末端带有刚体的旋转梁运动稳定性分析

在对含有柔性元件的复杂航天器进行稳定性等动力学行为的分析中, 通常采用的离散化方法, 可能会导致"动力刚化"等现 象.将梁作为带分布参数的子系统(无限自由度)分析, 基于Rumyancev定理, 通过计算系统相对势能泛函的一阶变分得到了系统的定常运动, 把系统定常运动稳定性的分析归结为系统变势能泛函存在孤立极小值的问题.在分析中不需要建立系统的运动微分方程, 简化了建模过程, 由系统相对势能泛函的二阶变分的正定性得到了使系统定常运动稳定的充分条件, 同时这个条件是使用基于李雅普诺夫直接法思想分析运动稳定性问题得到的最为广泛的充分条件.

THE MOTION STABILITY ANALYSIS OF A ROTATING BEAM WITH A RIGID BODY ON ITS END

Discretization method may lead to the phenomenon of "dynamic stiffening", which is commonly used in the analysis of the stability and other dynamic behavior of complex spacecraft with flexible components. In this paper, the beam is treated as a subsystem with distributed parameters (infinite degrees of freedom). Based on Rumyancev theorem, the steady motion of the system can be derived by calculating the first-order variation of relative potential energy functional of the system. Then the system stability analysis of steady state motion becomes to solve the isolation minimum problem of the system potential energy functional. The differential equations of the system's motion are not necessary in the analysis; consequently the modeling process is simplified. The sufficient condition for steady motion stability can be obtained by determining the positive definiteness of the second variation of the system relative potential energy functional variational. What's more, this condition is the most extensive one among those obtained by analyzing the stability of motion based on Liyapunov direct method.