Classical spinning particle assuming a covariant Hamiltonian

We consider a classical spinning particle in the frame of the relativistic physics by means of a covariant Hamiltonian and of a generalization of Poisson brackets which take into account the gauge fields. We obtain different equations of motion and evolution in this context and we compare our results with those of Bargmann-Michel-Telegdi. An extension to the case of a curved space and a link towards quantum theory are given at the end of the paper.