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

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 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. Graphical abstract