Dirac reduction of binary asteroid systems with symmetry and stability of relative equilibria

Kaori Onozaki, Hiroaki Yoshimura

    Research output: Contribution to journalArticle

    Abstract

    In this paper, we study symmetry reduction for a binary asteroid system modeled by a rigid body and a particle. In particular, we demonstrate how translational and rotational symmetry reduction appeared in the binary asteroid system can be carried out in the context of Dirac reduction by stages and with the associated reduction of implicit Hamiltonian systems. Then we investigate stability of relative equilibria of the asteroid pair and show stability regions by using the energy-momentum method. Lastly, we illustrate some numerical simulations for stable and unstable orbits near from relative equilibria of the Collinear and T configurations.

    Original languageEnglish
    Article number013011
    JournalTheoretical and Applied Mechanics Letters
    Volume3
    Issue number1
    DOIs
    Publication statusPublished - 2013

    Fingerprint

    Asteroids
    Hamiltonians
    Momentum
    Orbits
    Computer simulation

    Keywords

    • Binary asteroid
    • Dirac reduction
    • Stability

    ASJC Scopus subject areas

    • Aerospace Engineering
    • Biomedical Engineering
    • Civil and Structural Engineering
    • Computational Mechanics
    • Mechanical Engineering
    • Mechanics of Materials
    • Ocean Engineering
    • Environmental Engineering

    Cite this

    Dirac reduction of binary asteroid systems with symmetry and stability of relative equilibria. / Onozaki, Kaori; Yoshimura, Hiroaki.

    In: Theoretical and Applied Mechanics Letters, Vol. 3, No. 1, 013011, 2013.

    Research output: Contribution to journalArticle

    @article{0ef2c973b3b84b3c9d6ef11f3a4ade43,
    title = "Dirac reduction of binary asteroid systems with symmetry and stability of relative equilibria",
    abstract = "In this paper, we study symmetry reduction for a binary asteroid system modeled by a rigid body and a particle. In particular, we demonstrate how translational and rotational symmetry reduction appeared in the binary asteroid system can be carried out in the context of Dirac reduction by stages and with the associated reduction of implicit Hamiltonian systems. Then we investigate stability of relative equilibria of the asteroid pair and show stability regions by using the energy-momentum method. Lastly, we illustrate some numerical simulations for stable and unstable orbits near from relative equilibria of the Collinear and T configurations.",
    keywords = "Binary asteroid, Dirac reduction, Stability",
    author = "Kaori Onozaki and Hiroaki Yoshimura",
    year = "2013",
    doi = "10.1063/2.1301311",
    language = "English",
    volume = "3",
    journal = "Theoretical and Applied Mechanics Letters",
    issn = "2095-0349",
    publisher = "Elsevier BV",
    number = "1",

    }

    TY - JOUR

    T1 - Dirac reduction of binary asteroid systems with symmetry and stability of relative equilibria

    AU - Onozaki, Kaori

    AU - Yoshimura, Hiroaki

    PY - 2013

    Y1 - 2013

    N2 - In this paper, we study symmetry reduction for a binary asteroid system modeled by a rigid body and a particle. In particular, we demonstrate how translational and rotational symmetry reduction appeared in the binary asteroid system can be carried out in the context of Dirac reduction by stages and with the associated reduction of implicit Hamiltonian systems. Then we investigate stability of relative equilibria of the asteroid pair and show stability regions by using the energy-momentum method. Lastly, we illustrate some numerical simulations for stable and unstable orbits near from relative equilibria of the Collinear and T configurations.

    AB - In this paper, we study symmetry reduction for a binary asteroid system modeled by a rigid body and a particle. In particular, we demonstrate how translational and rotational symmetry reduction appeared in the binary asteroid system can be carried out in the context of Dirac reduction by stages and with the associated reduction of implicit Hamiltonian systems. Then we investigate stability of relative equilibria of the asteroid pair and show stability regions by using the energy-momentum method. Lastly, we illustrate some numerical simulations for stable and unstable orbits near from relative equilibria of the Collinear and T configurations.

    KW - Binary asteroid

    KW - Dirac reduction

    KW - Stability

    UR - http://www.scopus.com/inward/record.url?scp=84956951292&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84956951292&partnerID=8YFLogxK

    U2 - 10.1063/2.1301311

    DO - 10.1063/2.1301311

    M3 - Article

    AN - SCOPUS:84956951292

    VL - 3

    JO - Theoretical and Applied Mechanics Letters

    JF - Theoretical and Applied Mechanics Letters

    SN - 2095-0349

    IS - 1

    M1 - 013011

    ER -