  We prove that well known first-order (in spin, momentum, and space-time
coordinates) equations of motion of relativistic top are equivalent to the
third-order equations of Mathisson on the surface of the Mathisson-Pirani
auxiliary constraint. We then consider these third-order equations in flat
space-time with constant spin 4-vector and invent a Lagrange function for them.
Allowing physical interpretation to be applied to the complete set of extremals
yields a whole spectrum of spin-dependent effective 'proper mass' of the
relativistic top.
