基于能量–Casimir方法的刚–液–柔耦合航天器系统稳定性分析
Stability Analysis of Rigid-Liquid-Flexible Coupling Dynamics of Spacecraft Systems by Using the Energy-Casimir Method

摘要 采用能量-Casimir 法对含有柔性附件的充液航天器系统的稳定性进行研究。首先, 将燃料晃动和柔性附件分别简化为弹簧–质量块模型和剪切梁模型, 建立航天器系统的刚-液-柔耦合模型, 通过分析主刚体、液体燃料和柔性附件各部分的动能和势能, 推导得到系统的能量-Casimir 函数; 然后, 计算能量-Casimir 函数的一阶变分和二阶变分, 从而推导出航天器系统的非线性稳定条件; 最后, 通过数值计算, 得到参数空间中系统的稳定和不稳定区域。研究结果显示, 航天器刚体的转动惯量、剪切梁的长度、航天器自旋角速度及储液腔的充液比对航天器的姿态稳定性有较大影响。
Abstract The stability of liquid filled spacecraft with flexible appendage was researched by using energy-Casimir method. Liquid sloshing dynamics was simplified by spring-mass model, and flexible appendage was modeled as a linear shearing beam. Rigid-liquid-flexible coupling dynamics of spacecraft was built. The energy function and the Casimir function were derived by analyzing the energy function of a rigid body, liquid sloshing and a flexible appendage. The nonlinear stability condition of coupled spacecraft system was derived by computing the first and second variation of energy-Casimir function. The stable and unstable regions of the parameter space were given in the final section with numerical computation. Related results show that the inertia matrix, the length of shearing beam, the spacecraft spinning rate, and the filled ratio of liquid fuel tank have strong influence on the stability of coupled spacecraft system.