空间刚性杆——弹簧组合结构轨道、姿态耦合动力学分析

以空间太阳帆塔在轨运行中遇到的强耦合动力学问题为研究背景,建立了空间刚性杆-- 弹簧组合结构轨道与姿态耦合 问题的动力学模型,采用辛 (几何) 算法研究了其轨道与姿态耦合的动力学行为,研究结果可以从系统的能量保持情况间接得到验 证. 首先,基于变分原理,通过引入对偶变量将描述空间刚性杆-- 弹簧组合结构动力学行为的拉格朗日方程导入哈 密尔顿体系,建立简化模型的正则控制方程;随后,采用辛龙格库塔方法模拟分析了地球非球摄动对轨道、姿态的影响及系统能 量的数值偏差问题. 数值模拟结果显示:随着初始姿态角速度增大,轨道半径的扰动 增大,轨道与姿态之间的耦合效应加剧; 带谐摄动对空间刚性杆-- 弹簧组合结构模型的轨道、姿态产生的影响比田谐摄动要高出至少两个数量级;同时辛龙格库塔方法能更好 地快速模拟地球非球摄动影响下空间刚性杆-- 弹簧组合结构的动力学行为,并能够长时间保持系统的总能量,有望为 超大空间结构实时反馈控制提供实时动力学响应结果. 

DYNAMIC MODELLING AND SIMULATION OF ORBIT AND ATTITUDE COUPLING PROBLEMS FOR STRUCTURE COMBINED OF SPATIAL RIGID RODS AND SPRING

For the strong coupling dynamic problems of the sail tower solar power satellite in orbit, a simplified model combined of spatial rigid rods and spring that describes the coupling dynamic behaviours of orbit and attitude is established. The coupling dynamic effects of the simplified model are analyzed by the symplectic geometry method and the numerical results can be verified indirectly by the energy conservation of the system. Firstly, based on the variational principle, by introducing the symplectic variables the Lagrange equation describing the dynamic behaviour of the simplified model combined by spatial rigid rods and spring is expressed in the form of the Hamilton system, and the associated canonical governing equations of the simplified model are established. And then, the influence of the Earth non-shape perturbation on the orbit, attitude coupling dynamic motion is simulated by the symplectic Runge-Kutta method and the energy deviation of the simplified model is also analyzed by the symplectic Runge-Kutta method. According to the numerical results, it can be concluded that with the increase of the initial attitude angle velocity, the disturbance of the orbital radius increases and the coupling dynamics between orbit and attitude increases. The effect of zonal harmonic term is higher than that of the tesseral harmonic term at least about two orders of magnitude. And the symplectic Runge-Kutta method proposed could reproduce the dynamic properties of the sail tower solar power satellite associated with the Earth non-shape perturbation rapidly and preserve the energy well with excellent long-time numerical stability, which will give a new approach to obtain the real-time dynamic response of the ultra-large spatial structure for the real-time feedback controller design.