Free space multiple scattering by moving objects

Presently we study multiple-scattering problems involving moving objects. This also covers the class of problems of single-scattering from moving objects excited by arbitrary sources, e.g., spherical or cylindrical elementary antennas, as opposed to plane-wave excitation. Uniform motion, i.e., constant velocities, are assumed, and the wave propagation medium is taken as free space (vacuum), allowing for relatively simple transformations from one inertial reference-frame to another. A consistent use of plane-wave integral representations is conducive to a systematic and trackable relativistic formalism. The far-field forms, which are the leading terms of the inverse-distance differential-operator representations, facilitate a simple check, comparing them by inspection with the exact plane-wave integrals. To derive numerical results the plane wave integrals can be recast in terms of the differential-operator representations which are easier to evaluate. This is especially convenient when the moving objects recede to- or arrive from- large distances.