Rosette Central Configurations, Degenerate central configurations and bifurcations

Details Rosette Central Configurations, Degenerate central configurations and bifurcations Rosette Central Configurations, Degenerate central configurations and bifurcations

2009-09-26

arxiv.org/abs/0909.4890v1

Celestial Mechanics and Dynamical Astronomy, Volume 94, Number 3 March, 2006, 271-287

Physics

Mathematical Physics

16 pages, 6 figures

Scientific paper

10.1007/s10569-005-5534-2

In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian $n$-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where $n$ particles of mass $m_1$ lie at the vertices of a regular $n$-gon, $n$ particles of mass $m_2$ lie at the vertices of another $n$-gon concentric with the first, but rotated of an angle $\pi/n$, and an additional particle of mass $m_0$ lies at the center of mass of the system. This system admits two mass parameters $\mu=m_0/m_1$ and $\ep=m_2/m_1$. We show that, as $\mu$ varies, if $n> 3$, there is a degenerate central configuration and a bifurcation for every $\ep>0$, while if $n=3$ there is a bifurcations only for some values of $\epsilon$.

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