Small oscillations of a 3D electric dipole in the presence of a uniform magnetic field

The classical behavior of a 3D electric dipole in the presence of a uniform magnetic field is studied in the small oscillations approximation. Using the Lagrangian formulation, the equations of motion are obtained, as well as their solutions and constants of motion. Normal modes of oscillation and their corresponding normal coordinates are obtained. Furthermore, the existence of a type of bound states without turning points, so-called trapped states conjectured by Troncoso and Curilef [Eur. J. Phys 27 (2006) 1315-1322], is investigated.