Investigation of Lyapunov stability of a central configuration in the restricted four-body problem

Bardin, B. S.; Esipov, P. A.

doi:10.1063/1.5034607

AIP Conference Proceedings

2018

DOI: 10.1063/1.5034607

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Investigation of Lyapunov stability of a central configuration in the restricted four-body problem

B. S. Bardin¹,

P. A. Esipov²

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Cited by 5 publications

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“…In the paper [7] by B. Bardin and P. Esipov the crucial determinant (2.9) for B = L 1 is calculated numerically, as a function of μ; it has one zero and a pole corresponding to 2 : 1 resonance. Moreover, for the 2 : 1 resonance one has instability and for the 3 : 1 resonance one has stability.…”

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Qualitative Analysis of Some Libration Points in the Restricted Four-body Problem

Ligȩza¹,

Żołądek²

2021

Nelin. Dinam.

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We consider the situation where three heavy gravitational bodies form the Lagrange configuration rotating in a fixed plane and the fourth body of negligible mass moves in this plane. We present three cases of so-called libration points and we study their stability using linear approximation and KAM theory. In some situations we prove the Lyapunov stability for generic values of some parameter of the problem.

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Qualitative Analysis of Some Libration Points in the Restricted Four-body Problem

Ligȩza¹,

Żołądek²

2021

Nelin. Dinam.

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On bifurcations and stability of central configurations in the planar circular restricted four-body problem

Bardin

Волков

2021

J. Phys.: Conf. Ser.

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The restricted four-body problem is considered. That is, we consider motion of an infinitely small body (particle) under the Newtonian gravitational attraction of three bodies (primaries). It is assumed that the primaries move in circular orbits, forming a stable equilateral Lagrange triangle. It is supposed that four bodies move in a plane. There exist relative equilibriums of the particle in the rotating with the primaries coordinate system. In such an equilibrium the particle forms a central configuration with the primaries. In the case of small mass ofa primary the bifurcations ofthe central configurations are investigated, as well as conditions oflinear stability for the central configurations is obtained. The study is performed analytically by using small parameter method.

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Analysis of Linear Stability and Bifurcations of Central Configurations in the Planar Restricted Circular Four-Body Problem

Bardin

Волков

2021

IOP Conf. Ser.: Mater. Sci. Eng.

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Investigation of Lyapunov stability of a central configuration in the restricted four-body problem

Cited by 5 publications

References 13 publications

Qualitative Analysis of Some Libration Points in the Restricted Four-body Problem

Qualitative Analysis of Some Libration Points in the Restricted Four-body Problem

On bifurcations and stability of central configurations in the planar circular restricted four-body problem

Analysis of Linear Stability and Bifurcations of Central Configurations in the Planar Restricted Circular Four-Body Problem

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