A mechanical model for analyzing the runaway solutions in the radiation reaction problem
The Abraham-Lorentz equation is the focus in almost all studies on the dynamics of charged particles taking into account radiation reaction. Difficulties such as the runway solutions, among others, arising from this equation have made it famous. For more than a century, this controversial problem has been analyzed for several points of view. The aim of this work is the understanding of the origin of these difficulties. For this purpose a mechanical model, very similar to the one proposed by Burke, is exhaustively analyzed. First an exact solution in one dimension is found, then an analysis of the approximations is carried out and finally, some features of a three-dimensional mechanical model is exhibited in order to understand the origin of difficulties in electrodynamics.
scientific article; zbMATH DE number 5151354