Radiation of electromagnetic waves when changing smoothly parameters of a radiating system

Characteristics peculiarities of electromagnetic radiation for emitting systems which parameter variation is described with model smooth functions permitting to obtain exact solutions have been considered. A moving charge changing smoothly its velocity (in magnitude and direction), dipole having smoothly changed dipole momentum, charge moving uniformly in medium, which dielectric permeability smoothly changes in space or time, have been chosen as examples of the emitting systems. Exact expressions for the electromagnetic field and spectral density of the radiation energy in all the problems considered are given. It is shown that the exponential drop of spectrum in the region of high frequency is a common property for the electromagnetic radiation of similar systems