航天器伸展附件振动稳定性

以定轴转动的中心刚体和柔性伸展附件组成的刚柔耦合系统作为航天器模型，研究系统的部分变量稳定性问题。假设附件为有限变形梁，但其本构方程是线性的。利用能量积分构造Ｌｙａｐｕｎｏｖ函数，根据部分变量稳定性定理，证明等速伸展或收缩梁的横向非线性振动稳定。证明了这个结论可以推广到两种更一般的航天器模型：１）中心刚体质心运动而全系统质心在惯性空间中不动。２）中心刚体带有充满理想流体的充液腔。

Stability of vibrations of deploying appendage of a spacecraft

A rigid flexible coupled system which consists of a central rigid body deploying a flexible appendage is considered as a model of a spacecraft. Partial stability of the system is studied. The appendage is modelled as a finite deflection beam having linear constitutive equations. By taking the energy integral as Lyapunov function, it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam, according to the partial stable theorem. It is proved that this result can be generalized to two more general models of the spacecraft: 1) the rigid body moves meanwhile the center of all the system is fixed in the inertial space, 2) the rigid body contains a bank filled with ideal liquid.