New Equation of Motion for Classical Charged Particles

With the intuitive new ideas that (1) in classical electrodynamics, radiation reaction should be expressible by the external field and the charge's kinematics, (2) a charge experiences, in addition to the Lorentz forces, another "small" external force $e_1{F}^{\mu \lambda }{\dot{u}}_{\lambda }$ proportional to its acceleration, and (3) inertia plus radiation is balanced by these two external forces, we propose the new equation of motion,