Abstract
This study aims to show how to obtain the curvature of the ellipsoid depending on azimuth angle. The curvature topic is quite popular at an interdisciplinary level. It can be to the friends of geometry, geodesy, satellite orbits in space, in studying all sorts of elliptical motions (e.g., planetary motions), curvature of surfaces and concerning eye-related radio-therapy treatment, for example the anterior surface of the cornea is often represented as ellipsoidal in form. On the calculation of the curvature, there is a famous Euler formula for rotating ellipsoid that everyone knows. Let θ be the angle, in the tangent plane, measured clockwise from the direction of minimum curvature κ1. Then the normal curvature κn (θ) in direction θ is given by κn (θ) = κ1 cos2θ + κ2 sin2θ = κ1 + (κ2 - κ1) cos2θ I wonder how can a formula for a triaxial ellipsoid? So we started to work. And we finally found the formula for the triaxial ellipsoid.
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