The inverse problem of central configuration of the trapezoidal 5-body problems is investigated. In this 5-body setup, one of the masses is chosen to be stationary at the center of mass of the system and four-point masses are placed on the vertices of an isosceles trapezoid with two equal masses at positions and at positions . The regions of central configurations where it is possible to choose positive masses are derived both analytically and numerically. It is also shown that in the complement of these regions no central configurations are possible.

中文翻译：

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4 +1对称对称问题中的中心配置区域

研究了梯形五体问题的中心构型的反问题。在这种五体设置中，选择一个质量块固定在系统质量中心，将四点质量块放置在等腰梯形的顶点上，等腰梯形的位置和位置具有两个等质量的质量。可以选择正质量的中心构型区域是通过分析和数字得出的。还显示出，在这些区域的补充中，没有中心配置是可能的。