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

Universe ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 35 ◽  
Author(s):  
Fabao Gao ◽  
Ruifang Wang
Keyword(s):  
Binary System ◽  
Periodic Solutions ◽  
Libration Point ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Collinear Libration Point ◽  
The Third ◽  
Zero Velocity ◽  
Jacobian Constant ◽  
Zero Velocity Surface

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.

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

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 110
Author(s):  
Fabao Gao ◽  
Yongqing Wang
Keyword(s):  
Periodic Solutions ◽  
Body Problem ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
The Third ◽  
Velocity Surface ◽  
Solution Point ◽  
Zero Velocity Surface ◽  
Three Body

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.

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

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
R. F. Wang ◽  
F. B. Gao
Keyword(s):  
Body Problem ◽  
Numerical Study ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Regular Tetrahedron ◽  
Transfer Trajectory ◽  
Zero Velocity ◽  
Zero Velocity Surfaces ◽  
Zero Velocity Surface

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.

Resonant Three-Dimensional Periodic Solutions About the Triangular Equilibrium Points in the Restricted Problem

1983 ◽  
Vol 74 ◽  
pp. 235-247 ◽  
Author(s):  
C.G. Zagouras ◽  
V.V. Markellos
Keyword(s):  
Periodic Solutions ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Special Values ◽  
Three Body

AbstractIn the three-dimensional restricted three-body problem, the existence of resonant periodic solutions about L4 is shown and expansions for them are constructed for special values of the mass parameter, by means of a perturbation method. These solutions form a second family of periodic orbits bifurcating from the triangular equilibrium point. This bifurcation is the evolution, as μ varies continuously, of a regular vertical bifurcation point on the corresponding family of planar periodic solutions emanating from L4.

scholarly journals A Hydrodynamical Model of a Rotating Wind Source and Its Effects on the Collapse of a Rotating Core

2015 ◽  
Vol 2015 ◽  
pp. 1-21
Author(s):  
Guillermo Arreaga-Garcia
Keyword(s):  
Binary System ◽  
Angular Velocity ◽  
Three Dimensional ◽  
Rotation Velocity ◽  
Escape Velocity ◽  
The Third ◽  
The Core ◽  
Velocity Magnitude ◽  
Hydrodynamical Simulations ◽  
Wind Source

This work presents three-dimensional hydrodynamical simulations with the fully parallel GAGDET2 code, to model a rotating source that emits wind in order to study the subsequent dynamics of the wind in three independent scenarios. In the first scenario we consider several models of the wind source, which is characterized by a rotation velocityVrotand an escape velocityVesc, so that the models have a radially outward wind velocity magnitudeVradgiven by 1, 2, 4, 6, and 8 timesVrot. In the second scenario, we study the interaction of winds emitted from a binary system in two kinds of models: one in which the source remains during the wind emission and a second one in which all the source itself becomes wind. In the third scenario we consider the interaction of a rotating source that emits wind within a collapsing and rotating core. In this scenario we consider only wind models of the second kind built over a new initial radial mesh, such that the angular velocity of the windΩwis 1, 100, and 1000 times the angular velocity of the coreΩc.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

scholarly journals Modeling of dense well block point bar architecture based on geological vector information: A case study of the third member of Quantou Formation in Songliao Basin

2021 ◽  
Vol 13 (1) ◽  
pp. 39-48
Author(s):  
Chao Luo ◽  
Ailin Jia ◽  
Jianlin Guo ◽  
Wei Liu ◽  
Nanxin Yin ◽  
...  
Keyword(s):  
River Sediments ◽  
Three Dimensional ◽  
Songliao Basin ◽  
Point Bar ◽  
Meandering River ◽  
Architecture Model ◽  
The Third ◽  
Continuous Convergence ◽  
Vector Information ◽  
Architecture Modeling

Abstract Although stochastic modeling methods can achieve multiple implementations of sedimentary microfacies model in dense well blocks, it is difficult to realize continuous convergence of well spacing. Taking the small high-sinuosity meandering river sediments of the third member of Quantou Formation in Songliao Basin as an example, a deterministic modeling method based on geological vector information was explored in this article. Quantitative geological characteristics of point bar sediments were analyzed by field outcrops, modern sediments, and dense well block anatomy. The lateral extension distance, length, and spacing parameters of the point bar were used to quantitatively characterize the thickness, dip angle, and frequency of the lateral layer. In addition, the three-dimensional architecture modeling of the point bar was carried out in the study. The established three-dimensional architecture model of well X24-1 had continuous convergence near all wells, which conformed to the geological knowledge of small high-sinuosity meandering river, and verified the reliability of this method in the process of geological modeling in dense well blocks.

scholarly journals On the equivalence of three-dimensional differential systems

2020 ◽  
Vol 18 (1) ◽  
pp. 1164-1172
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Periodic Systems ◽  
Structural Form ◽  
Differential Systems

Abstract In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.

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