一类特殊球面螺旋线弧长的求解＊

摘要

根据微分几何基本理论，定义出一类特殊的球面螺旋线，针对该球面螺旋线弧长不可积的问题进行探讨与研究，证明了这类对于给定参数的球面螺旋线弧长存在上下界。通过引入第二类椭圆积分基本理论并结合微机计算的方法，提供了一种近似求解球面螺旋线弧长的公式。%Applying the relevant theory of differential geometry, defining a special spherical helix, the problem of not integrable of spherical spiral arc length is discussed. It is proved that there exist the upper and lower bounds of a given spherical spiral arc length . By introducing theory of the second kind elliptic integral and combining with the computer calculation method, it provides a solution way for a spherical helix arc length.