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

Bardin, B. S.; Волков, Е. В.

doi:10.1088/1757-899x/1191/1/012002

Cited by 2 publications

(2 citation statements)

References 6 publications

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“…1) with the coordinate transformation x = rξ, y = rη, where r is the distance between the primaries. The equations of motion of the small body P take the following canonical form [10]:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

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Numerical Orbital Stability Analysis of Nonresonant Periodic Motions in the Planar Restricted Four-Body Problem

Sukhov¹,

Volkov²

2022

Nelin. Dinam.

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We address the planar restricted four-body problem with a small body of negligible mass moving in the Newtonian gravitational field of three primary bodies with nonnegligible masses. We assume that two of the primaries have equal masses and that all primary bodies move in circular orbits forming a Lagrangian equilateral triangular configuration. This configuration admits relative equilibria for the small body analogous to the libration points in the three-body problem. We consider the equilibrium points located on the perpendicular bisector of the Lagrangian triangle in which case the bodies constitute the so-called central configurations. Using the method of normal forms, we analytically obtain families of periodic motions emanating from the stable relative equilibria in a nonresonant case and continue them numerically to the borders of their existence domains. Using a numerical method, we investigate the orbital stability of the aforementioned periodic motions and represent the conclusions as stability diagrams in the problem’s parameter space.

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“…1) with the coordinate transformation x = rξ, y = rη, where r is the distance between the primaries. The equations of motion of the small body P take the following canonical form [10]:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Thus, it is always unstable. The stability analysis of the configurations P 1 P 2 AP 3 and P 1 P 2 CP 3 has been performed in [8][9][10]. It was established that the configuration P 1 P 2 AP 3 is unstable for any possible values of μ.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Numerical Orbital Stability Analysis of Nonresonant Periodic Motions in the Planar Restricted Four-Body Problem

Sukhov¹,

Volkov²

2022

Nelin. Dinam.

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The Lyapunov Stability of Central Configurations of the Planar Circular Restricted Four-Body Problem

Bardin,

Volkov

2024

Cosmic Res

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

Cited by 2 publications

References 6 publications

Numerical Orbital Stability Analysis of Nonresonant Periodic Motions in the Planar Restricted Four-Body Problem

Numerical Orbital Stability Analysis of Nonresonant Periodic Motions in the Planar Restricted Four-Body Problem

The Lyapunov Stability of Central Configurations of the Planar Circular Restricted Four-Body Problem

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