Four-body Central Configurations with Adjacent Equal Masses

Yiyang Deng; Bingyu Li; Shiqing Zhang

doi:10.1016/j.geomphys.2016.12.009

Four-body Central Configurations with Adjacent Equal Masses

Dynamical Systems 2017-02-01 v1 Mathematical Physics math.MP

Authors: Yiyang Deng , Bingyu Li , Shiqing Zhang

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Abstract

For any convex non-collinear central configuration of the planar Newtonian 4-body problem with adjacent equal masses $m_1=m_2\neq m_3=m_4$ , with equal lengths for the two diagonals, we prove it must possess a symmetry and must be an isosceles trapezoid; furthermore, which is also an isosceles trapezoid when the length between $m_1$ and $m_4$ equals the length between $m_2$ and $m_3$ .

Keywords

n-body problem

Cite

@article{arxiv.1608.06206,
  title  = {Four-body Central Configurations with Adjacent Equal Masses},
  author = {Yiyang Deng and Bingyu Li and Shiqing Zhang},
  journal= {arXiv preprint arXiv:1608.06206},
  year   = {2017}
}

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