ON THE CLASSICAL DYNAMICS OF NONROTATING EXTENDED CHARGES

Abstract

We go further with the analysis of Kaup's equation of motion for extended charges, including radiation reaction, begun by Franca et al. We offer two series expansions which incorporate properly the time delay condition t' = t -- R(t')/c and allow to show the non-linear terms mentioned by Franca et al., clarifying the meaning of the usual approximations done and giving an alternative derivation of the Lorentz-Dirac equation. Our work offers a unified version of several studies of the dynamics of extended charges and gives arguments to establish that the general non-linear integro-differential equation of Kaup must have a causal behaviour. The difficulties to make the point charge limit found previously by Teitelboim are also exhibited.