Classical dynamics of two electric charges

\indent From Li?nard-Wiechert fields that describe the classical electromagnetic effect of a
moving electric point charge, we construct the equations of motion for two
particles. To build the equations of motion we use the Lorentz force $ \frac{d \mathbf{p}}{dt} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) $ where $ \mathbf{E} $ and $ \mathbf{B} $ are the Li?nard-Wiechert fields and $ \mathbf{p} $ is the relativistic momentum. Rescheduling to simplify this equations and thus get only one parameter, the ratio of masses. As the system depending only on the ratio of the masses and the boundary conditions we
can simulate a electron-positron system, a electron-proton system and any two electric point charge system varying the ratio of mass.
For each system we can analyze the position and velocity of each particle, the center of mass and the decay time. Analyzing
the equations of motion in polar coordinates, and the results of the numerical solutions can be analytically deduce the decay
time of the particles depends on the initial radius and the ratio of the mass. From the Langevin equation that is a stochastic differential equation we search the noise term that generates the stability of existing orbits on the electron-proton model.