NOVEL COORDINATE SYSTEM AND ROTATION TRANSFORMATIONS FOR ANTENNA APPLICATIONS

General coordinate system transformations and rotation transformations for antenna applications are presented in a novel coherent and unified fashion. In coordinate system transformations, the Cartesian transformation matrix (CTM) is used to relate the representations of a vector in two Cartesian coordinate systems. Useful CTMs such as the Cartesian-spherical transformation and the Eulerian transformation are formulated based on three elementary CTMs. In rotation transformations, the rotation transformation matrix (RTM) is used to describe the rotation of an object, which may be a point, a vector, a coordinate system, or any physical entity. The relationship between the representations of an RTM in different Cartesian coordinate systems are developed. Three examples: (i) Scanning dual-reflector antennas, (ii) Map generation for satellite antennas, and (iii) Coordinate systems for antenna measurement (EL-over-AZ and AZ-over-EL) are given to demonstrate the versatility of the combined applications of RTMs and CTMs in solving practical transformation problems.