Regular n-gon rotating equilibria with logarithm gravitational interaction

Anna-Monika Muscaş,Daniel Paşca,Cristina Stoica

Celestial Mechanics and Dynamical Astronomy(2024)

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Abstract
We study the linear stability of regular n-gon rotating equilibria in the n-body problem with logarithm interaction. We find that linear stability is insured if a central mass M if M is bounded below and above by constants depending on the number and mass of the (equal) outer n bodies. Moreover, we provide explicit formulae for these bounds. In the absence of a central mass, we find that the regular n-gon is linearly stable for n =2,3,… 6 only.
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Key words
Logarithm potential,Regular n-gon,Rotating equilibria
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