Stability analysis of nonlinear vibrations of a deploying flexible beam

Consider a rigid-flexible coupled system which consists of a central rigid body deploying a flexible appendage. The appendage is modeled as a finite deflection beam having linear constitutive equations. By taking the energy integral as Lyapunov function, it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam, according to the partial stability theorem.