Rotary dynamics of the rigid body electric dipole under the radiation reaction

TL;DR

This paper investigates the rotational behavior of a rigid body with an electric dipole under radiation reaction torque, deriving nonlinear equations and analyzing specific cases to understand its long-term dynamics.

Contribution

It introduces a new model for the rotation of polarized rigid bodies under radiation reaction, deriving and solving nonlinear equations for specific configurations.

Findings

Exact solution for axially symmetric top with longitudinal dipole

Power-law slowdown or exponential drift depending on initial conditions

Analysis of transverse dipole dynamics through qualitative and numerical methods

Abstract

Rotation of a permanently polarized rigid body under the radiation reaction torque is considered. Dynamics of the spinning top is derived from a balance condition of the angular momentum. It leads to the non-integrable nonlinear 2nd-order equations for angular velocities, and then to the reduced 1st-order Euler equations. The example of an axially symmetric top with the longitudinal dipole is solved exactly, with the transverse dipole is analyzed qualitatively and numerically. Physical solutions describe the asymptotic power-law slowdown to stop or the exponential drift to a residual rotation; this depends on initial conditions and a shape of the top.