Comment on "Dynamics of a Charged Particle" by F. Rohrlich [Phys. Rev. E 77, 046609 (2008), arXiv:0804.4614]

TL;DR

This paper discusses the historical and computational challenges of solving the Eliezer equation for a charged particle's dynamics, emphasizing its complexity and the need for revisiting its numerical solutions.

Contribution

It highlights the longstanding nature of the Eliezer equation and the difficulties in numerical solutions, prompting reconsideration of its application.

Findings

The Eliezer equation has been known for over 60 years.

Numerical solutions are difficult due to its recursive dependence on acceleration.

Revisiting the equation may improve understanding of charged particle dynamics.

Abstract

The equation derived by F. Rohrlich (Phys. Rev. E 77, 046609 (2008)) has been known for 60 years (C. J. Eliezer, Proc. Royal Soc. London. Ser. A 194, 543 (1948)). For a long time this equation has been considered to be incorrect. If there is any need to revisit this issue, the only relevant consideration is that the Eliezer equation is very difficult to solve numerically: the acceleration being expressed in terms of a function that, itself, depends on the acceleration.