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Nonlinear physics and mechanics
Numerical Orbital Stability Analysis of Nonresonant
Periodic Motions in the Planar Restricted Four-Body
Problem
E. A. Sukhova, E. V. Volkovba a Moscow Aviation Institute,
Volokolamskoye sh. 4, Moscow, 125080 Russia
b Mechanical Engineering Research Institute of the Russian Academy of Sciences,
M. Kharitonyevskiy per. 4, Moscow, 101990, Russia
Abstract:
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.
Keywords:
Hamiltonian mechanics, four-body problem, periodic motions, orbital stability.
Received: 25.10.2022 Accepted: 29.11.2022
Citation:
E. A. Sukhov, E. V. Volkov, “Numerical Orbital Stability Analysis of Nonresonant
Periodic Motions in the Planar Restricted Four-Body
Problem”, Rus. J. Nonlin. Dyn., 18:4 (2022), 563–576
Linking options:
https://www.mathnet.ru/eng/nd811 https://www.mathnet.ru/eng/nd/v18/i4/p563
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Abstract page: | 56 | Full-text PDF : | 36 | References: | 18 |
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