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A Symbolic Investigation of the Influence of Aerodynamic Forces on Satellite Equilibria

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Computer Algebra in Scientific Computing (CASC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9890))

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Abstract

Computer algebra methods 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 aerodynamic torques. An algorithm for the construction of a Gröbner basis is proposed for determining the equilibrium orientations of a satellite with given principal central moments of inertia and given aerodynamic torque in special cases, when the center of pressure of aerodynamic forces is located in one of the principal central planes of inertia of the satellite. The conditions of the equilibria existence are obtained, depending on three dimensionless parameters of the problem. The number of equilibria depending on the parameters is found by the analysis of real roots of algebraic equations from the constructed Gröbner basis. The evolution of domains with fixed number of equilibria from 24 to 8 is investigated in detail. All bifurcation values of the system parameters corresponding to the qualitative change of these domains are determined.

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Author information

Authors and Affiliations

  1. Moscow State Institute of International Relations (University), 76, Prospekt Vernadskogo, Moscow, 119454, Russia

    Sergey A. Gutnik

  2. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 4, Miusskaya Square, Moscow, 125047, Russia

    Vasily A. Sarychev

Authors
  1. Sergey A. Gutnik
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  2. Vasily A. Sarychev
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Corresponding author

Correspondence to Sergey A. Gutnik .

Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Werner M. Seiler

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Gutnik, S.A., Sarychev, V.A. (2016). A Symbolic Investigation of the Influence of Aerodynamic Forces on Satellite Equilibria. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2016. Lecture Notes in Computer Science(), vol 9890. Springer, Cham. https://doi.org/10.1007/978-3-319-45641-6_16

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  • DOI: https://doi.org/10.1007/978-3-319-45641-6_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45640-9

  • Online ISBN: 978-3-319-45641-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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