Abstract A general periodicity condition is presented by analyzing the relative motion between two spacecraft performing formation flight in Keplerian elliptic orbits. The Tschauner–Hempel equation is used to describe the relative motion, and the general periodicity condition is derived through a state transition matrix with a true anomaly as a free variable. The general periodicity condition is also derived by using the energy matching condition, and the resulting periodic conditions by two approaches are compared to each other. Moreover, the zero offset condition is presented to locate the leader spacecraft at the center of the formation geometry. Then, the periodic relative motion in the elliptic reference orbit is expressed using the periodicity condition and the zero offset condition. Numerical simulations demonstrate the periodic relative motion in the elliptic reference orbit, and the results show that the general periodicity condition guarantees the bounded periodic relative motion in arbitrary elliptic orbits, and the zero offset condition makes the formation center coincide with the leader spacecraft.

    Highlights ► General periodic condition is derived at arbitrary position in elliptic orbits. ► Zero offset condition is derived to make the leader locate at the formation center. ► State transition matrix and energy matching condition approaches are used. ► The periodic relative motion is expressed in arbitrary elliptic orbits. ► Numerical simulation results show the bounded relative motion in elliptic orbits.


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    Titel :

    Revisiting the general periodic relative motion in elliptic reference orbits


    Beteiligte:
    Bae, Jonghee (Autor:in) / Kim, Youdan (Autor:in)

    Erschienen in:

    Acta Astronautica ; 85 ; 100-112


    Erscheinungsdatum :

    2012-12-18


    Format / Umfang :

    13 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch






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