Abstract
We show the existence of planar central configurations for \((pN+gN)\)-body problems with Newtonian potentials; in such configurations, \((pN+gN)\)-bodies are located at the vertices of \(p+g\) regular \(N\)-gons with a common center, where \(p\) regular \(N\)-gons are homothetic, and \(g\) regular \(N\)-gons are homothetic rotated by \(\frac{\pi }{N}\) compared to the first set of \(N\)-gons, and all masses on the same \(N\)-gon are equal.
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Acknowledgments
The authors express their gratitude to Professor A. Albouy for his valuable suggestions, and Professor Zhang Shiqing for his support and discussions. We also thank Li Fengying Alexander Wires and Zhifu Xie for their assistance in the English preparation of this paper. This work is supported by the Fund of Mianyang Normal University.
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Zhao, F., Chen, J. Central configurations for \((pN+gN)\)-body problems. Celest Mech Dyn Astr 121, 101–106 (2015). https://doi.org/10.1007/s10569-014-9593-0
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DOI: https://doi.org/10.1007/s10569-014-9593-0