基于积分因子方法研究Chaplygin非完整系统的守恒律  

A STUDY OF CONSERVATION LAWS FOR CHAPLYGIN NONHOLONOMIC SYSTEMS BY MEANS OF INTEGRATING FACTORS METHOD

作　　者：张毅[1] Zhang Yi(College of Civil Engineering, Siizhou University of Science and Technology, Suzhou 215011 , China)

机构地区：[1]苏州科技大学土木工程学院,苏州215011

出　　处：《动力学与控制学报》2019年第1期15-20,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11572212;11272227)~~

摘　　要：提出并研究了构建Chaplygin非完整系统守恒律的积分因子方法.基于正则形式的Chaplygin方程,定义了积分因子,给出了系统存在守恒量的必要条件,建立了Chaplygin非完整系统的守恒定理及其逆定理.研究表明:对应于必要条件的每一组非奇异函数解,系统存在一个守恒量;反之,对于一个已知守恒量,可找到相应的积分因子,且解是不唯一的.文末以匀质圆球在粗糙水平面上纯滚动为例,讨论了该方法的应用.The method of integrating factors for the construction of conservation laws of a Chaplygin nonholonomic system is presented and studied. Based on the Chaplygin equations with canonical form, the integrating factors of the equations is defined, the necessary condition for the existence of conserved quantities of the system is given, and the conservation theorem and its inverse for the Chaplygin nonholonomic system are established. The studies show that for each group of nonsingular functions that correspond to the necessary condition, the system has a conserved quantity, while for a known conserved quantity, the corresponding integrating factor can be found, and the solution is not unique. Finally, we take an uniform sphere rolling on a perfectly rough horizontal plane as an example to discuss the application of the method.

关 键 词：非完整系统 Chaplygin方程 积分因子 守恒定理 逆定理 

分 类 号：O175[理学—数学]