A Study on Periodic Solutions for the Circular Restricted Three-Body Problem

2020

Universe

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Against the background of a restricted three-body problem consisting of a supergiant eclipsing binary system, the two primaries are composed of a pair of bright oblate stars whose mass changes with time. The zero-velocity surface and curve of the problem are numerically studied to describe the third body’s motion area, and the corresponding five libration points are obtained. Moreover, the effect of small perturbations, Coriolis and centrifugal forces, radiative pressure, and the oblateness and mass parameters of the two primaries on the third body’s dynamic behavior is discussed through the bifurcation diagram. Furthermore, the second- and third-order approximate analytical periodic solutions around the collinear solution point L3 in two-dimensional plane and three-dimensional spaces are presented by using the Lindstedt-Poincaré perturbation method.

“…Expanding the right hand side of Equation ( 13) to the second-order yields (14) and to the third-order in the same way, then we obtain…”

Section: Expansion Of Two-dimensional Dynamic Equationsmentioning

confidence: 99%

“…Assuming that the periodic solutions for Equation (14) with respect to orbital parameter e (|e| 1) have the following form…”

Section: Two-dimensional Periodic Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximate Analytical Periodic Solutions to the Restricted Three-Body Problem with Perturbation, Oblateness, Radiation and Varying Mass

2020

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“…Several analytical and numerical methods for searching periodic solutions of restricted three-body problems can be found in the review article Musielak and Quarles [1]. Regarding the existence of periodic solutions of a circular RTBP, Gao and Zhang [2] gave a rigorous proof and found that the periodic solutions were mainly affected by factors such as the initial values and the masses of the two primaries.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Periodic Solutions of the HD 191408 System with Triaxial and Radiative Perturbations

2020

Universe

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The nonlinear orbital dynamics of a class of the perturbed restricted three-body problem is studied. The two primaries considered here refer to the binary system HD 191408. The third particle moves under the gravity of the binary system, whose triaxial rate and radiation factor are also considered. Based on the dynamic governing equation of the third particle in the binary HD 191408 system, the motion state manifold is given. By plotting bifurcation diagrams of the system, the effects of various perturbation factors on the dynamic behavior of the third particle are discussed in detail. In addition, the relationship between the geometric configuration and the Jacobian constant is discussed by analyzing the zero-velocity surface and zero-velocity curve of the system. Then, using the Poincaré–Lindsted method and numerical simulation, the second- and third-order periodic orbits of the third particle around the collinear libration point in two- and three-dimensional spaces are analytically and numerically presented. This paper complements the results by Singh et al. [Singh et al., AMC, 2018]. It contains not only higher-order analytical periodic solutions in the vicinity of the collinear equilibrium points but also conducts extensive numerical research on the bifurcation of the binary system.

“…Here we list some recent or interesting research results. Gao and Zhang [1] studied the existence of periodic orbits of the circular restricted three-body problem. According to the existing literature, the first type of Poincaré periodic orbit generally requires that the mass parameter of the system is sufficiently small, and the periodic orbit studied in this paper is applied to any between (0, 1), solving the problem that the first type of Poincaré's periodic orbit has always been considered to occur only when the masses of primaries are quite different.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of the Zero Velocity Surface and Transfer Trajectory of a Circular Restricted Five-Body Problem

Mathematical Problems in Engineering

2018

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We focus on a type of circular restricted five-body problem in which four primaries with equal masses form a regular tetrahedron configuration and circulate uniformly around the center of mass of the system. The fifth particle, which can be regarded as a small celestial body or probe, obeys the law of gravity determined by the four primaries. The geometric configuration of zero-velocity surfaces of the fifth particle in the three-dimensional space is numerically simulated and addressed. Furthermore, a transfer trajectory of the fifth particle skimming over four primaries then is designed.