  This work is devoted to an examination of Stern-Gerlach forces consistent
with special relativity and is motivated by recent interest in the relativistic
Stern-Gerlach force acting on polarized protons in high-energy particle
accelerators. The equations for the orbital and spin motion of a classical
charged particle with arbitrary intrinsic magnetic dipole moment in an external
electromagnetic field are considered and by imposing the constraints of special
relativity and restricting to first order in spin (= first order $\hbar$) a
well-defined class of spin-orbit systems is obtained. All these systems can be
treated on an equal footing including such prominent cases as those considered
by Frenkel and by Good. The Frenkel case is considered in great detail because
I show that this system is identical with the one introduced by Derbenev and
Kondratenko for studying spin motion in accelerators. In particular I prove
that the spin-orbit system of Derbenev and Kondratenko is (nonmanifestly)
Poincar\'e covariant and identify the transformation properties of this system
under the Poincar\'e group. The Derbenev-Kondratenko Hamiltonian was originally
proposed as a way to combine relativistic spin precession and the Lorentz
force. The aforementioned findings now demonstrate that the
Derbenev-Kondratenko Hamiltonian also provides a legitimate framework for
handling the relativistic Stern-Gerlach force. Numerical examples based on the
Frenkel and Good cases for the HERA proton ring and electromagnetic traps are
provided.
