Obtaining and Analysis of the Necessary Conditions of Stability of Orbital Gyrostat by Means of Computer Algebra
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.
- 1.Sarychev, V.A.: Problems of orientation of satellites. Itogi Nauki i Tekhniki. Series “Space Research” 11, 5–224 (1978). VINITI Publication, Moscow (in Russian)Google Scholar
- 2.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)Google Scholar
- 3.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)Google Scholar
- 9.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_5CrossRefGoogle Scholar
- 11.Chetaev, N.G.: Stability of Motion. Works on Analytical Mechanics. AS USSR, Moscow (1962). (in Russian)Google Scholar