[en] An integrable dynamical problem of a classical neutral particle interacting with an inhomogeneous magnetic field via a magnetic dipole moment is considered, which had previously been studied quantum mechanically. The equation for the centre of mass velocity is of second order resembling that of an anharmonic oscillator with velocity replacing position in the equation. The velocity undergoes curious oscillations, where the spin and centre of mass degrees of freedom exchange energy, although there is also, in general, a uniform component to the velocity. An application to the motion of a classical ''neutron'' in a magnetic domain wall is discussed, and comparison with previous quantum treatments made. (author)