  The motion of spinning test-masses in curved space-time is described with a
covariant hamiltonian formalism. A large class of hamiltonians can be used with
the model- independent Poisson-Dirac brackets, to obtain equations of motion.
Here we apply it to the minimal hamiltonian and also to a non-minimal
hamiltonian, describing the gravi- tational Stern-Gerlach force. And a note on
ISCO has been added.
