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Symbolic Investigation of the Dynamics of a System of Two Connected Bodies Moving Along a Circular Orbit

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Computer Algebra in Scientific Computing (CASC 2019)

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Abstract

The dynamics of the system of two bodies, connected by a spherical hinge, that moves along a circular orbit under the action of gravitational torque is investigated. Computer algebra method based on the resultant approach was applied to reduce the satellite stationary motion system of algebraic equations to a single algebraic equation in one variable that determines all planar equilibrium configurations of the two–body system. Classification of domains with equal numbers of equilibrium solutions is carried out using algebraic methods for constructing discriminant hypersurfaces. Bifurcation curves in the space of system parameters that determine boundaries of domains with a fixed number of equilibria of the two–body system were obtained symbolically. Depending on the parameters of the problem, the number of equilibria was found by analyzing the real roots of the algebraic equations.

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Author information

Authors and Affiliations

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

    Sergey A. Gutnik

  2. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny, 141701, Russia

    Sergey A. Gutnik

  3. 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. Coventry University, Coventry, UK

    Matthew England

  2. University of Kassel, Kassel, Germany

    Wolfram Koepf

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. University of Kassel, Kassel, Germany

    Werner M. Seiler

  5. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Gutnik, S.A., Sarychev, V.A. (2019). Symbolic Investigation of the Dynamics of a System of Two Connected Bodies Moving Along a Circular Orbit. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_12

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  • DOI: https://doi.org/10.1007/978-3-030-26831-2_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26830-5

  • Online ISBN: 978-3-030-26831-2

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