The Force Tracking Moment Action on the Gyrostat Motion

Abstract

The gyrostat moves around a fixed point under the forces influence in pseudo-Euclidean space with signature (3,1). The resulting moment of the external forces system and the gyrostatic moment are specified relative to the coordinate orthoreper, invariably associated with the gyrostat carrier, and are constant. Three types of gyrostat motion are given, in each of which the resulting force vector-moment is collinear to of the main axis of the gyrostat inertia, and the gyrostatic moment is orthogonal to this axis. The vector manifold of the gyrostat angular velocities and the field of its phase trajectories in the state space are found with the parametric integration method using. Integration of the gyrostat motion equations is carried out in quadratures and elliptic functions of time.