散度、旋度和梯度在共同模式上的统一定义及其在一般坐标系中的应用

Unified Definition of Divergence,Curl and Gradient Based on a Common Model and It's Application in a General Coordinate System

本文在推广的散度定理的基础上给出了散度、旋度和梯度与坐标无关的统一定义。着重在一般曲线坐标系中利用以三对坐标面为包容面的微元体为共同模式,把散度、旋度和梯度统一表示为某一微分量的极限值,从而直接导出了张量分析中这三种量的熟知的表达式。

In this paper,the unified definition of divergence,curl and gradientindependent of the coordinate system is given by the extended divergencetheorem.Stressed on using a common model which is a volume elementenclosed by the three pairs of coordinate surfaces,all the divergence,curland gradient are denoted uniformly in the form of the limiting value of adifferential quantity.So the known expressions of these three quantities intensor analysis can be derived directly.