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<p>In this paper we investigate rhomboidal central configurations for the planar five-body problem.These are configurations whose convex hulls are rhombuses, and one interior mass lies on a diagonal of the rhombus.Consider partition of the configuration space by orderings of mutual distances,our main theorem provides criteria for central configurations in every region of this partition.For some regions we obtain existence and uniqueness of central configurations, for some we obtainnonexistence, for others our criteria are necessary conditions on masses.Our proofs are elementary and completely analytic.</p>

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Rhomboidal Central Configurations of the Five-Body Problem

  • 期刊论文

  • 发表日期：

    2025年12月30日

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  • Ke-Ming Chang,
  • Kuo-Chang Chen

摘要

In this paper we investigate rhomboidal central configurations for the planar five-body problem.These are configurations whose convex hulls are rhombuses, and one interior mass lies on a diagonal of the rhombus.Consider partition of the configuration space by orderings of mutual distances,our main theorem provides criteria for central configurations in every region of this partition.For some regions we obtain existence and uniqueness of central configurations, for some we obtainnonexistence, for others our criteria are necessary conditions on masses.Our proofs are elementary and completely analytic.