Abstract
Using the applied software developed on the basis of the computer algebra system “Mathematica” and its functions of symbolic-numerical modeling, the dynamics of the rotational motion along the circular orbit of a satellite-gyrostat in a Newtonian central field of forces is investigated. In accordance with the problem of Lyapunov’s stability from the equations of perturbed motion in the first approximation, the regions with an even degree of instability by Poincaré 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 is located in one of the planes formed by the principal central axes of inertia. The research results were obtained in a symbolic (analytic) form on a computer and by means of a numerical experiment with the graphic interpretation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Agafonov, S.A.: The stability and stabilization of the motion of non-conservative mechanical systems. J. Appl. Math. Mech. 74(4), 401–405 (2010)
Banshchikov, A.V.: Research on the stability of relative equilibria of oblate axisymmetric gyrostat by means of symbolic-numerical modelling. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2015. LNCS, vol. 9301, pp. 61–71. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24021-3_5
Banshchikov, A.V.: Symbolic-numerical analysis of the necessary stability conditions for the relative equilibria of an orbital gyrostat. J. Appl. Indust. Math. 14(2), 213–221 (2020)
Banshchikov, A.V., Burlakova, L.A., Irtegov, V.D., Titorenko, T.N.: Symbolic computation in modelling and qualitative analysis of dynamic systems. Comput. Technol. 19(6), 3–18 (2014). (in Russian)
Banshchikov, A.V., Chaikin, S.V.: Analysis of the stability of relative equilibria of a prolate axisymmetric gyrostat by symbolic-numerical modeling. Cosm. Res. 53(5), 378–384 (2015)
Banshchikov, A.V., Irtegov, V.D., Titorenko, T.N.: Software package for modeling in symbolic form of mechanical systems and electrical circuits. Certificate of State Registration of Computer Software. Federal service for intellectual property. No. 2016618253 (2016) (in Russian)
Banshchikov, A.V., Vetrov, A.A.: Application of software tools for symbolic description and modeling of mechanical systems. In: Bychkov, I.V. et al. (eds.) CEUR Workshop Proceedings of the 2nd International Workshop on Information, Computation, and Control Systems for Distributed Environments, pp. 33–42 (2020). http://ceur-ws.org/Vol-2638/paper3.pdf
Beletskii, V.V.: Motion of an Artificial Satellite Relative to the Center of Mass. Nauka, Moscow (1965).(in Russian)
Chetaev, N.G.: The Stability of Motion. Pergamon Press, New York (1961)
Gutnik, S.A., Sarychev, V.A.: Application of computer algebra methods for investigation of stationary motions of a gyrostat satellite. Program. Comput. Softw. 43(2), 90–97 (2017). https://doi.org/10.1134/S0361768817020050
Kozlov, V.V.: Stabilization of the unstable equilibria of charges by intense magnetic fields. J. Appl. Math. Mech. 61(3), 377–384 (1997)
Prokopenya, A.N., Minglibayev, M.Z., Mayemerova, G.M.: Symbolic calculations in studying the problem of three bodies with variable masses. Program. Comput. Softw. 40(2), 79–85 (2014). https://doi.org/10.1134/S036176881402008X
Sarychev, V.A.: Problems of orientation of satellites. In: Itogi Nauki i Tekhniki. Series "Space Research", vol. 11, pp. 5–224. VINITI Publication, Moscow (1978). (in Russian)
Sarychev, V.A., Mirer, S.A., Degtyarev, A.A.: Dynamics of a gyrostat satellite with the vector of gyrostatic moment in the principal plane of inertia. Cosm. Res. 46(1), 60–73 (2008)
Wolfram, S.: The Mathematica Book, 5th edn. Wolfram Media, Inc., Somerville (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Banshchikov, A.V. (2022). Application of Symbolic-Numerical Modeling Tools for Analysis of Gyroscopic Stabilization of Gyrostat Equilibria. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2022. Lecture Notes in Computer Science, vol 13366. Springer, Cham. https://doi.org/10.1007/978-3-031-14788-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-031-14788-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-14787-6
Online ISBN: 978-3-031-14788-3
eBook Packages: Computer ScienceComputer Science (R0)