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One-Dimensional Motion of Sommerfeld Sphere in Potential Hole in Classical Electrodynamics: Inside the Hole

Alexander A. Vlasov
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Abstract

Equation of motion of Sommerfeld sphere in the one-dimensional potential hole, produced by two equal charges on some distance from each other, is numerically investigated. Two types of solutions are found: (i) damping oscillations, (ii) oscillations without damping (radiationless motion). Solutions with growing amplitude ("climbing-up-the-wall solution") for chosen initial conditions were not founded.

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Alexander A. Vlasov. 1999-05-27. One-Dimensional Motion of Sommerfeld Sphere in Potential Hole in Classical Electrodynamics: Inside the Hole. https://arxiv.org/abs/physics/9902018

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