Spin precession in a quadrupole lens

In transporting a polarized proton beam through a channel consisting of dipole magnets and quadrupoles, one needs to calculate the depolarization effects due to the magnetic fields. Usually the dipole magnet has a homogeneous field and the spin precession is calculated straightforwardly. But an equation of motion of spin in a quadrupole lens has not yet been solved analytically. The author proposes here such a solution and the result obtained is applied to some interesting practical cases. (5 refs).