Geodesic paths of an ellipsoid-mounted antenna

In applying the high frequency ray technique (GTD) to the radiation problems of an Ellipsoid-mounted antenna, it is essential to determine the geodesic paths on the surface. An efficient, approximate solution for the geodesic paths on the ellipsoid surface, which in turn can be used to model an aircraft or missile fuselage is studied here. Another elaborate method for the geodesic paths employing the calculus of variations is also presented to show the validity of the approximation solution. Typical ellipsoid geometries were chosen and tested for various antenna locations on those surfaces. Good agreement between both methods within the significant energy region confirms that the geodesic paths are efficiently solved via this numerical approach.