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本文讨论带有挠性附件和速率受控飞轮的航天器的姿态运动方程式及其稳定性。建立了系统的力学模型,利用准坐标 Lagrange 方程,并基于中心体固定时的振型分析结果推导了运动方程。用Ляпуноъ直接法证明了非线性运动方程零解对部分变量的稳定性,给出了渐近稳定的充分必要条件,证明了由飞轮速率反馈引入的不完全阻尼不一定能获得相应的渐近稳定性,但是在一定的条件下可以使中心体和挠性附件的运动得到阻尼。
This article discusses the attitude motion equations and their stability for spacecraft with flexible attachments and rate-controlled flywheels. The mechanical model of the system is established, and the equations of motion are deduced based on the Lagrange equation of quasi-coordinates and the analysis of the mode shapes of the center body. The stability of some variables for the nonlinear solution of the nonlinear equations is proved by the direct method of Ляпуноъ, and the necessary and sufficient conditions for the asymptotic stability are given. It is proved that the incomplete damping introduced by the feedback of the flywheel can not obtain the corresponding asymptotic stability However, the movement of the center body and the flexible attachment can be damped under certain conditions.