Symmetric planar central configurations of five bodies: Euler plus two
Gidea, Marian (Northeastern Illinois University. Department of Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica

Imprint: Centre de Recerca Matemàtica 2009
Description: 21 p.
Abstract: We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration, the two bodies at the extremities have equal masses and the third one is at the middle point between the two. The fourth and fifth bodies are placed in a symmetric way: either with respect to the line containing the three bodies, or with respect to the middle body in the collinear configuration, or with respect to the perpendicular bisector of the segment containing the three bodies. The possible stacked five-body central configurations satisfying these types of symmetries are: a rhombus with four masses at the vertices and a fifth mass in the center, and a trapezoid with four masses at the vertices and a fifth mass at the midpoint of one of the parallel sides.
Rights: Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. Creative Commons
Language: Anglès.
Series: Prepublicacions del Centre de Recerca Matemàtica
Series: Prepublicacions del Centre de Recerca Matemàtica ; 907
Document: article ; submittedVersion
Subject: Mecànica celest ; Configuracions i esquemes combinatoris ; Cossos-múltiples, Problema dels

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21 p, 391.2 KB

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Research literature > Preprints

 Record created 2010-09-07, last modified 2019-07-20

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