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Classification of \((n+1, 1)\)-Stacked Central Configurations in \(R^3\)

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Abstract

We classify the extensions of n-body central configurations to \((n+1)\)-body central configurations in \(R^3\), in both the collinear case and the non-collinear case. We completely solve the two open questions posed by Hampton (Nonlinearity 18: 2299-2304, 2005). This classification is related with study on co-circular and co-spherical central configurations. We also obtain a general property of co-circular central configurations.

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Notes

  1. According to Theorem 1, there is no five-body collinear central configuration with a subset forming a four-body central configuration.

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Acknowledgements

Xiang Yu was supported by NSFC (No. 11701464) and the Fundamental Research Funds for the Central Universities (No. JBK1805001). Shuqiang Zhu was supported by NSFC (No. 11801537, No. 11721101) and the Fundamental Research Funds for the Central Universities (No. WK0 010450010).

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  1. School of Economic and Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Xiang Yu & Shuqiang Zhu

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  1. Xiang Yu
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  2. Shuqiang Zhu
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Correspondence to Shuqiang Zhu.

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Communicated by Jeff Moehlis.

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Yu, X., Zhu, S. Classification of \((n+1, 1)\)-Stacked Central Configurations in \(R^3\). J Nonlinear Sci 31, 11 (2021). https://doi.org/10.1007/s00332-020-09659-0

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