Application of computer algebra for analysis of gyroscopic stabilization of equilibriums of orbital gyrostat

Using the applied software developed on the basis of the computer algebra system Mathematica, the dynamics of the rotational motion along the circular orbit of a satellite-gyrostat in a Newtonian central field of forces are investigated. Assuming the instability of the potential system, the regions with an even degree of instability by Poincare are found in the space of introduced parameters. The paper considers the question of the possibility of gyroscopic stabilization of unstable relative equilibrium positions of the gyrostat, when the vector of the gyrostatic moment of the system lays in one of the planes formed by the principal central axes of inertia. The research results were obtained in a symbolic (analytical) form on a computer and by means of a numerical experiment with graphic interpretation.