Abstract
With the help of software developed on the basis of the “Mathematica” computer algebra system, the dynamics of a satellite-gyrostat moving in a Newtonian central field of forces along the circular Keplerian orbit was investigated. The linearized equations of perturbed motion in the vicinity of the relative equilibrium of the system are constructed in the symbolic form on PC and the necessary conditions for its stability are obtained. The parametric analysis of the inequalities considers one of the cases when the vector of the gyrostatic moment of the system is in one of the planes formed by the principal central axes of inertia. The obtained stability regions have an analytical form or a graphical representation in the form of 2D images.
The work has been partially supported by the Russian Foundation for Basic Research (grant No. 19-01-00301).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Sarychev, V.A.: Problems of orientation of satellites. Itogi Nauki i Tekhniki. Series “Space Research” 11, 5–224 (1978). VINITI Publication, Moscow (in Russian)
Anchev, A.A., Atanasov, V.A.: Analysis of the necessary and sufficient conditions for the stability of the equilibrium of a gyrostatic satellite. Kosm. Issled. 28(6), 831–836 (1990). (in Russian)
Banshchikov, A.V., Irtegov, V.D., Titorenko, T.N.: Software package for modeling in symbolic form of mechanical systems and electrical circuits. In: Certificate of State Registration of Computer Software No. 2016618253. Federal Service for Intellectual Property. Issued 25 July 2016. (in Russian)
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)
Kozlov, V.V.: Stabilization of the unstable equilibria of charges by intense magnetic fields. J. Appl. Math. Mech. 61(3), 377–384 (1997)
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. J. Comput. Syst. Sci. Int. 54(3), 469–482 (2015)
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)
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)
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., Chaikin, S.V.: Analysis of the stability of relative equilibriums of a prolate axisymmetric gyrostat by symbolic-numerical modeling. Cosm. Res. 53(5), 378–384 (2015)
Chetaev, N.G.: Stability of Motion. Works on Analytical Mechanics. AS USSR, Moscow (1962). (in Russian)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Banshchikov, A.V. (2019). Obtaining and Analysis of the Necessary Conditions of Stability of Orbital Gyrostat by Means of Computer Algebra. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-26831-2_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-26830-5
Online ISBN: 978-3-030-26831-2
eBook Packages: Computer ScienceComputer Science (R0)