  The Lorentz-Abraham-Dirac equations (LAD) may be the most commonly accepted
equation describing the motion of a classical charged particle in its
electromagnetic field. However, it is well known that they bare several
problems. In particular, almost all solutions are dynamically unstable, and
therefore, highly questionable. The question remains whether better equations
of motion than LAD can be found to describe the dynamics of charges in the
electromagnetic fields. In this paper we present an approach to derive such
equations of motions, taking as input the Maxwell equations and a particular
charge model only, similar to the model suggested by Dirac in his original
derivation of LAD in 1938. We present a candidate for new equations of motion
for the case of a single charge. Our approach is motivated by the observation
that Dirac's derivation relies on an unjustified application of Stokes' theorem
and an equally unjustified Taylor expansion of terms in his evolution
equations. For this purpose, Dirac's calculation is repeated using an extended
charge model that does allow for the application of Stokes' theorem and enables
us to find an explicit equation of motion by adapting Parrott's derivation,
thus avoiding a Taylor expansion. The result are second order differential
delay equations, which describe the radiation reaction force for the charge
model at hand. Their informal Taylor expansion in the radius of the charge
model used in the paper reveals again the famous triple dot term of LAD but
provokes the mentioned dynamical instability by a mechanism we discuss and, as
the derived equations of motion are explicit, is unnecessary.
