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中文核心期刊

一类刚-梁耦合系统定态运动的稳定性

Stability of stationary motion for a rigid body with a flexible beam

  • 摘要: 采用带有一悬臂梁的刚体模型, 研究了一类自由的刚-弹耦合系统定态运动的稳定性. 直接从原始系统出发(未做离散化处理),综合考虑了系统的平动与姿态运动的耦合,在非完整坐标的Lagrange力学体系下选取状态变量,结合Lyapunov直接方法和Chetaev的从运动方程的首次积分构造Lyapunov泛函的方法. 引入的变量使得Lyapunov泛函形式简单,给运动稳定性分析带来了很大的方便.最终给出了系统的定态运动按尺度稳定的充分条件.

     

    Abstract: Stability of stationary motion for a rigid Body with a flexible beam wasinvestigated, and both of translation and attitude motion were underconsideration. Quasi-coordinates play an important role in electing statevariables. The Lyapunov functional was constructed by the first integrals ofthe dynamical equations. The state variables introduced in this papersimplify the Lyapunov functional, and make stability analyse easy. As aresult, the sufficient conditions for the normal stability of two classes ofstationary motion were given.

     

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