Hamiltonian action of spinning particle with gravimagnetic moment

We develop Hamiltonian variational problem for spinning particle non-minimally interacting with gravity through the gravimagnetic moment kappa. For kappa = 0 our model yields Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations, the latter show unsatisfactory behavior of MPTD-particle in ultra-relativistic regime: its longitudinal acceleration increases with velocity. kappa = 1 yields a modification of MPTD-equations with the reasonable behavior: in the homogeneous fields, both longitudinal acceleration and (covariant) precession of spin-tensor vanish as v -> c.