  The goal of this paper is to improve the performance of an electric motor by
modifying the geometry of a specific part of the iron core of its rotor. To be
more precise, the objective is to smooth the rotation pattern of the rotor. A
shape optimization problem is formulated by introducing a tracking-type cost
functional to match a desired rotation pattern. The magnetic field generated by
permanent magnets is modeled by a nonlinear partial differential equation of
magnetostatics. The shape sensitivity analysis is rigorously performed for the
nonlinear problem by means of a new shape-Lagrangian formulation adapted to
nonlinear problems.
