The geodesic constant method: a novel approach to analytical surface-ray tracing on convex conducting bodies

A generalized approach to analytical surface-ray tracing in three dimensions, and a review of its application to convex conducting bodies, is presented, using the Eisenhart coordinate system. The ray-parameters so obtained, for quadric cylinders (QUACYLs) and surfaces of revolution (QUASORs), are in a one-parameter form for UTD mutual-coupling applications. The ray analysis is also extended to the hybrid QUACYLs (e.g. aircraft wings) and hybrid QUASORs (e.g., satellite-launch vehicles), by introducing Hertz´s principle of particle dynamics to EM theory. This mathematical formulation is applicable even to other important non-Eisenhart surfaces, such as the ogive. A summary of the mathematical formulations is included