Invariant manifolds and Lagrangian coherent structures in the planar circular restricted three-body problem

Kaori Onozaki, Hiroaki Yoshimura

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    For the sake of spacecraft mission design, it is indispensable to develop a low energy transfer of spacecrafts using very little fuel for interplanetary transport network. The Planar Circular Restricted Three-Body Problem (PCR3BP) has been a fundamental tool for the analysis of such a space mission design. In this paper, we explore stable and unstable invariant manifolds associated with the collinear Lagrange points L1, L2 of the PCR3BP, in which geometrical structures of the invariant manifolds are clarified on a Poincaré section. Further, we compute the Finite Time Lyapunov Exponent fields (FTLE fields) to obtain Lagrangian Coherent Structures (LCS) as the ridges of the FTLE fields. In particular, we compare the LCS with the invariant manifolds on the Poincare section from the viewpoint of the numerical integration times.

    Original languageEnglish
    Pages (from-to)119-128
    Number of pages10
    JournalTheoretical and Applied Mechanics Japan
    Volume62
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    Restricted Three-body Problem
    Coherent Structures
    three body problem
    Invariant Manifolds
    Spacecraft
    Lyapunov Exponent
    spacecraft
    exponents
    Energy transfer
    Poincaré Section
    Unstable Manifold
    Space Missions
    Collinear
    space missions
    Energy Transfer
    Ridge
    numerical integration
    Lagrange
    Numerical integration
    ridges

    ASJC Scopus subject areas

    • Condensed Matter Physics
    • Mechanics of Materials
    • Mathematics(all)

    Cite this

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    abstract = "For the sake of spacecraft mission design, it is indispensable to develop a low energy transfer of spacecrafts using very little fuel for interplanetary transport network. The Planar Circular Restricted Three-Body Problem (PCR3BP) has been a fundamental tool for the analysis of such a space mission design. In this paper, we explore stable and unstable invariant manifolds associated with the collinear Lagrange points L1, L2 of the PCR3BP, in which geometrical structures of the invariant manifolds are clarified on a Poincar{\'e} section. Further, we compute the Finite Time Lyapunov Exponent fields (FTLE fields) to obtain Lagrangian Coherent Structures (LCS) as the ridges of the FTLE fields. In particular, we compare the LCS with the invariant manifolds on the Poincare section from the viewpoint of the numerical integration times.",
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