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Symbolic-Numeric Investigation of the Aerodynamic Forces Influence on Satellite Dynamics

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Computer Algebra in Scientific Computing (CASC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6885))

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Abstract

An approach for symbolic-numeric stability analysis of equilibrium orientations of a satellite in a circular orbit under the influence of gravitational and aerodynamic forces is considered. The stationary motions of a satellite are governed by a system of nonlinear algebraic equations. A computer algebra method based on an algorithm for the construction of a Groebner basis and the resultant concept is proposed for determining all equilibrium orientations of a satellite with a given aerodynamic torque and given principal central moments of inertia. It is shown that equilibrium orientations are determined by real solutions of algebraic equation of the twelfth degree. Evolution of domains with a fixed number of equilibria is investigated in detail. The stability analysis of equilibria is performed on the basis of Lyapunov theorem. The equilibrium orientations and their stability are analyzed numerically.

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References

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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

Authors
  1. Sergey A. Gutnik
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Evgenii V. Vorozhtsov

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© 2011 Springer-Verlag Berlin Heidelberg

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Gutnik, S.A. (2011). Symbolic-Numeric Investigation of the Aerodynamic Forces Influence on Satellite Dynamics. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2011. Lecture Notes in Computer Science, vol 6885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23568-9_15

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  • DOI: https://doi.org/10.1007/978-3-642-23568-9_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23567-2

  • Online ISBN: 978-3-642-23568-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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