Application of Symbolic Computation Methods for Investigation of Stationary Motions of an Axisymmetric Satellite

• Published in: Programming and computer software Vol. 44; no. 2; pp. 94 - 99
• Main Authors: Gutnik, S. A., Sarychev, V. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.03.2018; Springer Nature B.V
• Subjects: Active damping; Algebra; Algorithms; Artificial Intelligence; Circular orbits; Computer algebra; Computer Science; Hyperspaces; International relations; Motion systems; Operating Systems; Software; Software Engineering; Software Engineering/Programming and Operating Systems; Velocity
• ISSN: 0361-7688; 1608-3261
• DOI: 10.1134/S0361768818020056

With the help of computer algebra methods properties of the algebraic system that determines stationary motions of an axisymmetric satellite moving along a circular orbit subject to gravitational and active damping moments are investigated. The main attention is paid to the study of the conditions for the existence of stationary satellite motions. Computer algebra methods based on the algorithm for the construction of Gröbner bases are applied to reduce the satellite stationary motion system of six algebraic equations in six variables to a single algebraic equation in one variable that determines all stationary motions of the satellite. A classification of domains with equal numbers of stationary solutions is carried out using algebraic methods for constructing discriminant hypersurfaces. The effectiveness of various algorithms for constructing Gröbner bases for the solution of the problem under consideration was compared.