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The extensive analysis of the dynamics of relativistic spinning particles ispresented. Using the coadjoint orbits method the Hamiltonian dynamics isexplicitly described. The main technical tool is the factorization of generalLorentz transformation into pure boost and rotation. The equivalent constraineddynamics on Poincare group (viewed as configuration space) is derived andcomplete classification of constraints is performed. It is shown that the firstclass constraints generate local symmetry corresponding to the stabilitysubgroup of some point on coadjoint orbit. The Dirac brackets for second classconstraints are computed. Finally, canonical quantization is performed leadingto infinitesimal form of irreducible representations of Poincare group.

Spinning particles, coadjoint orbits and Hamiltonian formalism