非完整系统动力学中的Vakonomic模型和Четаев模型

综述了非完整系统动力学中Чｅтａｅв模型和Ｖａｋｏｎｏｍｉｃ模型．论证了Ｈｅｒｔｚ，Ｃａｐｏｎ和Ｌｉｎｄｅｌｏｆ的工作与Ｖａｋｏｎｏｍｉｃ模型相吻合，而Ｈｏｌｄｅｒ，Ｐａｒｓ和Чаплыгин的工作与Четаев模型相吻合；Ｖａｋｏｎｏｍｉｃ模型和четаев模型两类模型并存的局面可以追溯到非完整力学发展的初期．说明了伴随两类模型并存的现象而出现的两个问题:ｄ－δ交换性问题和∫－δ交换性问题．综述了我国学者为统一两类模型作出的贡献．最后，展望了该领域的研究方向． 

THE VAKONOMIC MODEL AND CHETAEV'S MODEL IN ANALYTICAL DYNAMICS OF NONHOLONOMIC SYSTEMS

The Chetaev's model and Vakonomic model are described in this paper. It is proved that the model of Hertz, Capon and Lindelof are identical to Vakonomic model while the model of Holder, Pars and Chaplygin are identical to Chetaev's model. The fact that Vakonomic model and Chetaev's model exist simultanously can be traced back to the early days of non-holonomic mechanics. These two models cause two problems: the d-δ and ∫-δ permutable problems. A review of the contribution of scholars in China to unify these...