Formulating the two-body problem of classical relativistic electrodynamics in terms of action at a distance and using retarded potential, the equations of one-dimensional motion are functional differential equations of the retarded type. For this kind of equations, in general it is not enough to specify instantaneous data to specify unique trajectories. Nevertheless, Driver (1969) has shown that under special conditions for these electrodynamic equations, there exists an unique solution for this problem of instantaneous data. One of these conditions is required by technical reasons but it seems physically unnatural. In this paper we use a different method of proof which allowed us to avoid that condition, but still getting the existence of trajectories for instantaneous data. However, the method doesn't give uniqueness.
@article{urn:eudml:doc:39780,
title = {On a two-body problem of classical relativistic electrodynamics.},
journal = {Revista Matem\'atica Hispanoamericana},
volume = {40},
year = {1980},
pages = {17-24},
zbl = {0525.34055},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39780}
}
Casal, A.; Martinez Herrero, Rosario; Vences, M.A. On a two-body problem of classical relativistic electrodynamics.. Revista Matemática Hispanoamericana, Tome 40 (1980) pp. 17-24. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39780/