We present the analysis and computational results for the inclination relative effect of moonlets of triple asteroidal systems. Perturbations on moonlets due to the primary’s non-sphericity gravity, the solar gravity, and moonlets’ relative gravity are discussed. The inclination vector for each moonlet follows a periodic elliptical motion; the motion period depends on the moonlet’s semi-major axis and the primary’s J2 perturbations. Perturbation on moonlets from the Solar gravity and moonlet’s relative gravity makes the motion of the x component of the inclination vector of moonlet 1 and the y component of the inclination vector of moonlet 2 to be periodic. The mean motion of x component and the y component of the inclination vector of each moonlet forms an ellipse. However, the instantaneous motion of x component and the y component of the inclination vector may be an elliptical disc due to the coupling effect of perturbation forces. Furthermore, the x component of the inclination vector of moonlet 1 and the y component of the inclination vector of moonlet 2 form a quasi-periodic motion. Numerical calculation of dynamical configurations of two triple asteroidal systems (216) Kleopatra and (153591) 2001 SN263 validates the conclusion.

中文翻译：

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三重小行星系统中小卫星倾角的相对影响

我们提出了三重小行星系统小卫星倾角相对效应的分析和计算结果。讨论了由于初级的非球形引力、太阳引力和小卫星的相对引力对小卫星的扰动。每个小卫星的倾角矢量遵循周期性的椭圆运动；运动周期取决于小卫星的半长轴和主要的 J2 扰动。太阳引力和小卫星的相对引力对小卫星的扰动使得小卫星 1 的倾角矢量的 x 分量和小卫星 2 的倾角矢量的 y 分量具有周期性的运动。每个小卫星倾角矢量的 x 分量和 y 分量的平均运动形成一个椭圆。然而，由于扰动力的耦合作用，倾角矢量的x分量和y分量的瞬时运动可能是一个椭圆盘。此外，小卫星1的倾角矢量的x分量和小卫星2的倾角矢量的y分量形成准周期运动。两个三重小行星系统 (216) Kleopatra 和 (153591) 2001 SN263 的动力学配置的数值计算验证了该结论。