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

Abstract

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.

Periodic Orbits of the Restricted Three-Body Problem Based on the Mass Distribution of Saturn’s Regular Moons

“…Considering that the mass and radiation of celestial bodies are constantly changing in practical problems, this has prompted scholars to study the variable-mass three-body problem that is more in line with the actual situation. Therefore, considering variable mass, radiation, albedo, etc., in the restricted three-body problem will be more realistic [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. For example, if a star has a strong radiation ability, the dynamic equation established by ignoring its radiation factor will become unreliable.…”

Orbital Dynamics in the Restricted Three Body Problem: Overview of Recent Analytical Advances Obtained by Separating Rapid and Slow Subsystems in Non-Planar Configurations

“…Most of the successes in the restricted three-body problem were limited either to the planar geometry, to the motion around the Lagrange points, or to the Kozai-Lidov effect. The interested reader can refer to books, e.g., by Butikov [1], Brouwer and Clemence [2], Smart [3], Fitzpatrick [4], Sterne [5], Koon et al [6], Beutler [7], Celetti [8], and Valtonen and Karttunen [9] (and the references in these books); and reviews by Naoz [10] and Musielac and Quarles [11] (and the references in these reviews); as well as recent papers by Napier et al [12], Vashkov'yak [13], Wang et al [14], Quarles et al [15], Gao and Wang [16][17][18], Mittal et al [19], Abouelmagd et al [20], Li and Liao [21], Sindik et al [22], Vinson and Chiang [23], Naoz et al [24], Orlov et al [25], Lei and Xu [26], and the references in these papers.…”

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

“…For the three-body problem in the spherical universe, their perturbation theory analysis showed that the rate of precession of two small and nearly circular solutions of identical particles is proportional to the square root of their initial distance and inversely proportional to the square of the radius of the universe [5]. In addition, the three-body problem is also widely used in the evolution of binary systems [6] and the dynamic analysis of binary asteroids [7,8], as well as other fields in the universe such as dark matter, galaxies, GW170817 (GW is short for gravitational wave), and Mukhanov-Sasaki Hamiltonian dynamics, and so forth (see References [9][10][11][12][13] for more information).…”

“…When the more extensive primary is an oblate sphere, Zotos [51] numerically studied the dynamic behavior of the circular R3BP under the initial conditions of the solution are bounded, escaping and collisional, and found that the oblateness factor has a significant influence on the characteristics of the solutions. Based on the model of the binary system proposed in Reference [39], Gao and Wang [6] continued to study the analytical approximate periodic solutions around the collinear libration points. They examined the influence of the small perturbation in Coriolis and centrifugal forces, the triaxiality, and radiation pressure of the primaries on the third body's dynamic behavior through the bifurcation diagram.…”