  The article is devoted to the description of dynamics of magnets with
arbitrary spin on the basis of the Hamiltonian formalism. The relationship
between the magnetic ordering and Poisson bracket subalgebras of the magnetic
degrees of freedom for spin s=1/2; 1; 3/2 has been established. We have been
obtained non-linear dynamic equations without damping for normal and degenerate
non-equilibrium states of high-spin magnets with the properties of the SO(3),
SU(4), SU(2)$\times$SU(2), SU(3), SO(4), SO(5) symmetry of exchange
interaction. The connection between models of the magnetic exchange energy and
the Casimir invariants has been discussed.
