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A Symbolic Study of the Satellite Dynamics Subject to Damping Torques

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Computer Algebra in Scientific Computing (CASC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10490))

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Abstract

The dynamics of the rotational motion of a satellite moving in the central Newtonian force field in a circular orbit under the influence of gravitational and active damping torques is investigated with the help of computer algebra methods. The properties of a nonlinear algebraic system that determines equilibrium orientations of a satellite under the action of gravitational and active damping torques were studied. An algorithm for the construction of a Gröbner basis is proposed for determining the equilibrium orientations of a satellite with given central moments of inertia and given damping torques. The conditions of the equilibria’s existence were obtained by the analysis of real roots of algebraic equations from the constructed Gröbner basis. The domains with an equal number of equilibria were specified by using algebraic methods for the construction of discriminant hypersurfaces. The conditions of asymptotic stability of the satellite’s equilibria were determined as a result of the analysis of linearized equations of motion using Routh–Hurwitz criterion.

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Acknowledgements

The authors thank the reviewers for very useful remarks and suggestions and Professor V. Gerdt for the advice on the effectiveness of methods and algorithms of Gröbner basis construction.

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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 .

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Editors and Affiliations

  1. Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Universität Kassel, Kassel, Germany

    Werner M. Seiler

  4. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Gutnik, S.A., Sarychev, V.A. (2017). A Symbolic Study of the Satellite Dynamics Subject to Damping Torques. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2017. Lecture Notes in Computer Science(), vol 10490. Springer, Cham. https://doi.org/10.1007/978-3-319-66320-3_13

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  • DOI: https://doi.org/10.1007/978-3-319-66320-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66319-7

  • Online ISBN: 978-3-319-66320-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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