Mechanical quantities in elastic electromagnetic bodies

Mechanical quantities, such as kinetic energy, momentum and inertia can be possibly associated with moving electromechanical bodies in a unique way, provided that a variational formulation is possible for these materials. Based on a Lagrangian density that is inherent the electromagnetic body of interest, the mechanical equations and the Maxwell equations stem in a natural way from this Lagrangian. Extended momentum and inertia can be introduced also in a natural way. The notion of kinetic energy is less immediate. Nonetheless, it can be recovered by introducing the notion of kinetic co-energy, a density of which is assumed to exist and to depend on the kinetic variables. The Lagrangian density is then viewed as a combination of the kinetic co-energy with other physical quantities. It is worth remarking that the kinetic co-energy happens to coincide with the kinetic energy in classical continua. Additional mechanical quantities, such as material momentum and material stress, can be excerpted from the Lagrangian. These quantities that are unused in classical mechanics, are enlightening in some classical problems of dielectrics. The questionable form for the momentum of light finds a solution in this context.