高阶非完整系统的共形不变性与Noether守恒量  

CONFORMAL INVARIANCE AND NOETHER CONSERVED QUANTITY OF HIGHER-ORDER NONHOLONOMIC SYSTEM

作　　者：李燕[1] 方建会[1] 张克军[1] 

机构地区：[1]中国石油大学物理科学与技术学院,东营257061

出　　处：《动力学与控制学报》2010年第4期300-304,共5页Journal of Dynamics and Control

基　　金：中央高校基本科研业务费专项资金资助(09CX04018A)~~

摘　　要：研究了高阶非完整系统的共形不变性与Noether守恒量,给出了与高阶非完整系统相应的完整系统的共形不变性的定义及其确定方程,通过系统共形不变性与Lie对称性的关系,推导出了系统运动方程具有共形不变性并且是Lie对称性的共形因子,利用限制方程和附加限制方程,给出了高阶非完整系统的弱Lie对称性和强Lie对称性的共形不变性,得到了共形不变性导致的Noether守恒量,举例说明了结果的应用.This paper studied the conformal invariance and conserved quantity of the holonomic system, which corresponds to a higher-order nonholonomic system. Firstly, the definition and determining equation of conformal invariance of the system were presented. The conformal factor, which is the necessary and sufficient condition that conformal invarlanee of the system would be Lie symmetry, was deduced from conformal invarianee and Lie symmetry. The conformal invariance of weak and strong Lie symmetry for the higher-order nonholonomic system was given using restriction equations and additional restriction equations. Secondly, the Noether conserved quan- tity of conformal invariance of the system was derived. Lastly, an example was given to illustrate the application of the results.

关 键 词：高阶非完整系统 共形不变性 NOETHER守恒量 

分 类 号：O316[理学—一般力学与力学基础]