一些曲面测地线方程的几种计算方法

Several Calculation Methods of Geodesic Equation on Quadric Surface

从一道2018年大学生数学竞赛赛题引出,通过对原赛题的分析,对四种求解椭圆柱面上测地线方程的方法加以推广,给出了相应旋转曲面、二次曲面和可展曲面的测地线方程求解方法,这四种方法是:参数变换法、微分方程求解法、变分法和曲面展开法.最后给出了四种方法的评价.

This article is from The Chinese Mathematics Competitions(2018).four methods for solving the geodesic equation on elliptic cylinder are generalized through the analysis of the original problem.These four methods are:parameter transformation method,differential equation solution method,variational method and surface expansion method.Moreover,the evaluation of the four methods is given.