椭圆柱面上测地线的几种求解方法研究

Study on Several Kinds for Geodesic Lines of Elliptic Cylinder to Solve the Method

根据测地线的几何性质,应用微分方程及变分法从数学角度阐述了椭圆柱面上测地线的求解方法。应用曲面展开方法建立椭圆柱面上测地线的几何模型,并由几何模型推导出数学模型,通过计算机编程实现在椭圆柱面上任意两点间绘制测地线的功能,使求解结果具有直观性。

According to the geometry properties of geodesic line several kinds for geodesic lines of elliptic cylinder to solve the method are expatiated. Two methods are applied, the first is curved surface development to establish geometry model of the geodesic line on the elliptic cylinder. And secondly is mathematics the model that is deduced by geometry model. The function of draw geodesic lines on the elliptic cylinder arbitrarily between two points is realized by applying computer program and make beg the solution to consequently have the visualization.