再论Vacco模型与Chetaev模型之间的关系

借鉴国内外多位知名学者对线性微分约束可积性条件的论证，论证了非线性微分约束的可积性条件，按照Ｖａｃｃｏ模型的方法来处理问题，应用氏乘子法，将非线性非完整约束方程纳入Ｈａｍｉｌｔｏｎ原理的泛函中，经变分运算，并统一泛函变分式中的含义，导出Ｃｈｅｔａｅｖ模型的结果，从而实现了Ｖａｃｃｏ模型向Ｃｈｅｔａｅｖ模型的过渡，并将这一结果退化到线性非完整系统。文章还论证了，正像线性系统是非线性系统的特例一样，完整系统也是非完整系统的一个特例。通过对非完整约束方程的变分式应用可积性条件，推导出Ｃｈｅｔａｅｖ条件；并且指出，如此应用可积条件，不会使非完整系统变为完整系统。

Further Study of the Relationship Between Vacco Model and Chetaev's Model

By using the proof of integrable conditions of linear nonholonomic systems for reference,the integrable conditions of nonlinear nonholonomic systems were proved in this paper.According to Vacco model,by using Lagrangian multiplier method and by unifying the meaning of the variables,the results of Chetaev's model were derived.The transition from Vacco model to Chetaev's model was realized.By using integrable conditions for nonholonomic systems,the Chetaev's condition was derived.The work of this paper shows that holonomic system is a special case of nonholonmic system,as linear system is a special case of nonlinear system.