| 一类刚-梁耦合系统定态运动的稳定性 |
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| 引用本文： | 马晓燕,程耀. 一类刚-梁耦合系统定态运动的稳定性[J]. 力学学报, 2007, 39(6): 813-821. DOI: 10.6052/0459-1879-2007-6-2006-322 |
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| 作者姓名： | 马晓燕 程耀 |
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| 作者单位： | 北京航空航天大学理学院,北京,100083;北京航空航天大学理学院,北京,100083 |
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| 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.
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| 关 键 词： | 运动稳定性 刚-弹耦合 定态运动 能量-动量方法 Lyapunov函数 |
| 文章编号： | 0459-1879（2007）06-0813-09 |
| 收稿时间： | 2006-07-10 |
| 修稿时间： | 2006-07-10 |
STABILITY OF STATIONARY MOTION OF A RIGID BODY WITH A FLEXIBLE BEAM |
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| Ma Xiaoyan,Cheng Yao. STABILITY OF STATIONARY MOTION OF A RIGID BODY WITH A FLEXIBLE BEAM[J]. chinese journal of theoretical and applied mechanics, 2007, 39(6): 813-821. DOI: 10.6052/0459-1879-2007-6-2006-322 |
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| Authors: | Ma Xiaoyan Cheng Yao |
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| Affiliation: | School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China |
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| Abstract: | Stability of stationary motion of a rigid body with a flexible beam is investigated, and both translation and attitude motions are considered. Quasi-coordinates play an important role in selecting state variables. The Lyapunov functional is constructed by the first integrals of the dynamical equations. The state variables introduced in this paper simplify the Lyapunov functional, and make stability analyses easy. As a result, the sufficient conditions for the normal stability of two classes of stationary motion are obtained. |
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| Keywords: | functional coupled rigid-elastic body stationary motion stability energy-momentum method Lyapunov |
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