论Четаев条件

On Chetayev's Conditions

迄今为止,人们普遍学用切塔耶夫(Четаев)条件获得广义坐标虚位移所满足的线性方程。本文用变分法有关条件极值问题的理论很自然地获得所需方程。这一方法对于δf_β=0和δ(?)=(d/dt)δq(?)均成立的一阶或任意阶非完整系统都是有效的。同时也给出了判断一个非完整系统是否具备上述条件的一个办法。将方法用于Appell-Hamel例,得到比用Четаев条件更为合理的结果。由此可见,Четаев条件不是十全十美的。

Up to now, Chetayev's condition has been adopted generally to obtain linear equations that virtual displacements of generalized coordinates satisfy. By use of the theory on problems of the conditioned extreme value in the calculus of variations, the desired equations are obtained guite naturally. This method is valid for one order or arbitrary order nonholonomic systems in which not only δ(?)=(d/dt)δq(?) but also δf_β=0 are tenable. A measure is given to determine whether the conditions mentioned above are coincident for a nonholonomic system. Applying this method to Appell-Hamel example, we have obtained more rational results than the one obtained with Chetayev's condition. It will be seen from this that Chetayev's conditions are not perfect in every way.