Abstract
The functional-differential equation which describes the one-dimensional symmetric motion of two charged particles in the framework of classical electrodynamics is considered. In the case of the charges of a like sign it is proved that the global solution exists and it is specified uniquely by the instantaneous initial data, if the classical energy at the initial moment is sufficiently small. In the case of the charges of opposite sign there are additional restrictions on the initial data. The estimates are given which allow one to obtain an approximate description of motion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Driver, R. D. (1963).Annals of Physics (New York),21, 122.
Driver, R. D. (1969).Physical Review,178, 2051.
Driver, R. D. (1970).The Proceedings of Vth International Conference on Nonlinear Oscillations, Vol. 2, p. 178. Edition of the Kiev Institute of Mathematics.
Driver, R. D. and Norris, M. J. (1967).Annals of Physics (New York),42, 347.
Elsgolts, L. E. (1966).Introduction to the Theory of Differential Equations with Deviating Arguments, Holden-Day.
Kasher, X. and Schwebel, Y. (1971).Physical Review, D,4, 2956.
Hushilt, J., Baylis, W. E., Leiter, D., and Szamosi, G. (1973).Physical Review, D,7, 2884.
Zhdanov, V. I., (1974).International Journal of Theoretical Physics 11, 249.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhdanov, V.I. On the one-dimensional symmetric two-body problem of classical electrodynamics. Int J Theor Phys 15, 157–167 (1976). https://doi.org/10.1007/BF01807756
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01807756