On the motion of a body with a fixed point in a particle flow

The problem of the 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 a body generalize the classical Euler-Poisson equations of motion of a heavy rigid body with a fixed point and are represented in the form of the classical Euler-Poisson equations in the case when the surface of a body flown by a particle flow is a sphere. Questions of the existence of first integrals in the problem under consideration are discussed.