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.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

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


    Contributors:
    Burov, A. (author) / Dugain, A. (author)

    Published in:

    Cosmic Research ; 49 , 4 ; 353-359


    Publication date :

    2011-08-01


    Size :

    7 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    Boom Forces in Librating Dumbbell-Type Satellites

    SUBHASH CHANDER SHARMA AND WILLEM STUER | AIAA | 1974





    VIBRATING BODY SUPPORT STRUCTURE

    OMORI IKUO | European Patent Office | 2015

    Free access