On Simplified Models for Dynamics of Pointlike Objects  

作　　者：Marijan Ribarič  Luka Š uš terš ič [1] Marijan Ribarič;Luka Šušteršič(Jožef Stefan Institute, Ljubljana, Slovenia)

机构地区：[1]Jož ef Stefan Institute, Ljubljana, Slovenia

出　　处：《Journal of Applied Mathematics and Physics》2021年第8期1853-1869,共17页应用数学与应用物理（英文）

摘　　要：<strong>Motivation:</strong> 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. <strong>Objective:</strong> 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 <em>t</em> ∈ (<em>t_m</em>, +∞) and<em> t_m</em> > 0 is large, say <img src="Edit_6f0f7522-7319-4b30-a451-0453ff0f75d3.bmp" alt="" />! <strong>Method:</strong> 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. <strong>Results:</strong> We make simplified models for the long-term dynamics of pointlike objects by Taylor polynomials in time derivatives of the external force. <strong>Application:</strong> We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where <em>t</em> ≥ <em>t_m</em> <span style="white-space:nowrap;">&#8811;</span> 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.<strong>Motivation:</strong> 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. <strong>Objective:</strong> 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 <em>t</em> ∈ (<em>t_m</em>, +∞) and<em> t_m</em> > 0 is large, say <img src="Edit_6f0f7522-7319-4b30-a451-0453ff0f75d3.bmp" alt="" />! <strong>Method:</strong> 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. <strong>Results:</strong> We make simplified models for the long-term dynamics of pointlike objects by Taylor polynomials in time derivatives of the external force. <strong>Application:</strong> We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where <em>t</em> ≥ <em>t_m</em> <span style="white-space:nowrap;">&#8811;</span> 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.

关 键 词：Point Mass Long-Term Dynamics Harmonic Oscillator Drag Force Lorentz-Abraham-Dirac Equation Taylor Series Expansion 

分 类 号：O17[理学—数学]