Lagrangian theoretical framework of dynamics of nonholonomic systems |
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Authors: | Liang LiFu Hu HaiChang Chen DeMin |
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Institution: | 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 |
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Abstract: | 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.
Supported by the National Natural Science Foundation of China (Grant No. 10272034), the Research Fund for the Doctoral Program
of Higher Education of China and the Basic Research Foundation of Harbin Engineering University (Grant No. 20060217020) |
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Keywords: | generalized variational principle nonholonomic systems Chetaev's model Vakonomic model the Lagrangian classical relationship the Lagrangian theoretical framework |
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