Abstract This paper examines the effects of triaxiality of both the primaries on the position and stability of the oblate infinitesimal mass in the neighborhood of triangular equilibrium points in the framework of Elliptical restricted three body problem. We have found the solutions for the locations of triangular equilibrium points. We have investigated the stability of infinitesimal mass around the triangular equilibrium points. It is observed that the infinitesimal motion around triangular equilibrium points are stable under certain condition with respect to triaxiality of primaries. We have applied the method of averaging used by Grebenivok, throughout the analysis of the stability of the infinitesimal mass around the triangular equilibrium points. We have exploited simulation technique using MATLAB 15 to analyze the stability of the system. The critical mass ratio depends on the triaxiality, oblateness, semi- major axis and eccentricity of the elliptical orbits.

中文翻译：

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椭圆受限三体问题中原形三轴性对扁球无穷小的影响

摘要 本文在椭圆受限三体问题的框架下，研究了两个初级的三轴性对三角形平衡点附近扁无穷小质量的位置和稳定性的影响。我们已经找到了三角平衡点位置的解。我们已经研究了三角形平衡点周围的无穷小质量的稳定性。观察到三角形平衡点附近的无穷小运动在一定条件下相对于初级三轴性是稳定的。我们已经应用了 Grebenivok 使用的平均方法，贯穿三角形平衡点周围无穷小质量的稳定性分析。我们利用MATLAB 15 的仿真技术来分析系统的稳定性。