  We propose classical equations of motion for a charged particle with magnetic
moment, taking radiation reaction into account. This generalizes the
Landau-Lifshitz equations for the spinless case. In the special case of
spin-polarized motion in a constant magnetic field (synchrotron motion) we
verify that the particle does lose energy. Previous proposals did not predict
dissipation of energy and also suffered from runaway solutions analogous to
those of the Lorentz-Dirac equations of motion.
