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Investigation of the Dynamics of Two Connected Bodies in the Plane of a Circular Orbit Using Computer Algebra Methods

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Abstract

Computer algebra methods are used to investigate the equilibrium orientations of a system of two bodies connected by a spherical hinge that moves along a circular orbit under the action of gravitational torque in the plane of the orbit. An algebraic method based on the resultant approach is applied to reduce the satellite stationary motion system of algebraic equations to a single algebraic equation in one variable, which determines the equilibrium configurations of the two-body system in the orbital plane. Classification of domains with equal numbers of equilibrium solutions is carried out using algebraic methods for constructing discriminant hypersurfaces. Discriminant curves in the space of system parameters that determine boundaries of domains with a fixed number of equilibria for the two-body system are obtained symbolically. Using the proposed approach it is shown that the satellite-stabilizer system can have up to 24 equilibrium orientations in the plane of a circular orbit. Some simple cases of the problem were studied in detail.

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Authors and Affiliations

  1. 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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Correspondence to Sergey A. Gutnik.

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Gutnik, S.A., Sarychev, V.A. Investigation of the Dynamics of Two Connected Bodies in the Plane of a Circular Orbit Using Computer Algebra Methods. Math.Comput.Sci. 17, 17 (2023). https://doi.org/10.1007/s11786-023-00569-4

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