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

Dynamics of spherical distributions of charge with small internal dipolar motion