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Lagrangian theoretical framework of dynamics of nonholonomic systems

Science China(Physics,Mechanics & Astronomy) 2007年第6期50卷 766-778页

作者： LIANG LiFu1,HU HaiChang2 & CHEN DeMin3 1 College of Civil Engineering,Harbin Engineering University,Harbin 150001,China 2 Institute of Spacecraft System Engineering,Chinese Academy of Space Technology,Beijing 100086,China 3 College of Vehicle Engineering,Beijing Institute of Technology,Beijing 100081,China College of Civil Engineering Harbin Engineering University Harbin China Institute of Spacecraft System Engineering Chinese Academy of Space Technology Beijing China College of Vehicle Engineering Beijing Institute of Technology Beijing China

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.

关键词： generalized variational principle, nonholonomic systems, Chetaev's model, Vakonomic model, the Lagrangian classical relationship, the Lagrangian theoretical framework By the generalized variational principle of two kinds of variables in general mechanics, 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 Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships 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. ……

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