Motion dynamics of a multicharging system in an electric field

In electrotechnical research there is a problem of analysis of the interaction of moving charged bodies on their trajectories. Its practical solution is possible only on the basis of an adequate mathematical model. To this end, we have adapted the law of force interaction of stationary charges by Charles Coulomb in the case of motion at all possible speeds. This takes into account the finite rate of propagation of the electrical interaction. Differential equations of motion of a closed system of charged moving bodies in their electric field are obtained. On this basis, the transients in a three-charge proton-electron system are simulated, such as the electromechanical equilibrium of an atom of a periodic table of elements. The simulation results are attached.