Modeling of the long-time asymptotic dynamics of a point-like object
  We introduce four original concepts: First, the point-like object (PO) specified as a classical extended real object whose response to an external force is aptly specified solely by the trajectory of a single point, whose velocity eventually stops changing after the cessation of the external force. Second, the dynamic models of an PO that generalize the Newton second law by the explicit modeling of PO-acceleration by nonlinear functions of the external force. Third, the long-time asymptotic dynamics of an PO (LTAD) modeled by polynomials in time-derivatives of the external force (by LTAD-models). To make LTAD-models we do not need to know the PO equation of motion. Given the PO equation of motion, without solving it, we can calculate the appropriate LTAD-models, but not vice verse. Fourth, the asymptotic differential equations about the LTAD. They are equivalent to the LTAD-models, but not to the PO equation of motion.   To resolve the conceptual controversy surrounding the relativistic Lorentz-Abraham-Dirac equation, we interpret this equation as an asymptotic differential equation about the LTAD of an electrified PO, and not as a differential equation of motion for an electrified PO.   Keywords: Point-like; asymptotic dynamics; cyclic motion; differential equation; Lorentz-Abraham-Dirac equation 
Marijan Ribaric and Luka Sustersic
physics.gen-ph