The translational–rotational motions of a symmetrical dumbbell are considered in a circular restricted three-body problem where two primaries of equal mass move in circular orbits about common barycenter. A new type of motion is described for the dumbbell whereby its barycenter moves along the normal to the plane of rotation of the two primaries, whilst the dumbbell itself rotates continuously around the normal, forming a constant angle of π/2 with it (the invariant manifold “gravitational propeller”). It is shown that this manifold includes several two-dimensional invariant submanifolds. The dynamics of a dumbbell on these submanifolds is described. Relative equilibria were found on a “gravitational propeller” when the dumbbell mass center rests at the barycenter of the system, while the dumbbell is oriented parallel to the axis connecting the primaries or perpendicular to it. The stability of these equilibria is investigated. Small spatial nonlinear oscillations on a “gravitational propeller” manifold in the vicinity of a stable relative equilibrium were studied for the dumbbell of infinitesimal length. It is shown that these oscillations have the nature of a nonlinear parametric resonance, which sets a “slow” amplitude modulation of “fast” harmonic oscillations along the angle of rotation of the dumbbell.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    On Dumbbell Motions in the Generalized Circular Sitnikov Problem


    Additional title:

    Cosmic Res


    Contributors:

    Published in:

    Cosmic Research ; 62 , 3 ; 302-309


    Publication date :

    2024-06-01


    Size :

    8 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    On equilibrium stability in the Sitnikov problem

    Kalas, V. O. / Krasil’nikov, P. S. | Springer Verlag | 2011


    On equilibrium stability in the Sitnikov problem

    Kalas, V. O. / Krasil’nikov, P. S. | Online Contents | 2011


    Dumbbell-shaped wheel circular rail transport vehicle

    LIU XINMING / ZENG CHAOLIN / TANG ERLONG et al. | European Patent Office | 2021

    Free access