  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".
