Abstract We investigated the dynamical behavior in the potential of the primary in the triple asteroid (45) Eugenia with the calculation of the full gravitational potential caused by its 3D irregular shape. We presented the whole structure of the gravitational potential and the effective potential of (45) Eugenia in the coordinate planes, and showed the surface height, surface gravitational force accelerations, and the surface effective potential. The surface gravitational environment has been discussed. The zero-velocity curves and the position of external equilibrium points are calculated and showed relative to the 3D shape of the asteroid to help compare the relationship of the characteristic of the gravitational potential and the shape of the asteroid. There are five equilibrium points in the gravitational potential (45) Eugenia. We presented the positions, eigenvalues, topological cases, and stability of these equilibrium points. To analyze the variety of the orbital parameters close to (45) Eugenia, we computed two different orbits and compared the results. The mechanical energy, the semi-major axis, and the eccentricity have two different periods: the long period and the short period. The inclination have three different periods, an intermediate period is occurred. The longitude of the ascending node and the argument of periapsis not only have two periodic terms, but also have a secular term.

中文翻译：

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三重小行星 (45) Eugenia 初级动力环境

摘要 我们通过计算由其 3D 不规则形状引起的全部引力势，研究了三重小行星 (45) Eugenia 中初级势的动力学行为。我们在坐标平面上给出了引力势和(45) Eugenia的有效势的整体结构，并给出了表面高度、表面引力加速度和表面有效势。已经讨论了表面重力环境。计算零速度曲线和外部平衡点的位置，并相对于小行星的 3D 形状显示出来，以帮助比较引力势特征与小行星形状的关系。在引力势 (45) Eugenia 中有五个平衡点。我们给出了这些平衡点的位置、特征值、拓扑情况和稳定性。为了分析接近 (45) Eugenia 的轨道参数的多样性，我们计算了两个不同的轨道并比较了结果。机械能、半长轴和偏心有两个不同的周期：长周期和短周期。倾角有三个不同的时期，出现一个中间时期。升交点经度和近点论证不仅有两个周期项，而且还有一个长期项。而偏心有两个不同的周期：长周期和短周期。倾角有三个不同的时期，出现一个中间时期。升交点经度和近点论证不仅有两个周期项，而且还有一个长期项。而偏心有两个不同的周期：长周期和短周期。倾斜有三个不同的时期，中间时期发生。升交点经度和近点论证不仅有两个周期项，而且还有一个长期项。