Application of Hertz´s principle to ray tracing on hybrid quadric surfaces of revolution (h-QUASORs)

Summary form only given, as follows. A large number of axisymmetric scattering structures, such as those commonly encountered with aerospace vehicles and satellites, can be accurately modelled as combinations (hybrids) of truncated sections of quadric surfaces which are called hybrid quadric surfaces of revolution (h-QUASORs). The developability property of a surface is a potent tool in the determination of the geometric parameters needed in high frequency ray-theoretic mutual coupling analysis. Since h-QUASORs in general are not developable, this property cannot be used to find the junction transition point of geodesics from one quadric surface to another. A more powerful technique, based on the use of Hertz´s principle of particle dynamics, has been developed to analyze surface ray behaviour on developable as well as nondevelopable h-QUASORs. Even when the two sections of an h-QUASOR are individually developable (e.g. a cone-cylinder combination), the composite surface may not be so. The resulting expression for azimuth angle phi will still not be in a closed form. The quasianalytical method outlined here is valid for these cases as well.<>