Unified approach to electromagnetic shape-inverse and mechanically coupled problems via a Lagrangian technique

The aim of this paper is to present a Lagrangian unified approach to shape-dependent electromagnetic problems (equilibrium, dynamic coupled, shape inverse, trajectory inverse problems). The main features of this approach are illustrated, and a comparison with the usual Eulerian point of view is made, from both the analytical and the numerical side, showing several advantages of the Lagrangian approach. A simple analytical example is presented in order to help comprehension and to show the effectiveness of the method. In addition, some practical applications are described.