Equations of motion for particles of arbitrary spin invariant under the Galileo group

The first and the second order differential equations are derived which are invariant under the Galilei group and describe the motion of a particle with arbitrary spin. These equations admit the Lagrangian formulation and describe the dipole, spin-orbital and Darwin couplings of a particle with external electromagnetic field which are considered traditionally as pure relativistic effects. The problem of the motion of spin $1/2$ nonrelativistic particle in an external electromagnetic field is exactly solved.