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Analysis of the stability of relative equilibriums of a prolate axisymmetric gyrostat by symbolic—numerical modeling

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Abstract

Applying Lyapunov’s approach to the investigation of the stability of the motion according to first order approximation equations, the regions are singled out in the space of the inputed parameters where the stability, instability, or gyroscopic stabilization of relative equilibriums of a prolate axisymmetric orbital gyrostat with a constant gyrostatic moment vector are ensured. In particular, the result concerning instability and impossibility of gyroscopic stabilization of one in two existing equilibrium classes of the system have been formulated. The investigation was carried out using the LinModel software package and the symbolic—numerical modeling functions of the Mathematica Computer Algebra System.

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Authors and Affiliations

  1. Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033, Russia

    A. V. Banshchikov & S. V. Chaikin

Authors
  1. A. V. Banshchikov
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  2. S. V. Chaikin
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Correspondence to A. V. Banshchikov.

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Original Russian Text © A.V. Banshchikov, S.V. Chaikin, 2015, published in Kosmicheskie Issledovaniya, 2015, Vol. 53, No. 5, pp. 414–420.

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Banshchikov, A.V., Chaikin, S.V. Analysis of the stability of relative equilibriums of a prolate axisymmetric gyrostat by symbolic—numerical modeling. Cosmic Res 53, 378–384 (2015). https://doi.org/10.1134/S0010952515050020

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