On Three Invariant Relations of the Equations of Motion of a Body in a Potential Field of Force

Abstract

The problem of the motion of a rigid body having a fixed point in a potential field of forces is considered. The existence conditions of three invariant relations of a special type, the choice of which is due to the integration of the Poisson equations by quadrature, are investigated. A new solution of the equations of motion of a dynamically symmetric body is found. A dynamically symmetric body is characterized by one arbitrary function of the vertical vector component. The case where the angular momentum modulus is constant is studied.