A Special Family of Stacked Central Configurations: Lagrange Plus Euler in One
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We show the existence of a family of stacked central configurations in the planar five-body problem with a special property. Three bodies \(m_1\), \(m_2\) and \(m_3\), ordered from left to right, are collinear and form an Euler central configuration, and the other two bodies \(m_4\) and \(m_5\), together with \(m_2\) are at the vertices of an equilateral triangle and form a Lagrange central configuration.
KeywordsCollinear central configurations Equilateral central configuration Laura-Andoyer equations
The authors would like to thank the anonymous referee for valuable comments and suggestions, which help us to improve this paper.