Dynamics of a dipole in a stationary electromagnetic field

Abstract

The non-relativistic dynamics of an electric dipole in a uniform and stationary electromagnetic field is considered. The equations of motion are derived ab initio . It is shown that they are Hamiltonian with respect to a certain degenerated Poisson structure. The system has a ‘hidden’ symmetry which allows its dimension to be reduced. The reduced system is also Hamiltonian with respect to a degenerated Poisson structure. We show how to perform this reduction in the framework of the Lagrange formalism. Integrability of the reduced system is investigated. It was proved that the system is non-integrable except for two cases when, for specific values of parameters, the system admits an additional first integral.