Regularization of the collision in the electromagnetic two-body problem

We derive a differential equation that is regular at the collision of two equal-mass bodies with attractive interaction in the relativistic action-at-a-distance electrodynamics. We use the energy constant related to the Poincare invariance of the theory to define finite variables with finite derivatives at the collision. The collision orbits are calculated numerically using the regular equation adapted in a self-consistent minimization method (a stable numerical method that chooses only nonrunaway solutions). This dynamical system appeared 100 years ago as an example of covariant time-symmetric two-body dynamics and acquired the status of electrodynamics in the 1940s by the works of Dirac, Wheeler, and Feynman. We outline the method with an emphasis on the physics of this complex conservative dynamical system.