相空间中非完整力学系统的对称性与非Noether守恒量  

Non-Noether Conserved Quantities of Mechanical Systems with Nonholonomic Constraints in Phase Space

作　　者：张毅[1] 尚玫[2] 

机构地区：[1]苏州科技学院土木工程系,江苏苏州215011 [2]北京理工大学理学院,北京100081

出　　处：《苏州科技学院学报（自然科学版）》2007年第1期1-8,共8页Journal of Suzhou University of Science and Technology （Natural Science Edition）

基　　金：江苏省高校自然科学基金资助项目(04KJA130135);江苏省青蓝工程基金资助项目

摘　　要：在增广相空间中研究非完整约束力学系统的对称性与守恒量。建立了系统的运动微分方程;给出了系统的Noether对称性、Lie对称性和Mei对称性的判据;研究了三种对称性之间的关系;得到了相空间中非完整约束力学系统的两类非Noether守恒量——Hojman守恒量和Mei守恒量,研究了对称性和守恒量之间的内在关系。文末,举例说明结果的应用。This paper studies the symmetries and conserved quantities of mechanical systems with northolonomic constraints in extended phase space. The systematic differential equations of motion are established. The criteria for Noether symmetry, Lie symmetry and Mei symmetry are given, and the relations among three symmetries are researched. Two types of new non-Noether conserved quantities- Hojman quantity and Mei quantity,for the mechanical systems with nonholonomic constraints in phase space are obtained, and the intrinsic relations between symmetries and conserved quantities are explored. At the end of this paper, an example is given to illustrate the application of the results.

关 键 词：分析力学 非完整约束 对称性 守恒量 相空间 

分 类 号：O316[理学—一般力学与力学基础]