1D Particle, 1D Field, 1D Interaction. Simple Exactly Solvable Models based on Finite Rank Perturbations Methods. III. Linear Friction as Radiation Reaction

TL;DR

This paper explores simple exactly solvable models of linear friction based on radiation reaction mechanisms, using mathematical tools like d'Alembert-Kirchhoff formulas to analyze phenomena such as radiation reaction, braking radiation, and friction.

Contribution

It introduces and analyzes exactly solvable models of linear friction driven by radiation reaction, connecting mathematical methods with physical phenomena.

Findings

Models demonstrate radiation reaction as a source of linear friction.

Mathematical framework uses d'Alembert-Kirchhoff-like formulas.

Results elucidate physical phenomena of braking radiation and friction.

Abstract

This paper is an electronic application to my set of lectures, subject:`Formal methods in solving differential equations and constructing models of physical phenomena'. Addressed, mainly: postgraduates and related readers. Content: a discussion of the simple models of linear friction, the models, that have the mechanism that is based on radiation reaction. The interactions we will deal are based on equation arrays of the kind: d^2 q(t)/dt^2 =-\Omega^2 q(t)+f_{compl}(t,q,Q), d^2 u(t,x)/dt^2=c^{2}d^2 u(t,x)/dx^2 -4{\gamma}c\delta(x-x_0) F_{src}(t,q,Q) +f_1(t,x), Q(t) = <l(t)|u> >. Central mathematical points: d'Alembert-Kirchhoff-like formulae. Central physical points: phenomena of Radiation Reaction, Braking Radiation and Friction.