Abstract
Methods of computer algebra are used to study the properties of a nonlinear algebraic system that determines equilibrium orientations of a satellite moving along a circular orbit under the action of gravitational and constant torques. An algorithm for the construction of a Groebner basis is proposed for determining the equilibrium orientations of a satellite with a given constant torque and given principal central moments of inertia. The number of equilibria depending on the parameters of the problem is found by the analysis of real roots of algebraic equation of degree 6 from constructed Groebner basis. The domains with different numbers of equilibria are specified by the discriminant hyper surface given by discriminant of 6 degree polynomial, which was computed symbolically. The equations of boundary curves of two-dimensional section of the discriminant hypersurface are determined in function of values of the components of constant torque. Classification of domains with different number of equilibria from 24 to 0 is carried out for arbitrary values of the parameters.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Sarychev, V.A.: Problems of Orientation of Satellites, Itogi Nauki i Tekhniki. Ser. Space Research, vol. 11. VINITI, Moscow (1978)
Beletsky, V.V.: Attitude Motion of Satellite in Gravitational Field. MGU Press, Moscow (1975)
Likins, P.W., Roberson, R.E.: Uniqueness of equilibrium attitudes for earth-pointing satellites. J. Astronaut. Sci. 13, 87–88 (1966)
Garber, T.B.: Influence of constant disturbing torques on the motion of gravity-gradient stabilized satellites. AIAA J. 1, 968–969 (1963)
Sarychev, V.A., Gutnik, S.A.: Equilibria of a satellite subjected to gravitational and constant torques. Cosmic Research 32, 43–50 (1994)
Sarychev, V.A., Paglione, P., Guerman, A.: Influence of constant torque on equilibria of a satellite in a circular orbit. Celestial Mechanics and Dynamical Astronomy 87, 219–239 (2003)
Buchberger, B.: Theoretical basis for the reduction of polynomials to canonical forms. SIGSAM Bulletin, 19–29 (1976)
Char, B.W., Geddes, K.O., Gonnet, G.H., Monagan, M.B., Watt, S.M.: Maple Reference Manual. Watcom Publications Limited, Waterloo (1992)
Meiman, N.N.: Some problems on the distribution of the zeros of polynomials. Uspekhi Mat. Nauk 34, 154–188 (1949)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Gutnik, S.A., Guerman, A., Sarychev, V.A. (2015). Application of Computer Algebra Methods to Investigation of Influence of Constant Torque on Stationary Motions of Satellite. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2015. Lecture Notes in Computer Science(), vol 9301. Springer, Cham. https://doi.org/10.1007/978-3-319-24021-3_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-24021-3_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24020-6
Online ISBN: 978-3-319-24021-3
eBook Packages: Computer ScienceComputer Science (R0)