  The Lorentz symmetry group entails physical equations whose solutions are
retarded. This leads to the concept of a relativistic engine resulting from
retardation of electromagnetic fields. We have shown that Newton'n third law
cannot strictly hold in a distributed system, where the different parts are at
a finite distance from each other and thus force imbalance is created at the
system's center of mass. As the system is affected by a total force for a
finite period, mechanical momentum and energy are acquired by the system. In
previous works we relied on the fact that the bodies were macroscopically
natural. Lately we relaxed this assumption and studied charged bodies, thus
analyzing the consequences on a possible electric relativistic engine. On the
first paper on this subject we investigated this phenomena in general but gave
an example of a system only at the stage of reaching a stationary state, a
second paper was devoted to the same but on the atomic scale, here we shall
analyze the charge relativistic engine in a general time dependent setting.
