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On central configurations of the kn-body problem

Author
Barrabés, E.; Cors, J.
Type of activity
Journal article
Journal
Journal of mathematical analysis and applications
Date of publication
2019-08-15
Volume
476
Number
2
First page
720
Last page
736
DOI
10.1016/j.jmaa.2019.04.010
Repository
http://hdl.handle.net/2117/132982 Open in new window
URL
https://www.sciencedirect.com/science/article/pii/S0022247X19303178 Open in new window
Abstract
We consider planar central configurations of the Newtonian kn-body problem consisting in k groups of regular n-gons of equal masses, called (k, n)-crown. We derive the equations of central configurations for a general (k, n)-crown. When k = 2 we prove the existence of a twisted (2, n)-crown for any value of the mass ratio. Moreover, for n = 3,4 and any value of the mass ratio, we give the exact number of twisted (2, n)-crowns, and describe their location. Finally, we conjecture that for any valu...
Keywords
Celestial mechanics, N-body problem, Planar central configurations, Twisted central configurations

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