Classical states of an electric dipole in an external magnetic field: Complete solution for the center of mass and trapped states

We study the classical behavior of an electric dipole in the presence of a uniform magnetic field. Using the Lagrangian formulation, we obtain the equations of motion, whose solutions are represented in terms of Jacobi functions. We also identify two constants of motion, namely, the energy E and a pseudomomentum C→. We obtain a relation between the constants that allows us to suggest the existence of a type of bound states without turning points, which are called trapped states. These results are consistent with and complementary to previous results.