On the central configurations in the spatial 5-body problem with four equal masses

Álvarez-Ramírez, Martha; Corbera, Montserrat; Llibre, Jaume

doi:10.1007/s10569-015-9670-z

“…A previous study on the periodic solutions in this dynamical system has been presented in [36], while in [42] we numerically explored the orbital dy-namics of the five-body system, when all the primaries are sources of radiation. Over the years, the problem of five bodies has been proved a very fertile research ground (e.g., [4,18,21,22,28,30,31,33,34,37,47,49,50]). A generalization of the five-body problem has been performed in [28] where the motion of the massless test particle, under the influence of N − 1 primary bodies in a circular configuration, has been investigated.…”

Section: Introductionmentioning

confidence: 99%

Orbit classification and networks of periodic orbits in the planar circular restricted five-body problem

Zotos

¹

,

Papadakis

²

2019

International Journal of Non-Linear Mechanics

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The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three main categories: (i) bounded (regular or chaotic) (ii) escaping and (iii) close encounter orbits. In addition, we determine the influence of the mass parameter on the orbital structure of the system, on the degree of fractality, as well as on the families of symmetric and non-symmetric periodic orbits. The networks and the linear stability of both symmetric and non-symmetric periodic orbits are revealed, while the corresponding critical periodic solutions are also identified. The parametric evolution of the horizontal and the vertical linear stability of the periodic orbits is also monitored, as a function of the mass parameter.

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“…Kulesza et al (2011) and Marchesin & Vidal (2013) study various aspects of restricted rhomboidal five-body problem with four positive masses on the vertices of a rhombus and the fifth infinitesimal mass in the plane of the four masses. Alvarez-Ramírez, Corbera & Llibre (2016) study the central configurations of a rhombus like five-body problem with four equal masses and a fifth infinitesimal mass. Shoaib et al (2013) and Gidea & Llibre, (2010) derive regions of central configuration for a special case of rhomboidal five-body problem with two axes of symmetry and two pairs of equal masses and fifth mass at the centre of mass.…”

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confidence: 99%

On the planar central configurations of rhomboidal and triangular four- and five-body problems

Shoaib

¹

,

Kashif

²

,

Szücs-Csillik

³

2017

Astrophys Space Sci

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We consider a symmetric five-body problem with three unequal collinear masses on the axis of symmetry. The remaining two masses are symmetrically placed on both sides of the axis of symmetry. Regions of possible central configurations are derived for the four-and five-body problems. These regions are determined analytically and explored numerically. The equations of motion are regularized using Levi-Civita type transformations and then the phase space is investigated for chaotic and periodic orbits by means of Poincaré surface of sections.

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“…Kulesza et al (2011) and Marchesin & Vidal (2013) study various aspects of restricted rhomboidal five-body problem with four positive masses on the vertices of a rhombus and the fifth infinitesimal mass in the plane of the four masses. Alvarez-Ramírez, Corbera & Llibre (2016) study the central configurations of a rhombus like five-body problem with four equal masses and a fifth infinitesimal mass. Shoaib et al (2013) and Gidea & Llibre, (2010) derive regions of central configuration for a special case of rhomboidal five-body problem with two axes of symmetry and two pairs of equal masses and fifth mass at the centre of mass.…”

mentioning

confidence: 99%

On the planar central configurations of rhomboidal and triangular four- and five-body problems

Shoaib,

Kashif,

Szucs-Csillik

2017

Preprint

0

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We consider a symmetric five-body problem with three unequal collinear masses on the axis of symmetry. The remaining two masses are symmetrically placed on both sides of the axis of symmetry. Regions of possible central configurations are derived for the four-and five-body problems. These regions are determined analytically and explored numerically. The equations of motion are regularized using Levi-Civita type transformations and then the phase space is investigated for chaotic and periodic orbits by means of Poincaré surface of sections.

show abstract

On the central configurations in the spatial 5-body problem with four equal masses

Cited by 4 publications

References 21 publications

Orbit classification and networks of periodic orbits in the planar circular restricted five-body problem

Orbit classification and networks of periodic orbits in the planar circular restricted five-body problem

On the planar central configurations of rhomboidal and triangular four- and five-body problems

On the planar central configurations of rhomboidal and triangular four- and five-body problems

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