曲率半径的复数求法

A curvature radius formula by using complex functions

利用平面自然坐标系中的速度、加速度的复数表示来推导运动曲线的曲率半径的表达式,并验证了该公式与传统的微分几何方法给出的结果一致.研究表明不需要借助任何几何图形的复数法可以很好地给出曲率半径的表达式.

We deduce the curvature radius formula of motion curve by using the complex representation of the velocity and acceleration vector in the planar natural coordinate system.Our formula agrees with the formula by using traditional differential geometric method.The result shows the complex function method,which needs not anything geometric picture,can deduce the curvature radius formula very well.