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arXiv · 2205.10514

Linear stability of the elliptic relative equilibria for the restricted $4$-body problem: the Euler case

Bowen Liu·Qinglong Zhou
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Abstract

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.

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Bowen Liu, Qinglong Zhou. 2022-05-21. Linear stability of the elliptic relative equilibria for the restricted $4$-body problem: the Euler case. https://arxiv.org/abs/2205.10514

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