Abstract The problem of planar motions of a dumbbell-like body of variable length in a central field of Newtonian attraction is considered both in the exact formulation and in satellite approximation. In the satellite approximation the true anomaly of the center of mass is used as an independent variable, which has allowed us to represent the equation of planar oscillations of the dumbbell in the form similar to the Beletskii equation. Some exact solutions to the inverse problem are given both in the complete formulation and in satellite approximation. Under an assumption of small orbit eccentricity and amplitude of the dumbbell vibrations the conditions of existence are found for families of almost periodic motions and splitting separatrices. The phenomena of alternation of regular and chaotic motions are established numerically, as well as chaos suppression with increasing frequency of vibrations. Using the method of averaging the stabilization of tangent equilibria is proved to be impossible.


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    Titel :

    Planar oscillations of a vibrating dumbbell-like body in a central field of forces


    Beteiligte:
    Burov, A. (Autor:in) / Dugain, A. (Autor:in)

    Erschienen in:

    Cosmic Research ; 49 , 4 ; 353-359


    Erscheinungsdatum :

    2011-08-01


    Format / Umfang :

    7 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch




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