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.
Highlights
As we know, approximately two-thirds of the stars are part of the multistellar system in our galaxy
Singh et al [19] found three-dimensional periodic orbits around the collinear equilibrium points of the restricted three-body problem (RTBP) with oblate and radiating primaries
We focus on constructing the approximate analytical periodic solutions of the binary
Summary
Approximately two-thirds of the stars are part of the multistellar system in our galaxy. Tsirogiannis et al [5] and Singh et al [6] considered a modification of the RTBP with radiation and oblateness and studied the periodic motions around the collinear equilibrium points. Singh et al [17] studied the collinear equilibrium points and periodic motion around them in the RTBP for the binary HD 191408 system, where the two primaries are triaxial rigid bodies and emit radiation. Singh et al [19] found three-dimensional periodic orbits around the collinear equilibrium points of the RTBP with oblate and radiating primaries. Singh and Umar [20] found that the positions of the third particle depended on the oblateness, radiation coefficients of the primaries, and the eccentricity of their orbits in the elliptic RTBP They provided the numerical application of this problem in the stellar-oblate binary system.
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