Quasi Doppler effects associated with spatio-temporal translatory, moving,and active boundaries

Moving sources and spatiotemporally dependent boundaries have been introduc ed in the past, in order to facilitate analyses of the so called "Doppler e ffect" phenomena. Here a model is introduced for generalized situations inv olving translatory and moving surfaces on which certain boundary or source conditions are prescribed. The ambiguity arising from analyses of Doppler-l ike effects in electromagnetics as well as acoustics, in which the (mathema tical) translatory surface is not explicitly distinguished from the (physic al) moving object is carefully discussed here, and the role of physics, e.g ., in the form of Einstein's Special Relativity theory, is considered. The present approach facilitates the general reformulation of the Doppler effec t class of problems and suggests meaningful first order vie (relative veloc ity) approximations which can then be employed for more complicated problem s. Quasi Doppler effects are introduced in order to replace the inherent "i nverse problem" nature of the scattering Doppler effect with a "forward pro blem" formulation which allows for a broader scope of problems and approxim ations. This facilitates the representation of relativistically exact but c omplicated solutions in terms of simpler expressions involving first order velocity effects. In turn, this facilitates new approximate solutions for p roblems not considered previously. By further distinguishing amplitude and phase effects,, even simpler expressions, inconsistent in vie, can be used. This is also helpful in assessing the validity of some heuristic approxima tions suggested in the past. We start with a general analysis of the Dopple r effects initiated by complicated surfaces, providing some general guideli nes and insight for our ability to analyze increasingly complicated problem s.