Reflections from linearly vibrating objects: Plane mirror at normal incidence

The signal scattered by a moving object is traditionally evaluated by the quasistationary method. This method is not relativistically correct, although it yields satisfactory results in most practical cases. A correct approach implies solution of the problem in the accelerated reference system in which the object is at rest. The relevant Maxwell´s equations, boundary conditions, and constitutive equations are derived for axes in linear sinusoidal motion. As a first application the reflections from a perfectly conducting plane in sinusoidal vibration are evaluated.