caa a22 4500 445863064 CHVBK 20180317145449.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10569-010-9332-0 doi (NATIONALLICENCE)springer-10.1007/s10569-010-9332-0 Sidorenko Vladislav Russian Academy of Sciences, Keldysh Institute of Applied Mathematics, Miusskaya sq., 4, 125047, Moscow, Russia aut On the circular Sitnikov problem: the alternation of stability and instability in the family of vertical motions [Elektronische Daten] [Vladislav Sidorenko] This paper is devoted to 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 the paper 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. Springer Science+Business Media B.V., 2011 Sitnikov problem nationallicence Periodic motions nationallicence stability analysis nationallicence Celestial Mechanics and Dynamical Astronomy Springer Netherlands 109/4(2011-04-01), 367-384 0923-2958 109:4<367 2011 109 10569 https://doi.org/10.1007/s10569-010-9332-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-010-9332-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sidorenko Vladislav Russian Academy of Sciences, Keldysh Institute of Applied Mathematics, Miusskaya sq., 4, 125047, Moscow, Russia aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 109/4(2011-04-01), 367-384 0923-2958 109:4<367 2011 109 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer