Volume 14, no. 2Pages 70 - 77

Application of Computer Algebra for Analysis of Gyroscopic Stabilization of Equilibriums of Orbital Gyrostat

A.V. Banshchikov
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.
Full text
gyroscopic stabilization; degree of instability; system of inequalities; symbolic-numerical modelling.
1. Chetaev N.G. Ustoichivost dvizheniya. Raboty po analiticheskoy mekhanike [Stability of Motion. Works on Analytical Mechanics]. Moscow, AS USSR, 1962. (in Russian)
2. Aleksandrov A.Iu., Kosov A.A. [On Stability of Gyroscopic Systems]. Vestnik of Saint Petersburg University. Series: Applied Mathematics. Computer Science. Control Processes, 2013, no. 2, pp. 3-13. (in Russian)
3. Gutnik S.A., Santos L., Sarychev V.A., Silva A. Dynamics of a Gyrostat Satellite Subjected to the Action of Gravity Moment. Equilibrium Attitudes and Their Stability. Journal Computer and Systems Sciences International, 2015, vol. 54, no. 3, pp. 469-482.
4. Banshchikov A.V., Chaikin S.V. Analysis of the Stability of Relative Equilibriums of a Prolate Axisymmetric Gyrostat by Symbolic-Numerical Modelling. Cosmic Research, 2015, vol. 53, no. 5, pp. 378-384.
5. Gutnik S.A., Sarychev V.A. Application of Computer Algebra Methods for Investigation of Stationary Motions of a Gyrostat Satellite. Programming and Computer Software, 2017, vol. 43, no. 2, pp. 90-97.
6. Banshchikov A.V., Burlakova L.A., Irtegov V.D., Titorenko T.N. [Symbolic Computation in Modelling and Qualitative Analysis of Dynamic Systems]. Computational Technologies, 2014, vol. 19, no. 6, pp. 3-18. (in Russian)
7. Banshchikov A.V. Obtaining and Analysis of the Necessary Conditions of Stability of Orbital Gyrostat by means of Computer Algebra. Lecture Notes in Computer Science, 2019, vol. 11661, pp. 57-66.