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Subharmonic Oscillations in the Near-Circular Elliptic Sitnikov Problem

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Abstract—

We have considered the case of a restricted three-body problem (material points), when the masses of the two main attracting bodies are equal. Their orbits have been assumed to be ellipses. The problem regarding the third body’s motion of negligible mass under the influence of the main body’s gravitational attraction (the Sitnikov problem) allows particular solutions for the following: the third body moves along a straight line passing through the center of mass of the main bodies and perpendicular to the plane of their orbits. We have assumed that the eccentricity of the main body orbits is small and we investigated the nonlinear problem of the existence of the third body’s periodic motion with a period multiple of the revolution period of the main bodies in their orbits. The problem of stability (in Lyapunov’s sense) of these periodic motions under both perturbations keeping the trajectory of the third body rectilinear and arbitrary spatial perturbations has also been solved.

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Funding

This work was supported by he Russian Science Foundation, project no. 19-11-00116 at the Moscow Aviation Institute (National Research University) and the Ishlinsky Institute of Mechanical Problems, Russian Academy of Sciences.

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics of the RAS, Moscow, Russia

    A. P. Markeev

  2. Moscow Aviation Institute, Moscow, Russia

    A. P. Markeev

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  1. A. P. Markeev
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Correspondence to A. P. Markeev.

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Translated by N. Petrov

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Markeev, A.P. Subharmonic Oscillations in the Near-Circular Elliptic Sitnikov Problem. Mech. Solids 55, 1162–1171 (2020). https://doi.org/10.3103/S0025654420080154

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