非完整系统的Noether对称性与Hojman守恒量  

Noether symmetry and Hojman conserved quantity for nonholonomic mechanical systems

作　　者：罗绍凯[1] 郭永新[2] 梅凤翔[3] 

机构地区：[1]浙江工程学院数学力学与数学物理研究所 [2]辽宁大学物理系,沈阳110036 [3]北京理工大学理学院,北京100081

出　　处：《物理学报》2004年第5期1271-1275,共5页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10372053;10272021);湖南省自然科学基金(批准号:03JJY3005);湖南省教育厅科研基金(批准号:02C033)资助的课题~~

摘　　要：研究非完整力学系统的Noether对称性导致的非Noether守恒量———Hojman守恒量 .在时间不变的特殊无限小变换下 ,给出系统的特殊Noether对称性与守恒量 ,并给出特殊Noether对称性导致特殊Lie对称性的条件 .由系统的特殊Noether对称性 ,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 .给出一个例子说明本结果的应用 .A non-Noether conserved quantity, i. e. Hojman conserved quantity constructed using the Noether symmetry for the nonholonomic mechanical system is presented. Under special infinitesimal transformations in which the time is not variable, the special Noether symmetry and Noether conserved quantity are given, and the condition under which the special Noether symmetry is a special Lie symmetry is obtained. From the special Noether symmetry, the Hojman conserved quantity of the corresponding holonomic system, the weakly Hojman conserved quantity and the strongly Hojman conserved quantity of the nonholonomic systems are obtained. An example is given to illustrate the application of the result.

关 键 词：分析力学 非完整系统 NOETHER对称性 非NOETHER守恒量 HOJMAN守恒量 广义坐标 

分 类 号：O316[理学—一般力学与力学基础]