On a two-body problem of classical relativistic electrodynamics.

Casal, A., Martinez Herrero, Rosario, and Vences, M.A.. "On a two-body problem of classical relativistic electrodynamics.." Revista Matemática Hispanoamericana 40.1-2 (1980): 17-24. <http://eudml.org/doc/39780>.

@article{Casal1980,
abstract = {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.},
author = {Casal, A., Martinez Herrero, Rosario, Vences, M.A.},
journal = {Revista Matemática Hispanoamericana},
keywords = {Teoría de la relatividad; Electrodinámica; Problema dos cuerpos; two-body problem; classical relativistic electrodynamics; retarded potential; functional differential equations of the retarded type},
language = {eng},
number = {1-2},
pages = {17-24},
title = {On a two-body problem of classical relativistic electrodynamics.},
url = {http://eudml.org/doc/39780},
volume = {40},
year = {1980},
}

TY - JOUR
AU - Casal, A.
AU - Martinez Herrero, Rosario
AU - Vences, M.A.
TI - On a two-body problem of classical relativistic electrodynamics.
JO - Revista Matemática Hispanoamericana
PY - 1980
VL - 40
IS - 1-2
SP - 17
EP - 24
AB - 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.
LA - eng
KW - Teoría de la relatividad; Electrodinámica; Problema dos cuerpos; two-body problem; classical relativistic electrodynamics; retarded potential; functional differential equations of the retarded type
UR - http://eudml.org/doc/39780
ER -