Hip-hop solutions of the 2N-body problem

@article{Barrabs2006HiphopSO,
  title={Hip-hop solutions of the 2N-body problem},
  author={Esther Barrab{\'e}s and Josep M. Cors and C. Pinyol and Jaume Soler},
  journal={Celestial Mechanics and Dynamical Astronomy},
  year={2006},
  volume={95},
  pages={55-66}
}
Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame.