Lagrangian theoretical framework of dynamics of nonholonomic systems

作     者：LIANG LiFu HU HaiChang CHEN DeMin 

作者机构：College of Civil EngineeringHarbin Engineering UniversityHarbin 150001China Institute of Spacecraft System EngineeringChinese Academy of Space TechnologyBeijing 100086China College of Vehicle EngineeringBeijing Institute of TechnologyBeijing 100081China 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2007年第50卷第6期

页      面：766-778页

核心收录：

学科分类：08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10272034) the Research Fund for the Doctoral Program of Higher Education of China the Basic Research Foundation of Harbin Engineering University (Grant No. 20060217020) 

主　　题：generalized variational principle nonholonomic systems Chetaev’s model Vakonomic model the Lagrangian clas-sical relationship the Lagrangian theoretical framework 

摘      要：By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev s model,and thus Chetaev s model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.