Abstract
This paper proposes two simple methods for determining equilibrium orientations of a satellite moving in a central Newtonian force field along a circular orbit under the action of the gravitational torque. The first method uses linear algebra approaches, while the second one employs computer algebra algorithms. The equilibrium orientations of the satellite in the orbital coordinate system for given values of principal central moments of inertia are determined by the roots of a system of nonlinear algebraic equations. To determine the equilibrium solutions, the system of algebraic equations is decomposed using linear algebra methods and algorithms for Gröbner basis construction. The equilibria of the satellite are determined by analyzing the real roots of the algebraic equations from the Gröbner bases constructed. Using the proposed approach, it is shown that the satellite with unequal principal central moments of inertia has 24 equilibrium orientations on a circular orbit.
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Gutnik, S.A., Sarychev, V.A. Symbolic-Analytic Methods for Studying Equilibrium Orientations of a Satellite on a Circular Orbit. Program Comput Soft 47, 119–123 (2021). https://doi.org/10.1134/S0361768821020055
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DOI: https://doi.org/10.1134/S0361768821020055