散度、旋度、梯度的力学模型

A Mechanical Model on Divergence, Curl and Gradient

本文建立了散度、旋度、梯度的力学模型。在所考察的场中置入一个小薄壳空心球,把场看作为作用于小球的力场。于是矢量场的散度对应于小球受力膨胀时的球内等效附加压强,矢量场的旋度对应于小球受力旋转时的角加速度矢量,标量场的梯度对应于小球受力时的加速度矢量。最后举例说明了此模型的应用。

An unific model on divergence, curl and gradient is designed in this paper, Put a Small hollow ball into an explored field. We regard it as a field of force acting on the small hollow ball. Therefore, the divergence of a vector field corresponds to an equivalent additional pressure in the hollow ball as the ball is expanding for it experi ences the force of the field, the curl of a vector field corresponds to a vector of angular acceleration of the ball as the ball is rotating for it experiences the force of the field, the gradient of a scalar field corresponds to a vector of accelearation of the ball as the ball experiences the force of the field. Finally, Some instances illustrating the application of the model are cited.