  The symmetric top is a special case of the general top, and canonical Poisson
structure on $T^*SE(3)$ is the common method of its description. This structure
is invariant under the right action of $SO(3)$, but the Hamiltonian of the
symmetric top is invariant only under the right action of subgroup $S^1$ that
corresponds to the rotation around the symmetry axis of the symmetric top. So,
its Poisson structure was obtained as the reduction $T^*SE(3)/S^1$. Next we
propose the Hamiltonian that describes the wide class of the interaction models
of symmetric top and axially-symmetric external field. The stability of the
levitating Orbitron in relative equilibrium was proved.
