On the circular Sitnikov problem: the alternation of stability and instability in the family of vertical motions

Details On the circular Sitnikov problem: the alternation of stability and instability in the family of vertical motions On the circular Sitnikov problem: the alternation of stability and instability in the family of vertical motions

2011-02-16

arxiv.org/abs/1102.3315v1

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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