• Corpus ID: 59272139

A generalized Sitnikov problem

@article{Beltritti2017AGS,
  title={A generalized Sitnikov problem},
  author={Gast{\'o}n Beltritti and Fernando Mazzone and Martina Oviedo},
  journal={arXiv: Mathematical Physics},
  year={2017}
}

• Gastón Beltritti, F. Mazzone, M. Oviedo
• Published 7 October 2017
• Mathematics
• arXiv: Mathematical Physics

In this paper we address a $n+1$-body gravitational problem governed by the Newton's laws, where $n$ primary bodies orbit on a plane $\Pi$ and an additional massless particle moves on the perpendicular line to $\Pi$ passing through the center of mass of the primary bodies. We find a condition for that the configuration described be possible. In the case that the primaries are in a rigid motion we classify all the motions of the massless particle. We study the situation when the massless particle has a periodic motion with the same minimal period than primary bodies. We show that this fact is related with the existence of certain pyramidal central configuration.