The objection that velocity jumps across transition intervals near nonanalytic points produce delta functions in the radiated fields is shown to be incorrect.
Conservation of Momentum and Energy in the Lorenz-Abraham-Dirac Equation of Motion
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abstract
After a brief review of the modified (by transition forces) causal Lorentz-Abraham (LA) classical equation of motion for an extended charged sphere and its limit to the mass-renormalized modified causal Lorentz-Abraham-Dirac (LAD) equation of motion as the radius of the charged sphere approaches zero, a concise derivation is given for the conditions on the velocity and external force required for these modified equations of motion to satisfy conservation of momentum and energy. The effects of mass renomalization on the radiated momentum-energy is clarified. The solutions to the unmodified LAD equation of motion, the causal modified LA and LAD equations of motion, and the Landau-Lifshitz approximate solution to the unmodified LAD equation of motion are obtained for a charge traveling through a parallel-plate capacitor.
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Reply to "Comment on 'Absence of a consistent classical equation of motion for a mass-renormalized point charge'" (arXiv:2511.02865v1, 3 Nov 2025)
The objection that velocity jumps across transition intervals near nonanalytic points produce delta functions in the radiated fields is shown to be incorrect.