Using a toy model, we demonstrate how the variability pattern of a relativi
stically moving source of radiation that is subject to the action of a tran
sient force, depends on dynamical effects. The model is motivated by a rece
nt analysis of radiative fronts in magnetized, relativistic jets, but is ap
plicable also in other situations. The main effect analyzed in this paper i
s the strong dependence of the variability pattern on viewing angle, result
ing from changes of the beaming cone of emission. In particular, it is show
n that (1) the shape of the light curves reflects the time profile of the D
oppler factor when viewing the source at large enough angles to its directi
on of motion, whereas at small viewing angles it is determined by the time
evolution of the radiated power density; and (2) the characteristics of cor
related emission depend strongly on viewing angle by virtue of either optic
al depth effects or the difference in beaming patterns of different radiati
on sources.