Geodesic
Computation of periodic oscillations of a satellite
Matematičeskoe modelirovanie, Tome 9 (1997) no. 6, pp. 82-94 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the ordinary differential equation of the second order describing oscillations of a satellite in a plane of its elliptical orbit. The equation contains two parameters: $e$ and $\mu$. It is regular for $0\leq e<1$ and singular for $e=1$. We have computed five families of symmetric (odd) periodic solutions for $|\mu|\leq20$ and for $e=0,0.1,0.5,0.9,0.99,0.999$. We have also computed the corresponding values of the trace characterising their stability. For $e>0.9$ we use the regularization by means of the eccentric anomaly. Results are given in figures. They show that for $e\to1$ these families tend to some limiting positions. 
@article{MM_1997_9_6_a6,
     author = {A. D. Bruno and V. J. Petrovich},
     title = {Computation of periodic oscillations of a~satellite},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {82--94},
     year = {1997},
     volume = {9},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1997_9_6_a6/}
}
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A. D. Bruno; V. J. Petrovich. Computation of periodic oscillations of a satellite. Matematičeskoe modelirovanie, Tome 9 (1997) no. 6, pp. 82-94. http://geodesic.mathdoc.fr/item/MM_1997_9_6_a6/