The tether deployment of a tethered satellite system involves the consideration of complex dynamic properties of the tether, such as large deformation, slack, and even rebound, and therefore, the dynamic modelling of the tether is necessary for performing a dynamic analysis of the system. For a variable-length tether element, the absolute nodal coordinate formulation (ANCF) in the framework of the arbitrary Lagrange-Euler (ALE) description was used to develop a precise dynamic model of a tethered satellite. The model considered the gravitational gradient force and Coriolis force in the orbital coordinate frame, and it was validated through numerical simulation. In the presence of dynamic constraints, a deployment velocity of the tether was obtained by an optimal procedure. In the simulation, rebound behavior of the tethered satellite system was observed when the ANCF-ALE model was employed. Notably, the rebound behavior cannot be predicted by the traditional dumbbell model. Furthermore, an improved optimal deployment velocity was developed. Simulation results indicated that the rebound phenomenon was eliminated, and smooth deployment as well as a stable state of the station-keeping process were achieved. Additionally, the swing amplitude in the station-keeping phase decreased when a deployment strategy based on the improved optimal deployment velocity was used.

系留卫星系统的系绳部署涉及到系绳的复杂动态特性的考虑，例如大变形、松弛甚至回弹，因此，系绳的动力学建模对于执行系统的动力学分析是必要的。对于可变长度系链元素，使用任意拉格朗日-欧拉 (ALE) 描述框架中的绝对节点坐标公式 (ANCF) 来开发系链卫星的精确动态模型。该模型考虑了轨道坐标系中的重力梯度力和科里奥利力，并通过数值模拟进行了验证。在存在动态约束的情况下，系绳的展开速度通过最佳程序获得。在模拟中，当采用 ANCF-ALE 模型时，观察到系留卫星系统的回弹行为。值得注意的是，传统的哑铃模型无法预测反弹行为。此外，开发了改进的最佳部署速度。仿真结果表明，回弹现象得以消除，实现了平稳展开和稳定的站位过程。此外，当使用基于改进的最佳部署速度的部署策略时，在站保持阶段的摆动幅度减小。并实现了平稳部署和驻站过程的稳定状态。此外，当使用基于改进的最佳部署速度的部署策略时，在站保持阶段的摆动幅度减小。并实现了平稳部署和驻站过程的稳定状态。此外，当使用基于改进的最佳部署速度的部署策略时，在站保持阶段的摆动幅度减小。