  The Hamiltonian formulation of the motion of a spinning relativistic particle
in an external electromagnetic field is considered. The approach is based on
the introduction of new coordinates and their conjugated momenta to describe
the spin degrees of freedom together with an appropriate set of constraints in
the Dirac formulation. For particles with gyromagnetic ratio $g=2$, the
equations of motion do not predict any deviation from the standard Lorentz
force, while for $g \neq 2$ an additional force, which corresponds to the
magnetic dipole force, is obtained.
