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arXiv · 1608.06206

Four-body Central Configurations with Adjacent Equal Masses

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$.

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Yiyang Deng, Bingyu Li, Shiqing Zhang. 2016-08-05. Four-body Central Configurations with Adjacent Equal Masses. https://doi.org/10.1016/j.geomphys.2016.12.009

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