  We use the vector model of spinning particle to analyze the influence of
spin-field coupling on the particle's trajectory in ultra-relativistic regime.
The Lagrangian with minimal spin-gravity interaction yields the equations
equivalent to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations of a
rotating body. We show that they have unsatisfactory behavior in the
ultra-relativistic limit. In particular, three-dimensional acceleration of the
particle increases with velocity and becomes infinite in the ultra-relativistic
limit. The reason is that in the equation for trajectory emerges the term which
can be thought as an effective metric generated by the minimal spin-gravity
coupling. Therefore we examine the non-minimal interaction through the
gravimagnetic moment $\kappa$, and show that the theory with $\kappa=1$ is free
of the problems detected in MPTD-equations. Hence the non-minimally interacting
theory seem more promising candidate for description of a relativistic rotating
body in general relativity.
  The Lagrangian for the particle in an arbitrary electromagnetic field in
Minkowski space leads to generalized Frenkel and Bargmann-Michel-Telegdi
equations. The particle with magnetic moment in electromagnetic field and the
particle with gravimagnetic moment in gravitational field have very similar
structure of equations of motion. In particular, the spin-electromagnetic
coupling also produces an effective metric for the particle with anomalous
magnetic moment. If we use the usual special-relativity notions for time and
distance, then the critical speed, which the particle cannot exceed during its
evolution in electromagnetic field, is different from the speed of light. This
can be corrected assuming that the three-dimensional geometry should be defined
with respect to the effective metric.
