非完整系统的形式不变性与Hojman守恒量  

Form invariance and Hojman conserved quantity for nonholonomic mechanical systems

作　　者：罗绍凯[1,2] 郭永新[3] 梅凤翔[4] 

机构地区：[1]浙江理工大学数学力学与数学物理研究所 [2]长沙大学数学力学与数学物理研究所,长沙410003 [3]辽宁大学物理系 [4]北京理工大学理学院

出　　处：《物理学报》2004年第8期2413-2418,共6页Acta Physica Sinica

基　　金：国家自然科学基金 (批准号 :10 3 72 0 5 3 ;10 2 72 0 2 1);湖南省自然科学基金 (批准号 :0 3JJY3 0 0 5 );湖南省教育厅科研基金 (批准号 :0 2C0 3 3 )资助的课题~~

摘　　要：研究非完整力学系统的形式不变性导致的非Noether守恒量———Hojman守恒量 .在时间不变的特殊无限小变换下 ,给出非完整系统形式不变性的确定方程、约束限制方程和附加限制方程 ,提出并定义弱 (强 )形式不变性的概念 .研究特殊形式不变性导致特殊Lie对称性的条件 ,由系统的特殊形式不变性 ,得到相应完整系统的Hojman守恒量以及非完整系统的弱Hojman守恒量和强Hojman守恒量 .A non Noether conserved quantity, i.e. Hojman conserved quantity,constructed by using a form invariance for the nonholonomic mechanical systems is presented. Under special infinitesimal transformations in which the time is not changed, the determining equations of the special form invariance, the constrained restriction equations, the additional restriction equations, and the definitions of the weak form invariance and the strong form invariance of the nonholonomic mechanical systems are given. The condition under which the special form invariance is a special Lie symmetry are obtained. From the special form invariance, the Hojman conserved quantity of the corresponding holonomic systems, the weak Hojman conserved quantity and the strong Hojman conserved quantity of the nonholonomic systems are obtained. And two examples are given to illustrate the application of the result.

关 键 词：分析力学 非完整系统 形式不变性 非NOETHER守恒量 HOJMAN守恒量 

分 类 号：O313[理学—一般力学与力学基础]