Astronomy and Astrophysics – Astrophysics – Earth and Planetary Astrophysics
Scientific paper
2011-02-16
Astronomy and Astrophysics
Astrophysics
Earth and Planetary Astrophysics
18 pages, 6 figures
Scientific paper
10.1007/s10569-010-9332-0
We consider the special case of the restricted circular three-body problem, when the two primaries are of equal mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the primaries (so called periodic vertical motions). The main goal of our investigation is to study the stability of these periodic motions in the linear approximation. A special attention is given to the alternation of stability and instability within the family of periodic vertical motions, whenever their amplitude is varied in a continuous monotone manner.
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