Different Method for Determining Normal Section Curvatures on Earth Ellipsoid

Abstract

Normal curvatures formed at a point on any surface and relations regarding these are analogous to the deformations formed on distorted surfaces. By using the analogy, which is mentioned for the first time in this paper, graphic methods are given to find normal section curvatures from principal curvatures formed at one point on the rotational ellipsoid surface or to find principal curvatures and principal direction from normal curvatures. In addition, it is mentioned that these methods are valid for all types of surfaces. Then some interpretations are given regarding the different situations in finding the normal curvatures, which are formed on the various surfaces by the graphic method. In the application section, results are obtained by applying the given graphic method at a point on the surface of the rotational ellipsoid, and these results are compared with those from the analytic method.