  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.

Classical Physics