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Spatial equilateral chain central configurations of the five-body problem with a homogeneous potential

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Abstract

We consider central configurations of the strictly spatial five-body problem with a homogeneous potential which are equilateral chains, i.e., configurations with four sequential equilateral edges containing all five vertices. First, we prove that any such configuration must be a triangular bipyramid with an equilateral triangle base. Furthermore, we show that the masses located at the vertices of the triangle must be equal and the masses of the other two particles which are off the base also must be equal. We also found that a particular triangular bipyramid configuration with fixed masses is a central configuration for a range of homogenous potentials generalizing the Newtonian potential. Finally, we conclude that there is a unique triangular bipyramid central configuration with equal masses for these same homogenous potentials.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Yiyang Deng

  2. Department of Mathematics and Statistics, University of Minnesota, 1117 University Drive, Duluth, MN, 55812, USA

    Marshall Hampton

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  1. Yiyang Deng
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  2. Marshall Hampton
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Correspondence to Marshall Hampton.

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Deng, Y., Hampton, M. Spatial equilateral chain central configurations of the five-body problem with a homogeneous potential. Celest Mech Dyn Astr 134, 15 (2022). https://doi.org/10.1007/s10569-022-10073-9

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  • DOI: https://doi.org/10.1007/s10569-022-10073-9

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