几种常见回转曲面短程线的几何分析及其计算机绘制

CALCULATION AND COMPUTER DRAWING OF SHORTEST GEODESICS OF COMMON SURFACES OF REVOLUTION

本文在微分几何理论基础上，通过非线性方程求根与数值积分相结合的方法给出了回转抛物面、回转椭球面、单叶回转双曲面、圆环面等常见回转曲面上短程线的计算方法及其计算机绘制。计算机绘制短程线，在工程实际及数学、物理、力学理论中都是很重要的。

This paper gives numerical solutions of shortest geodesics of common surfaces of revolu-tion by combining numerical integration with the extraction of a root of nonlinear equation。The computer drawings of shortest geodesics are very important to the practical engineering,to the theories of mathematics,physics and mechanics。