Deriving Mathisson - Papapetrou equations from relativistic pseudomechanics

It is shown that the equations of motion of a test point particle with spin in a given gravitational field, so called Mathisson - Papapetrou equations, can be derived from Euler - Lagrange equations of the relativistic pseudomechanics -- relativistic mechanics, which side by side uses the conventional (commuting) and Grassmannian (anticommuting) variables. In this approach the known difficulties of the Mathisson - Papapetrou equations, namely, the problem of the choice of supplementary conditions and the problem of higher derivatives are not appear.