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.
Generalized periodic solutions to the equation of oscillations of a satellite
ZAMM. Zeitschrift für angewandte Mathematik und Mechanik ; 79 , Suppl.2 ; S283-S284
1999
2 Seiten
Conference paper
English
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