On central configurations

Moeckel, Richard

doi:10.1007/bf02571259

Cited by 172 publications

(145 citation statements)

References 7 publications

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“…See also the Refs. Moeckel 1990;Moulton 1910. The main general open problem for the planar central configurations is due to Wintner (1941) and Smale (1998): Is the number of classes of planar central configurations finite for any choice of the (positive) masses m 1 , . .…”

Section: Introductionmentioning

confidence: 99%

New stacked central configurations for the planar 5-body problem

Llibre

Mello

Pérez‐Chavela³

2011

Celest Mech Dyn Astr

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Abstract. 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 m1, m2, m3 (bodies 1, 2, 3) form an equilateral central configuration, and the other two with masses m4, m5 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.

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Section: Introductionmentioning

confidence: 99%

New stacked central configurations for the planar 5-body problem

Llibre

Mello

Pérez‐Chavela³

2011

Celest Mech Dyn Astr

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“…It is usual to study classes of central configurations modulo dilations and rotations. See Hagihara (1970), Moeckel (1990), Saari (1980), Smale (1970), Wintner (1941) and references therein for more details.…”

Section: Introductionmentioning

confidence: 99%

New classes of spatial central configurations for the -body problem

Mello

Fernandes

2011

Nonlinear Analysis: Real World Applications

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“…In fact this open question was already formulated by Wintner in 1941. Some background and motivation on central configurations can be found in [28,27,21,1]. See also [22].…”

Section: Introductionmentioning

confidence: 99%

“…It turns out that one cannot form a non-collinear stacked central configuration of four bodies by adding just one body to a collinear configuration of three bodies, as it follows from the Perpendicular Bisector Theorem -Theorem 3.1 below (see [1,21]). …”

Section: Introductionmentioning

confidence: 99%

Symmetric planar central configurations of five bodies: Euler plus two

Gidea

Llibre

2009

Celest Mech Dyn Astr

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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.

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On central configurations

Cited by 172 publications

References 7 publications

New stacked central configurations for the planar 5-body problem

New stacked central configurations for the planar 5-body problem

New classes of spatial central configurations for the -body problem

Symmetric planar central configurations of five bodies: Euler plus two

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