Abstract
We show the existence of central configurations in the planar five-body problem where four bodies are located at the vertices of a rhombus, called rhombus plus one central configurations. Concretely we prove analytically their existence when one diagonal is nearly equal to the sides of the rhombus and when the two diagonals are either equal or nearly equal. In addition, we prove that given a rhombus plus one configuration, the corresponding vector of positive masses that makes the configuration central, if exists, is unique.
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The authors would like to express their warmest thanks to the anonymous referee for the careful reading of the manuscript and for the comments which allowed us to improve both the quality and the clarity of the paper.
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M. Alvarez-Ramírez is partially supported by Programa Especial de Apoyo a la Investigación (UAM) grant number I5-2019. Josep M. Cors has been supported by grant PID2019-104658GB-I00, and Catalan (AGAUR) grant SGR 1617.
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Cornelio, J.L., Alvarez-Ramírez, M. & Cors, J.M. Central Configurations in the Five-Body Problem: Rhombus Plus One. Qual. Theory Dyn. Syst. 20, 51 (2021). https://doi.org/10.1007/s12346-021-00486-6
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DOI: https://doi.org/10.1007/s12346-021-00486-6