Two-Body Problem in Classical Relativistic Electrodynamics. I. Unlike Charges

Two arbitrary, equal masses with arbitrary, equal (but opposite) charges are held at rest at a certain distance apart for their entire past history up until $t=0\mathrm{}$. They are then released, and fall together under their mutual attraction until they pass through one another. No radiation forces are added to the equations of motion. The authors provide the exact analytic solution for the first part of the trajectory, and, through an analysis of the problem, derive further relationships that lead to a numerical solution on the computer for the rest of the trajectory, where retarded functions must be used.