Mathematical Model of Interaction of a Symmetric Top with an Axially Symmetric External Field

A symmetric top is considered, which is a particular case of a mechanical top that is usually described by the canonical Poisson structure on T * SE (3). This structure is invariant under the right action of the rotation group SO(3), but the Hamiltonian of the symmetric top is invariant only under the right action of the subgroup S 1 , which corresponds to the rotation of the symmetric top around its axis of symmetry. This Poisson structure is obtained as the reduction T * SE (3) / S 1 . A Hamiltonian and motion equations are proposed that describe a wide class of interaction models of the symmetric top with an axially symmetric external field.