Still The New Classical Relativistic Equation of Charge Motion in an Electromagnetic Field

The non-relativistic Goedecke equation (1975), which describes the motion of a point charge taking into account the radiation reaction, has no “runaway” solutions. A “physical” method of covariant generalization of this equation is proposed, a special case of which is based on the Lorentz transformations in a coordinate–free covariant representation. Two equivalent forms of a new classical relativistic equation of motion of a point charge are obtained. It is shown that the Abraham–Lorentz–Dirac (ALD) and the Mo–Papas (MP) equations are approximate consequences of the presented theory.