Four-body Central Configurations with Adjacent Equal Masses

Yiyang Deng; Bingyu Li; Shiqing Zhang

doi:10.1016/j.geomphys.2016.12.009

paper

Four-body Central Configurations with Adjacent Equal Masses

arXiv:1608.06206 · doi:10.1016/j.geomphys.2016.12.009

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 $m_{3}$ .

References in corpus (1)

Convex Four Body Central Configurations with Some Equal Masses