A Lagrangian Approach to Electromagnetic Bodies

A Lagrangian formulation for a deformable and moving electromagnetic body is here proposed in the framework of the Galilean approximation. As the proper choice of the independent electromagnetic fields for such a Lagrangian seems to be of basic importance, the first concern is with this choice. In this respect, a preliminary transformation of the electromagnetic fields in the referential frame of the solid body is suitably introduced. The resulting fields, which combine with the motion and with the deformation, enter into the proposed Lagrangian. Eventually, one shows that the related Lagrange equations provide both, the generalised equations of mechanics and the Maxwell equations, in the material form. Interesting quantities, such as canonical momenta and stresses, stem naturally from the adopted procedure and are commented hereby. These quantities are very helpful in describing the behaviour of defective materials