A family of stacked central configurations in the planar five-body problem |
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| Authors: | J Lino Cornelio M Álvarez–Ramírez Josep M Cors |
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| Institution: | 1.DACB, Universidad Juárez Autónoma de Tabasco,Cunduacán,Mexico;2.Departamento de Matemáticas,UAM–Iztapalapa,Iztapalapa,Mexico;3.Departament de Matemàtiques,Universitat Politècnica de Catalunya,Manresa,Catalonia |
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| Abstract: | We study planar central configurations of the five-body problem where three bodies, \(m_1, m_2\) and \(m_3\), are collinear and ordered from left to right, while the other two, \(m_4\) and \(m_5\), are placed symmetrically with respect to the line containing the three collinear bodies. We prove that when the collinear bodies form an Euler central configuration of the three-body problem with \(m_1=m_3\), there exists a new family, missed by Gidea and Llibre (Celest Mech Dyn Astron 106:89–107, 2010), of stacked five-body central configuration where the segments \(m_4m_5\) and \(m_1m_3\) do not intersect. |
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