  A covariant hamiltonian formalism for the dynamics of compact spinning bodies
in curved space-time in the test-particle limit is described. The construction
allows a large class of hamiltonians accounting for specific properties and
interactions of spinning bodies. The dynamics for a minimal and a specific
non-minimal hamiltonian is discussed. An independent derivation of the
equations of motion from an appropriate energy-momentum tensor is provided. It
is shown how to derive constants of motion, both background-independent and
background-dependent ones.
