Application of Computer Algebra Methods to Investigation of Influence of Constant Torque on Stationary Motions of Satellite

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• 刊名：Lecture Notes in Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：9301
• 期：1
• 页码：198-209
• 全文大小：405 KB
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  4.Garber, T.B.: Influence of constant disturbing torques on the motion of gravity-gradient stabilized satellites. AIAA J. 1, 968–969 (1963)
  5.Sarychev, V.A., Gutnik, S.A.: Equilibria of a satellite subjected to gravitational and constant torques. Cosmic Research 32, 43–50 (1994)
  6.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)
  7.Buchberger, B.: Theoretical basis for the reduction of polynomials to canonical forms. SIGSAM Bulletin, 19–29 (1976)
  8.Char, B.W., Geddes, K.O., Gonnet, G.H., Monagan, M.B., Watt, S.M.: Maple Reference Manual. Watcom Publications Limited, Waterloo (1992)
  9.Meiman, N.N.: Some problems on the distribution of the zeros of polynomials. Uspekhi Mat. Nauk 34, 154–188 (1949)
  
• 作者单位：Sergey A. Gutnik (17)
  Anna Guerman (18)
  Vasily A. Sarychev (19)
  
  17. Moscow State Institute of International Relations (University), 76, Prospekt Vernadskogo, Moscow, 119454, Russia
  18. University of Beira Interior, 6200-001, Covilha, Portugal
  19. Keldysh Institute of Applied Mathematics (Russian Academy of Sciences), 4, Miusskaya Square, Moscow, 125047, Russia
  
• 丛书名：Computer Algebra in Scientific Computing
• ISBN：978-3-319-24021-3
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

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.