  We extend the variational problem of Wheeler-Feynman electrodynamics by
putting the electromagnetic functional in a local space of absolutely
continuous trajectories possessing a derivative (velocities) of bounded
variation. Generalizing the calculus of variations for extrema with a finite
number of velocity discontinuities (breaking points), we prove that the
critical-point-conditions for the two-body problem in the extended local space
are Euler-Lagrange equations holding Lebesgue-almost-everywhere plus the
generalized Weierstrass-Erdmann conditions that (i) the partial momenta must be
absolutely continuous functions and (ii) the Legendre transforms of the partial
Lagrangians (i.e, the partial energies) must be absolutely continuous
functions.
