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.

中文翻译：

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具有三轴和辐射摄动的HD 191408系统的分叉分析和周期解

研究了一类摄动受限三体问题的非线性轨道动力学。这里考虑的两个原色是指二元系统HD191408。第三个粒子在二元系统的重力作用下移动，并且还考虑了三轴速率和辐射因子。基于二进制HD 191408系统中第三粒子的动态控制方程，给出了运动状态流形。通过绘制系统的分叉图，详细讨论了各种扰动因子对第三粒子动力学行为的影响。此外，通过分析系统的零速曲面和零速曲线，讨论了几何构型与雅可比常数之间的关系。然后，使用Poincaré–Lindsted方法和数值模拟，分析和数值表示了在二维和三维空间中共线解放点周围的第三粒子的二阶和三阶周期轨道。本文对Singh等人的结果进行了补充。[Singh等人，AMC，2018年]。它不仅包含共线平衡点附近的高阶分析周期解，而且还对二元系统的分歧进行了广泛的数值研究。