This article is cited in 3 papers

Symbolic-numerical analysis of the necessary stability conditions for the relative equilibria of an orbital gyrostat

A. V. Banshchikov

Matrosov Institute for System Dynamics and Control Theory SB RAS, ul. Lermontova 134, PO Box 292, Irkutsk 664033, Russia

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.

Keywords: orbital gyrostat, equilibrium stability, symbolic-numerical simulation, applied software, computer algebra. .

UDC: 519.688:531.36

Received: 30.10.2019
Revised: 30.10.2019
Accepted: 09.04.2020

DOI: 10.33048/SIBJIM.2020.23.201

 English version: Journal of Applied and Industrial Mathematics, 2020, 14:2, 213–221

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