  By means of the method of moving Frenet-Serret frame the set of equations of
motion is derived for spinning particle in an arbitrary external field, which
is determined by potential depending from both position and the state of
movement, as well as by two pseudo-vectors one of which is easily associated
with external magnetic field, and another still remains undetermined. The
equations give a possibility to describe the motion of both massive and
massless particles with spin. All solutions of the equations of motion in the
absence of external fields were found, and besides, we give more precise
definition of a free object. It turns out that the massive particles always
possess a longitudinal polarization. There are possible transversal motions of
the following types: 1) oscillatory motion with proper frequency, 2) circular
motion, and 3) complicated motion along rosette trajectories round the center
of inertia with the velocity, varying in finite limits. Free massless particles
can either fluctuate or move along complicated paths around fixed centers of
balance, when the spin of the particles can have any direction.
