This paper presents a general analytical method to describe the center manifolds of collinear libration points in the restricted three-body problem (RTBP). It is well known that these center manifolds include Lissajous orbits, halo orbits, and quasi-halo orbits. Previous studies have traditionally treated these orbits separately by iteratively constructing high-order series solutions using the Lindstedt–Poincaré method. Instead of relying on resonance between their frequencies, this study identifies that halo and quasi-halo orbits arise due to intricate coupling interactions between in-plane and out-of-plane motions. To characterize this coupling effect, a novel concept, coupling coefficient η , is introduced in the RTBP, incorporating the coupling term η Δ x in the z -direction dynamics equation, where Δ represents a formal power series concerning the amplitudes. Subsequently, a uniform series solution for these orbits is constructed up to a specified order using the Lindstedt–Poincaré method. For any given paired in-plane and out-of-plane amplitudes, the coupling coefficient η is determined by the bifurcation equation Δ = 0 . When η = 0 , the proposed solution describes Lissajous orbits around libration points. As η transitions from zero to nonzero values, the solution describes quasi-halo orbits, which bifurcate from Lissajous orbits. Particularly, halo orbits bifurcate from planar Lyapunov orbits if the out-of-plane amplitude is zero. The proposed method provides a unified framework for understanding these intricate orbital behaviors in the RTBP.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    Bifurcation Mechanism of Quasi-Halo Orbit from Lissajous Orbit


    Beteiligte:
    Lin, Mingpei (Autor:in) / Chiba, Hayato (Autor:in)

    Erschienen in:

    Erscheinungsdatum :

    01.01.2025




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch




    Sun-Earth L1 Region Halo-to-Halo Orbit and Halo-to-Lissajous Orbit Transfers

    Roberts, C. E. / German Space Operations Center / European Space Operations Centre | British Library Conference Proceedings | 2004


    Lissajous Orbits Around Halo Orbits

    Gomez, G. / Masdemont, J. / Simo, C. et al. | British Library Conference Proceedings | 1997


    ARTEMIS Orbit Determination Accuracy in the Earth-Moon Lissajous Region

    Woodard, Mark / Cosgrove, Daniel / Morinelli, Patrick | NTRS | 2011



    Halo orbit to science orbit captures at planetary moons

    Bokelmann, Kevin A | Online Contents | 2017