The problem of motion of a rigid body with a fixed point in a flow of particles

The problem of motion of a rigid body with a fixed point in a free molecular flow of particles is considered. It is shown that the equations of motion of the body generalize the classical Euler - Poisson equations of motion of a heavy rigid body with a fixed point and they are represented in the form of the classical Euler - Poisson equations in the case, when the surface of the body in a flow of particles is a sphere. Problems of the existence of first integrals in the considered system are discussed.