Could an Electromagnetic field produce the "3-body" problem?

[JorgeM]

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[olgerm]

If you know positions and velocitys of bodies and EM-field (($\vec{E}(t)$ and $\vec{B}(t))$) or (EM-poteintial $\vec{A}(t)$ and it's time deriative $\frac{\partial \vec{A}}{\partial t}$)) at given time, then you can calculate: EM-field, positions and velocities of bodies on any time.

If you make approximation $c\to \infty$, then it is just like classical 3-bodie problem, but with additional coulomb force.

If you tried to take into account magnetic force as function of positions of bodies, then the model mignt not be galileo invariant nor lorentz invariant.