Equation of motion for a radiating charged particle in classical electrodynamics

We propose classical equations of motion for charged particles in an electromagnetic field. These are general formulas for the particle acceleration that take the radiation-induced deceleration into account and contain no second derivatives of the particle velocity. In several particular cases considered, the new equations yield results coinciding with those known in the literature and experimentally verified. We show that in the range of ultrahigh energies, classical electrodynamics does not lead to inherent inconsistencies and in principle allows particle motion with energies exceeding the Pomeranchuk limit.