Nonlinear dynamics of flexible structures: geometrically exact formulation and stability

The stability of flexible structures coupled with rigid bodies performing large overall motions is investigated. The analysis is based on geometrically exact models which have no restriction on the degree of flexibility and enjoy the exact satisfaction of all invariance requirements under superposed rigid body motions. For these models there is a natural decomposition which decouples the dynamics into a space of rigid body motions and its complement. The stability of relative equilibria are then explored by a method referred to as the energy-momentum method, which incorporates the conserved quantities of the system. By exploiting these invariants along with the underlying structure, stability criteria for the relative equilibria can be found