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2013
Impact Factor

    Vladimir Beletsky

    Miusskaya sq. 4, Moscow, 125047, Russia
    M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

    Publications:

    Beletsky V. V., Rodnikov A. V.
    Abstract
    A particle steady motions in vicinity of dynamically symmetric precessing rigid body are studied in assumption that the body gravitational field is modeled as gravitational field of two centers being on imaginary distance. Such particle motion equations are a variant of motion equations of the Generalized Restricted Circular Problem of Three Bodies (GRCP3B). The number of Coplanar Libration Points, i.e. the particle equilibria in the plane passing through the body axis of dynamical symmetry and through the axis of precession are established. (This number is odd and can be equal to 5, 7 or 9). CLPs evolution are studied at changing values of the considered system parameters. Moreover, two Triangular Libration Points, i. e. the particle equilibria in the axis crossing the body mass center orthogonally to axes of precession and dynamical symmetry are found.
    Keywords: problem of three bodies, libration points, steady motions, asteroid, regular precession
    Citation: Beletsky V. V., Rodnikov A. V.,  Libration Points of the Generalized Restricted Circular Problem of Three Bodies in the case of imaginary distance between attracting centers, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp.  931-940
    DOI:10.20537/nd1205005
    Beletsky V. V., Rodnikov A. V.
    Abstract
    A particle steady motions in vicinity of dynamically symmetric precessing rigid body are studied in assumption that the body gravitational field is modeled as two centers gravitational field. The particle motion equations are written as two-parametric generalization for equations of Restricted Circular Problem of Three Bodies (RCP3B). Existence and number of the particle relative equilibria in the plane passing through the body axis of dynamical symmetry and through the vector of angular momentum are established. These equilibria called Coplanar Libration Points (CLP) are analogs of Eulerian Libration Points in RCP3B. Stability of CLP is studied for the first approximation in assumption that attracting centers have equal masses.
    Keywords: problem of three bodies, libration points, stability, steady motions, asteroid
    Citation: Beletsky V. V., Rodnikov A. V.,  Coplanar Libration Points in the Generalized Restricted Circular Problem of Three Bodies, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 3, pp.  569-576
    DOI:10.20537/nd1103012

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