Variational problem for Hamiltonian system on so(k, m) Lie-Poisson   manifold and dynamics of semiclassical spin
  We describe the procedure for obtaining Hamiltonian equations on a manifold with $so(k, m)$ Lie-Poisson bracket from a variational problem. This implies identification of the manifold with base of a properly constructed fiber bundle embedded as a surface into the phase space with canonical Poisson bracket. Our geometric construction underlies the formalism used for construction of spinning particles in [24-27], and gives precise mathematical formulation of the oldest idea about spin as the "inner angular momentum". 
A. A. Deriglazov
math-ph gr-qc hep-th math.MP quant-ph