弱非完整系统的Lagrange对称性与守恒量  

Lagrange symmetry and conserved quantity for a weakly nonholonomic system

作　　者：严斌[1] 张毅[2] 

机构地区：[1]苏州科技学院数理学院,江苏苏州215009 [2]苏州科技学院土木工程学院,江苏苏州215011

出　　处：《苏州科技学院学报（自然科学版）》2016年第1期17-22,共6页Journal of Suzhou University of Science and Technology （Natural Science Edition）

基　　金：国家自然科学基金资助项目(10972151;11272227)

摘　　要：研究弱非完整系统的Lagrange对称性与守恒量。首先,建立弱非完整系统对应的零次近似系统和一次近似系统的运动微分方程。其次,给出弱非完整系统的零次近似系统和一次近似系统的Lagrange对称性的定义与判据,并得到零次近似系统和一次近似系统的Lagrange对称性导致的守恒量的条件及其形式。最后,举例说明其结果的应用。This paper mainly investigated Lagrange symmetry and conserved quantity for a weakly nonholonomic system. Firstly, we provided the differential equations of motion for the zero-order approximate system and the first-order approximate system corresponding to the weakly nonholonomic system. Secondly, we offered the definitions and criteria of Lagrange symmetry for the zero-order approximate system and the first-order approximate system of the weakly nonholonomic system. Then the conditions under which the Lagrange symmetry leads to a conserved quantity were deduced and the form of the conserved quantity was obtained. Finally, an example was given to illustrate the application of the results.

关 键 词：弱非完整系统 近似系统 Lagrange对称性 守恒量 

分 类 号：O316[理学—一般力学与力学基础]