相对论Birkhoff系统的形式不变性与Noether守恒量  

Form Invariance and Noether Symmetrical Conserved Quantity of Relativistic Birkhoffian Systems

作　　者：罗绍凯[1] 

机构地区：[1]长沙大学数学力学与数学物理研究所

出　　处：《应用数学和力学》2003年第4期414-422,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(19972010);河南省自然科学基金(984053100;998040080);湖南省教育厅科研基金(02C033)

摘　　要：研究相对论Birkhoff系统的形式不变性,寻求系统的守恒量。在群的无限小变换下,给出相对论Birkhoff系统的形式不变性的定义和判剧。基于相对论Pfaff-Birkhoff-D’Alembert原理在群的无限小变换下的变形形式,建立相对论Birkhoff系统的Noether对称性理论。通过研究形式不变性与Noether对称性之间的关系,得到相对论Birkhoff系统的守恒量。研究结果表明:在一定的条件下,相对论Birkhoff系统的形式不变性导致Noether对称性的守恒量。A form invariance of the relativistic Birkhoffian system is studied,and the conserved quantities of the system are obtained. Under the infinitesimal transformation of groups, the definition and criteria of the form invariance of the system were given. In view of the invariance of relativistic Pfaff-Birkhoff-D' Alembert principle under the infinitesimal transformation of groups,the theory of Noether symmetries of the relativistic Birkhoffian system were constructed. The relation between the form invariance and the Noether symmetry is studied,and the results show that the form invariance can also lead to the Noether symmetrical conserved quantity of the relativistic Birkhoffian system under certain conditions.

关 键 词：相对论 BIRKHOFF系统 Pfaff-Birkhoff-D'Alembert原理 形式不变性 NOETHER对称性 守恒量 

分 类 号：O316[理学—一般力学与力学基础] O320[理学—力学]