Dynamics of spherical distributions of charge with small internal dipolar motion

This paper extends the Lorentz-Abraham model of an electron (i.e., the equations of motion for a small spherical shell of charge, which is rigid in its proper frame) to treat a small, spherically symmetric charge distribution, allowing for small internal dipolar motion. This is done by dividing the distribution into thin spherical shells (in the continuum limit), and tracking the interactions between shells. Dipolar motion of each constituent spherical shell is allowed along the net dipole moment, but higher-order multipole moments are ignored. The amplitude of dipolar motion of each spherical shell is assumed to be linearly proportional to the net dipole moment. Under these assumptions, low-velocity equations of motion are determined for both the center-of-mass motion and net dipolar motion of the distribution. This is then generalized to arbitrary (relativistic) center-of-mass velocity and acceleration, assuming the motion of individual shells is completely in phase or out of phase with the net dipole moment.