Periodic solutions for planar 2N-body problems

Zhang, Shiqing; Zhou, Qing

doi:10.1090/s0002-9939-02-06795-3

Cited by 35 publications

(18 citation statements)

References 8 publications

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“…For p = 2 and n = 2, 3, 4, 5, 6 in [28], and for p = 2 and n ≥ 2 Zhang and Zhou [49] proved that there are central configurations of the 2n-body problem where n bodies with equal mass are in the vertices of a regular n-gon, and the remainder n bodies with equal mass but not necessarily equal to the previous n bodies, are also in the vertices of another regular n-gon homothetic to the first n-gon.…”

Section: Planar Nested Central Configurationsmentioning

confidence: 99%

On the central configurations of the n-body problem

Llibre

2017

Applied Mathematics and Nonlinear Sciences

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Section: Planar Nested Central Configurationsmentioning

confidence: 99%

On the central configurations of the n-body problem

Llibre

2017

Applied Mathematics and Nonlinear Sciences

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“…In 1985, Perko and Walter [4] showed that for ≥ 4, masses at the vertices of a regular polygon rotating about their common center of masses with an appropriate angular velocity describe a periodic solution of the -body problems if and only if the masses are equal. In 1995 and in 2002, Moeckel and Simo [5] and Zhang and Zhou [6] studied the sufficient and necessary conditions for planar nested 2 -body problems. In this paper, we study the following problems.…”

Section: ) Is a Central Configuration If And Only Ifmentioning

confidence: 99%

On a Periodic Solution of the 4-Body Problems

Chen

2014

Advances in Mathematical Physics

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We study the necessary and sufficient conditions on the masses for the periodic solution of planar 4-body problems, where three particles locate at the vertices of an equilateral triangle and rotate with constant angular velocity about a resting particle. We prove that the above periodic motion is a solution of Newtonian 4-body problems if and only if the resting particle is at the origin and the masses of the other three particles are equal and their angular velocity satisfies a special condition.

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“…Um resultado similar ao Teorema 2.1 pode ser encontrado no Corolário 5, p. 2164 da Ref. [12]. Gostaríamos de salientar que na Ref.…”

Section: Observações Finaisunclassified

Configurações centrais planares encaixantes

Mello¹,

Fernandes²

2007

Rev. Bras. Ensino Fís.

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Neste artigo estudamos configurações centrais planares para o problema de seis corpos, mostrando a existência de uma família de tais configurações com as seguintes propriedades: os seis corpos estão sobre os vértices de dois triângulos equiláteros com baricentros coincidentes, estando o triângulo equilátero de lado menor girado de π/3 em relação ao triângulo equilátero de lado maior. Palavras-chave: problema de n corpos, configurações centrais planares. In this paper we show the existence of a family of planar central configurations for the 6-body problem with the following properties: the six bodies are on the vertices of two equilateral triangles with common barycenters and the smaller triangle is rotated of π/3 with respect to the larger one.

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Periodic solutions for planar 2N-body problems

Abstract: Abstract. In this paper we study some necessary conditions and sufficient conditions for the nested polygonal solutions of planar 2N-body problems.

Cited by 35 publications

References 8 publications

On the central configurations of the n-body problem

On the central configurations of the n-body problem

On a Periodic Solution of the 4-Body Problems

Configurações centrais planares encaixantes

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