论文标题
椭圆形相对平衡的线性稳定性限制为$ 4 $ - 身体问题：Euler案
Linear stability of the elliptic relative equilibria for the restricted $4$-body problem: the Euler case
论文作者
论文摘要
在本文中，我们考虑了限制性$ 4 $的问题的椭圆相对平衡，其中三个初选形成了Euler Collinear配置，而四个主体跨越$ \ Mathbf {r}^2 $。我们将符合性减少到一般受限的$ n $ body问题。通过分析限制$ 4 $的物体问题与椭圆形拉格朗日解决方案之间的关系，我们通过$ω$ -Maslov index获得了限制性$ 4 $的物体问题的线性稳定性。通过数值计算，我们还获得了对称案例的质量参数的稳定性条件。
In this paper, we consider the elliptic relative equilibria of the restricted $4$-body problems, where the three primaries form an Euler collinear configuration and the four bodies span $\mathbf{R}^2$. We obtain the symplectic reduction to the general restricted $N$-body problem. By analyzing the relationship between this restricted $4$-body problems and the elliptic Lagrangian solutions, we obtain the linear stability of the restricted $4$-body problem by the $ω$-Maslov index. Via numerical computations, we also obtain conditions of the stability on the mass parameters for the symmetric cases.
