斜螺旋曲线的构造

The Construction of Slant Helices

斜螺旋曲线是指三维欧氏空间中主法向量场与一固定方向成固定角的曲线.研究斜螺旋曲线的构造.首先求解一个关于活动标架的线性常微分方程组,然后通过积分来确定斜螺旋曲线的位置向量.最后给出了一个例子.

A slant helix is a curve in Euclidean 3-space for which the principal normal vector field makes a constant angle with a fixed direction. In this paper we explicitly construct slant helices. We first solve a system of linear ordinary differential equations involving an alternative moving frame, then determine the position vectors of slant helices through integration. We also give an example.