  The problem of the electromagnetic radiation of an accelerated charged
particle is one of the most controversial issues in Physics since the beginning
of the last century, representing one of the most popular unsolved problems of
the Modern Physics. Different equations of motion have been proposed throughout
history for a point charge including the electromagnetic radiation emitted, but
all these expressions show some limitations. An equation based on the principle
of conservation of energy is proposed in this work for the ultra-relativistic
motion. Different examples are analyzed showing that the energy lost by the
charge agrees with the Li\'enard formula. This proposed equation has been
compared with the Landau-Lifshitz equation obtaining a good agreement in the
range of application of the Landau-Lifshitz formula.
