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arXiv · 1903.10270

Linear stability of the elliptic relative equilibrium with $(1 +n)$-gon central configurations in planar $n$-body problem

Xijun Hu·Yiming Long·Yuwei Ou
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Abstract

We study the linear stability of $(1+n)$-gon elliptic relative equilibrium (ERE for short), that is the Kepler homographic solution with the $(1+n)$-gon central configurations. We show that for $n\geq 8$ and any eccentricity $e\in[0,1)$, the $(1+n)$-gon ERE is stable when the central mass $m$ is large enough. Some linear instability results are given when $m$ is small.

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Xijun Hu, Yiming Long, Yuwei Ou. 2019-03-25. Linear stability of the elliptic relative equilibrium with $(1 +n)$-gon central configurations in planar $n$-body problem. https://doi.org/10.1088/1361-6544%2Fab5927

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