Spatial convex but non-strictly convex double-pyramidal central configurations of the (2n+ 2)-body problem
Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya. Departament de Tecnologies Digitals i de la Informació)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	2019
Resum:	A configuration of the N bodies is convex if the convex hull of the positions of all the bodies in R³ does not contain in its interior any of these bodies. And a configuration is strictly convex if the convex hull of every subset of the N bodies is convex. Recently some authors have proved the existence of convex but non-strictly convex central configurations for some N-body problems. In this paper we prove the existence of a new family of spatial convex but non-strictly convex central configurations of the (2n+ 2)-body problem. More precisely, we prove that for n ≥ 4 there are spatial convex but non-strictly convex central configurations of the (2n + 2)-body problem consisting of n masses equal to m₁ at the vertices of a regular n-gon, n masses equal to m₂ at the vertices of the n-gon whose vertices are the midpoints of the edges of the initial n-gon, and two masses equal to m₃ on the straight line orthogonal to the plane containing the two n-gons passing through their barycenters. Moreover, we show that for n = 3 does not exist such spatial convex but non-strictly convex central configurations. Note that the convex hull of such central configurations is formed by two equal pyramides with the base formed by the big n-gon, glued by their bases. So we call them spatial convex but non-strictly convex double-pyramidal central configurations of the 2n + 2-body problem.
Ajuts:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
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Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Publicat a:	Journal of dynamics and differential equations, Vol. 32, Issue 4 (December 2020) , p. 1965-1982, ISSN 1572-9222

DOI: 10.1007/s10884-019-09798-3

Postprint 25 p, 331.3 KB

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