Abstract
In this paper we answer the following question posed by Hampton (Nonlinearity 18:2299–2304, 2005). In addition to symmetric collinear configurations and the square with a mass at its center are there any planar five-body central configurations with a subset forming a four-body central configuration? We prove that, for non-collinear configurations, the only possible strictly planar central configuration for the five-body problem for which it can be removed one body such that the remaining four bodies are already in a central configuration is obtained with four bodies of equal masses at the vertices of a square and the fifth body of arbitrary mass at the center of the square.
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17 May 2018
We correct an error in the proof of Lemma 2.7 in the article mentioned in the title. This correction does not affect the main results of the article.
17 May 2018
We correct an error in the proof of Lemma 2.7 in the article mentioned in the title. This correction does not affect the main results of the article.
17 May 2018
We correct an error in the proof of Lemma 2.7 in the article mentioned in the title. This correction does not affect the main results of the article.
17 May 2018
We correct an error in the proof of Lemma 2.7 in the article mentioned in the title. This correction does not affect the main results of the article.
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Fernandes, A.C., Mello, L.F. On Stacked Planar Central Configurations with Five Bodies when One Body is Removed. Qual. Theory Dyn. Syst. 12, 293–303 (2013). https://doi.org/10.1007/s12346-012-0084-y
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DOI: https://doi.org/10.1007/s12346-012-0084-y