In 1943 Eliezer showed that, according to the Abraham-Lorentz-Dirac equation, a point charge cannot fall on a centre of attractive Coulombian forces, if one considers only motions constrained on a line. In other words, the Abraham-Lorentz-Dirac equation on a line does not admit solutions x(t) such that x → 0 for t → tc, with either a finite or infinite tc. In this paper it is shown that this remain true for the full three-dimensional problem.
An extension of Eliezer's theorem on the Abraham-Lorentz-Dirac equation / A. Carati. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - 34:30(2001 Aug), pp. 5937-5944.
An extension of Eliezer's theorem on the Abraham-Lorentz-Dirac equation
A. Carati
2001
Abstract
In 1943 Eliezer showed that, according to the Abraham-Lorentz-Dirac equation, a point charge cannot fall on a centre of attractive Coulombian forces, if one considers only motions constrained on a line. In other words, the Abraham-Lorentz-Dirac equation on a line does not admit solutions x(t) such that x → 0 for t → tc, with either a finite or infinite tc. In this paper it is shown that this remain true for the full three-dimensional problem.
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