Some notes on four-body co-circular central configurations
Some notes on four-body co-circular central configurations
复制标题
DOI：
10.1016/j.jmaa.2017.03.064
复制
发表时间：
2017-09
影响因子：
1.3
通讯作者：
Yiyang Deng;Bingyu Li;Shiqing Zhang
中科院分区：
文献类型：
--
作者：
Yiyang Deng;Bingyu Li;Shiqing Zhang
四体共圆中心构型有两类对称构型，即风筝构型和等腰梯形构型。以相互距离为坐标，证明了如果四体中心构型是等腰梯形，则等腰梯形的对角线不能相互垂直。此外，我们表明，对于任何四体共圆中心配置，四边形的对角线不能是垂直的，除了配置是一个风筝。
There are two symmetric families of four-body co-circular central configurations, namely the kite and isosceles trapezoid. Using mutual distances as coordinates, we prove that if the four-body central configuration is an isosceles trapezoid, then the diagonals of the isosceles trapezoid cannot be perpendicular to each other. Furthermore, we show that for any four-body co-circular central configuration, the diagonals of the quadrilateral cannot be perpendicular except that the configuration is a kite.