Petroleum (East China) (Grant NoS2009-19)

摘　　要：This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non- conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invaxiance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non- conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invaxiance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.

关 键 词：conformal invariance conserved quantity third-order Lagrange equation non-conserved mechanical system 

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