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Symbolic-Numerical Analysis of the Necessary Stability Conditions for the Relative Equilibria of an Orbital Gyrostat

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Abstract

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.

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Funding

The author was supported by the Russian Foundation for Basic Research (project no. 19–01–00301).

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory, Irkutsk, 664033, Russia

    A. V. Banshchikov

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  1. A. V. Banshchikov
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Correspondence to A. V. Banshchikov.

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Translated by L.B. Vertgeim

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Banshchikov, A.V. Symbolic-Numerical Analysis of the Necessary Stability Conditions for the Relative Equilibria of an Orbital Gyrostat. J. Appl. Ind. Math. 14, 213–221 (2020). https://doi.org/10.1134/S1990478920020015

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  • DOI: https://doi.org/10.1134/S1990478920020015

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