The nonlinear dynamics of a flexible rotating multi-tethered satellite formation in a Halo orbit with uncertain-but-bounded parameters are examined in this paper via an interval analysis method. In Hill's problem, equations of motion for the focused system are derived with the flexibility and extensibility of tethers involved. Not limited to the system of concern, the developed dynamic model could be generally applied to any N-body multi-tethered satellite system of arbitrary configurations. In addition, the space environmental perturbation of the thermal effect is considered in the dynamics modeling to improve accuracy. Based on interval descriptions, a bounds estimation problem is formulated for the station keeping phase of the system with uncertain interval parameters. Furthermore, an interval method of high efficiency, which utilizes the Chebyshev series for approximation, is presented to solve this problem by only using the lower and upper bounds of the uncertain parameters and avoiding a global search in numerical results. Finally, numerical simulations have been performed to demonstrate the effectiveness and feasibility of the proposed method and to evaluate the influences of the uncertain interval parameters on the dynamic behaviors of the system.

本文通过区间分析的方法，研究了参数不确定但有界的Halo轨道柔性旋转多束卫星的非线性动力学。在希尔的问题中，聚焦系统的运动方程式是通过所涉及的系链的灵活性和可扩展性得出的。不限于所关注的系统，开发的动力学模型通常可以应用于任意配置的任何N体多链卫星系统。此外，在动力学建模中考虑了热效应的空间环境扰动，以提高精度。基于区间描述，为区间参数不确定的系统站保持阶段提出了边界估计问题。此外，一种高效的间隔方法 通过仅使用不确定参数的上下边界并避免对数值结果进行全局搜索，提出了利用Chebyshev级数进行逼近的方法来解决此问题。最后，进行了数值模拟，证明了该方法的有效性和可行性，并评估了不确定区间参数对系统动态行为的影响。