The relative equilibria for the spherical, finite density three-body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical five relative equilibria for the point-mass three-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the three-body problem and ensures that minimum energy configurations exist for all values of angular momentum.

中文翻译：

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球形有限密度三体问题中的相对平衡。

确定了球形有限密度三体问题的相对平衡。具体来说，在这个问题上有28个不同的相对平衡，其中包括点质量三体问题的经典5个相对平衡。在角动量的所有值上，没有一个确定的相对平衡存在或稳定。随着系统角动量的增加，这些相对平衡的稳定性和分叉路径被标出。这是在它们具有相同且恒定的密度并且整个系统围绕其最大惯性矩旋转的假设下完成的。向有限密度的过渡极大地增加了三体问题中的相对平衡数，并确保了所有角动量值都存在最小能量配置。