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We introduce an ad-hoc electrodynamics with advanced and retardedLienard-Wiechert interactions plus the dissipative Lorentz-Diracself-interaction force. We study the covariant dynamical system of theelectromagnetic two-body problem, i.e., the hydrogen atom. We perform thelinear stability analysis of circular orbits for oscillations perpendicular tothe orbital plane. In particular we study the normal modes of the linearizeddynamics that have an arbitrarily large imaginary eigenvalue. These largeeigenvalues are fast frequencies that introduce a fast (stiff) timescale intothe dynamics. As an application, we study the phenomenon of resonantdissipation, i.e., a motion where both particles recoil together in a driftingcircular orbit (a bound state), while the atom dissipates center-of-mass energyonly. This balancing of the stiff dynamics is established by the existence of aquartic resonant constant that locks the dynamics to the neighborhood of therecoiling circular orbit. The resonance condition quantizes the angular momentain reasonable agreement with the Bohr atom. The principal result is that theemission lines of quantum electrodynamics (QED) agree with the prediction ofour resonance condition within one percent average deviation.Comment: 1 figure, Notice that Eq. (34) of the Phys. Rev. E paper has a typo;  it is missing the square Brackets of eq. (33), find here the correct e

Stiff stability of the hydrogen atom in dissipative Fokker electrodynamics