On central configurations of twisted crowns
Abstract
We consider the planar central configurations of the Newtonian $\kappa n$body problem consisting in $\kappa$ groups of $n$gons where all $n$ bodies in each group have the same mass, called $(\kappa, n)$crown. We study the location and the number of central configurations when $\kappa=2$. For $n=3$ the number of central configurations varies depending on the mass ratio, whereas for $n\geq 4$ the number is at least three. We also prove that for $n\geq 3$ there always exist three disjoint regions where the configuration can be located. Finally, we study which $(\kappa, n)$crowns are convex.
 Publication:

arXiv eprints
 Pub Date:
 December 2016
 arXiv:
 arXiv:1612.07135
 Bibcode:
 2016arXiv161207135B
 Keywords:

 Mathematics  Dynamical Systems;
 70F15