We are interested in the motion of a classical charge acted upon an externalconstant electromagnetic field where the back reaction of the particle's ownfield is taken into account. The Landau-Lifshitz approximation to theLorentz-Abraham-Dirac equation is solved exactly and in closed form. It isshown that the ultrarelativistic limit of the Landau-Lifshitz equation for aradiating charge is the equation for eigenvalues and eigenvectors of theexternal electromagnetic field tensor.
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