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arXiv · 1505.05246

Linear stability of the n-gon relative equilibria of the (1+n)-body problem

Xingbo Xu
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Abstract

We consider the linear stabilities of the regular n-gon relative equilibria of the (1+n)-body problem. It is shown that there exist at most two kinds of infinitesimal bodies arranged alternatively at the vertices of a regular n-gon when n is even, and only one set of identical infinitesimal bodies when n is odd. In the case of n even, the regular n-gon relative equilibrium is shown to be linearly stable when n>=14. In each case of n=8,10,12, linear stability can also be preserved if the ratio of two kinds of masses belongs to an open interval. When n is odd, the related conclusion on the linear stability is recalled.

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Xingbo Xu. 2015-05-20. Linear stability of the n-gon relative equilibria of the (1+n)-body problem. https://doi.org/10.1007/s12346-012-0089-6

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