The paper deals with the problem of modeling classical motion of a particle like electron in a magnetic field. Applying a prescription similar to that of Landau and Lifshitz to the Barut-Zanghi equation, the authors propose a new equation of motion for a radiating spinning charged particle with gyromagmetic ration \(2\). They show that, at least for spin-polarized orbits in a constant magnetic field, the orbits decay as expected physically. Previous proposals did not predict dissipation of energy and also suffered from runaway solutions analogous to those of the Lorentz-Dirac equations of motion. Also, the authors present solutions of the Barut-Zanghi equation for a non-radiating charged particle in a constant magnetic field.