DOI: 10.1007/s10701-006-9072-x Foundations of Physics, Vol. 36, No. 10, October 2006 (© 2006) A Physical Deduction of an Equivalent Landau–Lifshitz Equation of Motion in Classical Electrodynamics. A New Expression for the Large Distance Radiation Rate of Energy G. Ares de Parga 1 Received November 3, 2005; revised April 28, 2006; Published online July 18, 2006 A new scheme is proposed in order to deduce an equation of motion for a spin- less charged point particle leading to an equivalent Landau–Lifshitz equation of motion. Consequently Larmor’s formula must be substituted by a new expres- sion for the large distance radiation rate of energy. A constraint appears on the applicability of the Maxwell electromagnetic tensor. The particular case of a sudden force is analyzed in order to show the physical results predicted by the new model. A geometrical rearrangement of the energy explains the balance. KEY WORDS: classical electron; radiation reaction; extended charge; point charge. 1. INTRODUCTION Due to the problematic solutions of the Lorentz–Dirac equation (1) [LD] such as runaway solutions and preaccelerations, many authors have devel- oped a series of different proposals. (2) Nevertheless, none is free of diffi- culties similar to those of the LD equation or worse. In 1991, for a charge with structure, Ford and O’Connell (3) proposed a new nonrelativistic equa- tion of motion [FO’] which is derived as an exact result and not as an approximation. (4) Nevertheless, it coincides with the nonrelativistic case of the Landau–Lifshitz equation (5) [LL]. It is very important to observe a fundamental difference between these last equations. Indeed, the FO’ 1 Dpto de F´ısica, Escuela Superior de F´ısica y Matem´ aticas, Instituto Polit´ ecnico Nacional, U.P. Adolfo L´ opez Mateos, Zacatenco, C.P. 07738 M´ exico D.F., M´ exico; e-mail: gonz- alo@esfm.ipn.mx 1474 0015-9018/06/1000-1474/0 © 2006 Springer Science+Business Media, Inc.