Dynamics of a gyrostat satellite with the vector of gyrostatic moment tangent to the orbital plane

In this paper, a gyrostat satellite in a circular orbit with its gyrostatic moment tangent to the orbital plane and collinear with the orbital speed is studied regarding its equilibria, bifurcation of equilibria, and asymptotic stability conditions. In the general case, where any gyrostat angular momentum is aligned with any of the orbital coordinate frames, interesting results arose regarding its equilibria bifurcation regarding conditions near to the ones presented in this paper, namely equilibria regions outside their main regions near to the orbital plane tangent. For equilibria and bifurcation of equilibria, a symbolic-numerical method is used to obtain the polynomial equations in function of non-dimensional parameters whose roots are equivalent to the number of equilibria positions. For the asymptotic stability, the results are tested using the Lyapunov stability theory scheme.(c) 2022 COSPAR. Published by Elsevier B.V. All rights reserved.

Automated summary

This paper investigates the equilibria, bifurcation of equilibria, and asymptotic stability conditions of a gyrostat satellite in a circular orbit with its gyrostatic moment tangent to the orbital plane and collinear with the orbital speed. The study reveals interesting results regarding the bifurcation of equilibria when the gyrostat angular momentum is aligned with any of the orbital coordinate frames. A symbolic-numerical method is used to obtain polynomial equations for equilibria positions, and the asymptotic stability is tested using the Lyapunov stability theory scheme.