四颗相同卫星的相对平衡
Relative equilibria of four identical satellites
摘要：
我们考虑平面上的牛顿五体问题，其中4个物体具有相同的质量m，与其余物体的质量M相比，质量m较小。我们考虑这个系统的（归一化）相对平衡，并在m/M -> 0时遵循它们。在某些情况下，两个小物体会在极限处合并。我们把其他均衡称为四个独立的相同卫星的相对均衡。我们严格证明，只有三个这样的平衡，所有已知的数值研究后，[说]。我们的主要贡献是证明了任何平衡构型都具有对称性，这是[CLO 2]中指出的证明没有其他平衡的缺失关键。
英文摘要：
We consider the Newtonian 5-body problem in the plane, where 4 bodies have the same mass m, which is small compared to the mass M of the remaining body. We consider the (normalized) relative equilibria in this system, and follow them to the limit when m/M -> 0. In some cases two small bodies will coalesce at the limit. We call the other equilibria the relative equilibria of four separate identical satellites. We prove rigorously that there are only three such equilibria, all already known after the numerical researches in [SaY]. Our main contribution is to prove that any equilibrium configuration possesses a symmetry, a statement indicated in [CLO2] as the missing key to proving that there is no other equilibrium.
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