Note on uniqueness for a one-dimensional two-body problem of classical electrodynamics

doi:10.1016/0003-4916(67)90076-0

Annals of Physics

Volume 42, Issue 2, April 1967, Pages 347-351

https://doi.org/10.1016/0003-4916(67)90076-0 Get rights and content

Abstract

A previous paper [Ann. Phys.21, 122 (1963)] gave a mathematical analysis of a two-body problem of classical electrodynamics incorporating retarded interactions (for the case of two charged particles remaining on the x axis). It was shown that the future trajectories would be uniquely determined, and well behaved, if past histories of the particles were given satisfying certin conditions, including a Lipschitz condition on the velocities. However, this Lipschitz condition has since become suspect as possibly unreasonable. The present note shows that it was, in fact, also superfluous.

References (4)

R.D. Driver
Ann. Phys. (N.Y.)
(1963)
R.D. Driver
A functional-differential system of neutral type arising in a two-body problem of classical electrodynamics

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^☆: This work was supported by the United States Atomic Energy Commission.

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Note on uniqueness for a one-dimensional two-body problem of classical electrodynamics☆

Abstract

Ann. Phys. (N.Y.)