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oai:recercat.cat:10256/197072024-06-18T12:18:15Zcom_2072_452955com_2072_2054col_2072_453069

Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two Barrabés Vera, Esther Cors Iglesias, Josep Maria Fernandes, A.C. Vidal, Claudio Mecànica celest Celestial mechanics Lagrange, Espais de Lagrange spaces Geometria diferencial Geometry, Differencial Problema dels cossos múltiples Many-body problem We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations. First, we prove that the two bodies out of the vertices of the triangle cannot be placed on certain lines. Next, we give a geometrical characterization of such configurations in the sense as that of Dziobek, and we describe the admissible regions where the two remaining bodies can be placed. Furthermore, we prove that any Lagrange plus two central configuration is concave. Finally, we show numerically the existence of non-symmetric central configurations of the five body problem 2024-06-18T12:18:14Z 2024-06-18T12:18:14Z 2024-06-18T12:18:14Z info:eu-repo/date/embargoEnd/2022-07-10 2021-07-10 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion peer-reviewed http://hdl.handle.net/10256/19707 info:eu-repo/semantics/altIdentifier/doi/10.1007/s12346-021-00504-7 info:eu-repo/semantics/altIdentifier/issn/1575-5460 info:eu-repo/semantics/altIdentifier/eissn/1662-3592 Tots els drets reservats info:eu-repo/semantics/openAccess Springer-Verlag © Qualitative Theory of Dynamical Systems, 2021, vol. 20, p. 63 Articles publicats (D-IMAE) Barrabés, E. Cors, J.M. Fernandes, A.C. Vidal, C. 2021 Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two Qualitative Theory of Dynamical Systems 20 63