Derivation of magnetic inertial effects from the classical mechanics of a circular current loop

The dynamical equation of a single magnetic moment constituted by a rigid circular current loop is derived from the mechanical Lagrange equations of motion, introducing the Lorentz force and the damping process, described by a well-defined dissipative mechanism. It is demonstrated that magnetic inertial effects arise naturally by simple mechanical considerations and superimpose onto the Gilbert original dynamical equation. The comparison with models proposed in the recent literature is drawn and discussed.