New stacked central configurations for the planar 5-body problem

被引：25

作者：

Llibre, Jaume ^{[1
]}

Fernando Mello, Luis ^{[3
]}

Perez-Chavela, Ernesto ^{[2
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

[2] Univ Autonoma Metropolitana Iztapalapa, Dept Matemat, Mexico City 09340, DF, Mexico

[3] Univ Fed Itajuba, Inst Ciencias Exatas, BR-37500903 Itajuba, MG, Brazil

来源：

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 2011年 / 110卷 / 01期

关键词：

Planar central configurations; n-body problem; Stacked central configurations; 5-body problem; RELATIVE EQUILIBRIA;

D O I：

10.1007/s10569-011-9342-6

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

A stacked central configuration in the n-body problem is one that has a proper subset of the n-bodies forming a central configuration. In this paper we study the case where three bodies with masses m(1), m(2), m(3) (bodies 1, 2, 3) form an equilateral central configuration, and the other two with masses m(4), m(5) are symmetric with respect to the mediatrix of the segment joining 1 and 2, and they are above the triangle generated by {1, 2, 3}. We show the existence and non-existence of this kind of stacked central configurations for the planar 5-body problem.

引用

页码：43 / 52

页数：10

共 20 条

[1] Alfaro F, 2002, DYNAM CONT DIS SER A, V9, P463
[2] [Anonymous], 1767, Novi Comm. Acad. Sci. Imp. Petrop
[3] [Anonymous], [No title captured]
[4] [Anonymous], 1970, CELESTIAL MECH
[5] Boccaletti D., 1996, THEORY ORBITS, V1
[6] On the central configurations of the planar 1+3 body problem
Corbera, Montserrat
Maria Cors, Josep
Llibre, Jaume
[J]. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2011, 109 (01) : 27 - 43
[7] On the existence of central configurations of p nested regular polyhedra
Corbera, Montserrat
Llibre, Jaume
[J]. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2010, 106 (02) : 197 - 207
[8] Symmetric planar central configurations of five bodies: Euler plus two
Gidea, Marian
Llibre, Jaume
[J]. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2010, 106 (01) : 89 - 107
[9] Finiteness of relative equilibria of the four-body problem
Hampton, M
Moeckel, R
[J]. INVENTIONES MATHEMATICAE, 2006, 163 (02) : 289 - 312
[10] Stacked central configurations: new examples in the planar five-body problem
Hampton, M
[J]. NONLINEARITY, 2005, 18 (05) : 2299 - 2304

← 1 2 →