Nonlinear Stability Analysis of Relative Equilibria of a Solid Carrying a Movable Point Mass in the Central Gravitational Field


    2019, Vol. 15, no. 4, pp.  505-512

    Author(s): Kholostova O. V.

    The motion of a solid (satellite) carrying a moving point mass in the central Newtonian gravitational field in an elliptical orbit of arbitrary eccentricity is considered. The law of motion of a point mass is assumed to allow for the existence of relative equilibria of the “body-point” system in the orbital coordinate system. A nonlinear stability analysis of these equilibria is carried out, based on the construction and normalization of the area-preserving mapping generated by the motions of the system.
    Keywords: solid carrying a point mass, elliptical orbit, relative equilibrium, stability, resonance
    Citation: Kholostova O. V., Nonlinear Stability Analysis of Relative Equilibria of a Solid Carrying a Movable Point Mass in the Central Gravitational Field, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 4, pp.  505-512
    DOI:10.20537/nd190409


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    References
    [1] Aslanov, V. S. and Bezglasnyi, S. P., “Gravitational Stabilization of a Satellite Using a Movable Mass”, J. Appl. Math. Mech., 76:4 (2012), 405–412  crossref  mathscinet  zmath  elib; Prikl. Mat. Mekh., 76:4 (2012), 563–573  mathscinet  zmath
    [2] Markeev, A. P., “Dynamics of a Satellite Carrying a Point Mass Moving about It”, Mech. Solids, 50:6 (2015), 603–614  crossref  adsnasa  elib; Izv. Akad. Nauk. Mekh. Tverd. Tela, 2015, no. 6, 3–16 (Russian)
    [3] Markeev, A. P., “Equations of Motion of a Solid in a Circular Orbit at Fast Relative Motion of Its Carried Material Point”, Dokl. Phys., 61:4 (2016), 184–187  crossref  mathscinet  adsnasa  elib; Dokl. Akad. Nauk, 467:4 (2016), 414–417 (Russian)  mathscinet
    [4] Burov, A. A. and Kosenko, I. I., “Planar Vibrations of a Solid with Variable Mass Distribution in an Elliptic Orbit”, Dokl. Phys., 56:10 (2011), 548–552  crossref  mathscinet  adsnasa  elib; Dokl. Akad. Nauk, 440:6 (2011), 760–764 (Russian)  mathscinet
    [5] Burov, A., Guerman, A., and Kosenko, I., “Satellite with Periodical Mass Redistribution: Relative Equilibria and Their Stability”, Celestial Mech. Dynam. Astronom., 131:1 (2019), 1, 12 pp.  crossref  mathscinet  adsnasa
    [6] Beletskii, V. V., Motion of an Artificial Satellite about Its Center of Mass, Israel Program for Scientific Translations, Jerusalem, 1966, x, 261 pp.
    [7] Duboshin, G. N., Celestial Mechanics: Basic Problems and Methods, Foreign Technology Division, Dayton, Ohio, 1969
    [8] Markeev, A. P., Libration Points in Celestial Mechanics and Space Dynamics, Nauka, Moscow, 1978, 312 pp. (Russian)  adsnasa
    [9] Markeyev, A. P., “A Method for Analytically Representing Area-Preserving Mappings”, J. Appl. Math. Mech., 78:5 (2014), 435–444  crossref  mathscinet  zmath  elib; Prikl. Mat. Mekh., 78:5 (2014), 612–624 (Russian)  mathscinet  zmath



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