一类最速降线与最短路径问题

A Kind of Problem on the Fastest Descending Path and on Shortest Distance Path

本文结合梯度讨论了椭球面上一类最速降线问题 ,应用变分法及 Mathematica软件讨论了椭球面上最短路径问题 ;分析了二者的关系 ,旨在加强应用数学知识的能力 .

In this paper, by applying gradient and calculus of variations we discussed a kind of problem on fastest descending path on the ellipsoid. Then by using the Mathematica Soft Ware, we discussed the shortest distance path on ellipsoid, and analyzed the relation ship between the lengths of the two paths, in order to improve the mathematical quality of the students.