Geodesic
Symbolic-numerical analysis of the necessary stability conditions
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 2, pp. 5-16.

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Using the software developed on the basis of the computer algebra system “Mathematica”, we study the rotational motion along the circular orbit of a satellite-gyrostat in a Newtonian central field of forces. The linearized equations of a perturbed motion in the vicinity of the relative equilibrium of the system are constructed on a computer in symbolic form, and the necessary stability conditions are obtained for the equilibrium. Implementing the parametric analysis of the derived inequalities, we consider one of the cases when the vector of the gyrostatic moment of the system lies 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 as 2D images.
Keywords: orbital gyrostat, equilibrium stability, symbolic-numerical simulation, applied software, computer algebra. . 
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A. V. Banshchikov. Symbolic-numerical analysis of the necessary stability conditions. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 2, pp. 5-16. http://geodesic.mathdoc.fr/item/SJIM_2020_23_2_a0/

[1] V. A. Sarychev, “Questions of orientation of artificial satellites”, Issledovanie kosmicheskogo prostranstva, 11 (1978), 5–224, VINITI AN SSSR, Moscow (in Russian)

[2] A. A. Anchev, V. A. Atanasov, “Analysis of necessary and sufficient conditions for stability of equilibria of a satellite-gyrostat”, Space Researches, 28:6 (1990), 831–836 (in Russian)

[3] A. V. Banshchikov, V. D. Irtegov, T. N. Titorenko, Bundled Software For Modeling In Symbolic Form Of Mechanical Systems And Electric Circuits, State registration certificate No. 2016618253 issued on July 25, 2016, Federal Service on Intellectual Property (ROSPATENT) (in Russian)

[4] A. V. Banshchikov, “Analysis of dynamics of high-dimension mechanical systems by using a computer algebra system”, Sib. zhurn. industr. matematiki, 12:3 (2009), 15–27 (in Russian)

[5] A. V. Banshchikov, L. A. Burlakova, V. D. Irtegov, T. N. Titorenko, “Symbolic computation in modeling and qualitative analysis of dynamical systems”, Vychisl. tekhnologii, 19:6 (2014), 3–18 (in Russian)

[6] V. V. Kozlov, “Stabilization of the unstable equilibria of charges by intense magnetic fields”, J. Appl. Math. Mech., 61:3 (1997), 377–384 | DOI | MR | MR | Zbl

[7] N. G. Chetaev, Stability of Motion. Studies in Analytical Mechanics, Izd. Akal. Nauk SSSR, M., 1962 (in Russian) | MR

[8] S. A. Gutnik, L. Santush, V. A. Sarychev, A. Silva, “Dynamics of a Gyrostat Satellite Subjected to the Action of Gravity Moment. Equilibrium Attitudes and Their Stability”, J. Comp. Syst. Sci. Internat., 54:3 (2015), 469–482 | DOI | DOI | MR | Zbl

[9] S. A. Gutnik, V. A. Sarychev, “Application of Computer Algebra Methods for Investigation of Stationary Motion of a Gyrostat Satellite”, Program. Comput. Softw., 43:2 (2017), 90–97 | DOI | MR | MR

[10] S. V. Chaikin, “The Set of Relative Equilibria of a Stationary Orbital Asymmetric Gyrostat”, J. Appl. Indust. Math., 13:1 (2019), 30–35 | DOI | MR | Zbl

[11] V. A. Sarychev, S. A. Mirer, A. A. Degtyarev, “Dynamics of a gyrostat satellite with the vector of gyrostatic moment in the principal plane of inertia”, Cosmic Research, 46:1 (2008), 60–73 | DOI

[12] A. V. Banshchikov, S. V. Chaikin, “Analysis of the stability of relative equilibria of a prolate axisymmetric gyrostat by symbolic-numerical modeling”, Cosmic Research, 53:5 (2015), 378–384 | DOI | DOI | MR

[13] A. V. Banshchikov, “Parametric analysis of conditions of gyroscopic stabilization of the relative equilibria of an oblate axisymmetric gyrostat”, Math. Modeling, 28:4 (2016), 33–42 (in Russian) | MR