We consider the ordinary differential equation of the second order, which describes plane oscillations of a satellite with respect to its mass center moving along an elliptic orbit with eccentricity e. The equation has two parameters: e and mu . It is regular for vertical stroke e vertical stroke <1 and singular when vertical stroke e vertical stroke =1. For e-> 1 we obtain two limit equations. The mu-depending families Kn, Lm, n=0, 1,..; m element of Z, of bounded solutions to the limit equations are isolated. One of the family is twisted into the self-similar spiral. When vertical stroke e vertical stroke <1 there exists an infinite number of two-parameter families Kn,k, n=0, 1,..; kappa element of Z, of the generalized (rotational and oscillatory) odd 2 pi-periodic solutions to the equation. It is shown that their topological limit when e-> +- 1 coincides with the families Kn or Lm respectively. The domains of stability in every family Kn,k are bounded by one-parameter subfamilies of critical solutions, which have the trace Tr = +- 2. The complete qualitative description of the families of generalized odd 2 pi-periodic solutions is given, as well as their domains of stability. It is shown that some of the domains of stability have a fractal structure.


    Access

    Access via TIB

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Generalized periodic solutions to the equation of oscillations of a satellite


    Contributors:
    Bruno, A.D. (author) / Varin, V.P. (author)

    Published in:

    Publication date :

    1999


    Size :

    2 Seiten



    Type of media :

    Conference paper


    Type of material :

    Print


    Language :

    English




    Periodic Solutions in Nonlinear Oscillations

    Longuski, James M. / Hoots, Felix R. / Pollock IV, George E. | Springer Verlag | 2021




    Non-linear free periodic oscillations of a tethered satellite system

    Luongo, A. / Vestroni, F. | Tema Archive | 1994


    Periodic solution of the generalized Rayleigh equation

    Cveticanin, L. | Online Contents | 2008