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.