Dynamics of a rigid body permanent motion in pseudo-Euclidean space

The conditions for the existence and properties of the permanent motion of an absolutely rigid body rotating around a fixed pole are studied in the pseudo-Euclidean space. The body is affected by a force vector-moment, which is constant relative to the coordinate system, invariably associated with the body, as well as a system of gyroscopic forces with a resulting vector-moment, which is linear relative to the angular velocity of the body. The first algebraic integrals of a dynamical system are found, as well as the necessary conditions for the existence of a permanent motion of a body. The equations of the moving hodograph of the angular velocity in this motion are obtained. The structural-kinetic properties of the axes of permanent rotation and the geometry of their distribution in space relative to the body are studied.