%0 Journal Article %T On Simplified Models for Dynamics of Pointlike Objects %A Marijan Ribarič %A Luka Š %A uš %A terš %A ič %J Journal of Applied Mathematics and Physics %P 1853-1869 %@ 2327-4379 %D 2021 %I Scientific Research Publishing %R 10.4236/jamp.2021.98119 %X Motivation: We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines solely by the trajectory of a single point. Its velocity eventually stops changing after cessation of the external force. The response of their acceleration to the long-term external force is slow and possibly nonlinear. Objective: Our objective is to present technique for making simplified models for the long-term dynamics of pointlike objects whose motion interacts with the surroundings. In the asymptotic-type long-term dynamics, the time variable t ¡Ê (t_m, +¡Ş) and t_m > 0 is large, say $\"\"$ ! Method: We apply Taylor series expansion to differential equations to model the acceleration of pointlike object whose response to the long-term external force is not instantaneous and possibly nonlinear. Results: We make simplified models for the long-term dynamics of pointlike objects by Taylor polynomials in time derivatives of the external force. Application: We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where t ¡İ t_m ≫ 0. This interpretation resolves the conceptual and usage controversy surrounding its troublesome application to determine the trajectory of a radiating charged particle, thus contributing to the development of more adequate modeling of physical phenomena. %K Point Mass %K Long-Term Dynamics %K Harmonic Oscillator %K Drag Force %K Lorentz-Abraham-Dirac Equation %K Taylor Series Expansion %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=111134