The planar version of the equilateral restricted four-body problem, with three unequal masses, is numerically investigated. By adopting the grid classification method we locate the coordinates, on the plane [Formula: see text], of the points of equilibrium, for all possible values of the masses of the primaries. The linear stability of the libration points is also determined, as a function of the masses. Our analysis indicates that linearly stable points of equilibrium exist only when one of the primaries has a considerably larger mass, with respect to the other two primary bodies, when the triangular configuration of the primaries is also dynamically stable.

中文翻译：

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等边受限四体问题中平衡点的位置和线性稳定性探索

对具有三个不等质量的等边受限四体问题的平面版本进行了数值研究。通过采用网格分类方法，我们在平面 [公式：见文本] 上定位平衡点的坐标，用于所有可能的初级质量值。振动点的线性稳定性也被确定为质量的函数。我们的分析表明，线性稳定的平衡点仅存在于其中一个初级物体相对于其他两个初级物体具有相当大的质量时，同时初级物体的三角形配置也是动态稳定的。