Stability Analysis of Interconnected Deformable Bodies with Closed-Loop Configuration

Equations of motion for a system of interconnected deformable bodies with closed-loop configuration are obtained on the basis of the principle of virtual work. The system is represented by an adequate topological graph in which the bodies are considered as vertices and the joints as oriented arcs. The equations of motion are then derived in terms of the tree variables and of the forces and torques in the arcs cut. The derived equations permit equilibrium synthesis by solving a system of algebraic equations. The stability of a particular equilibrium is studied from considerations on the linearized equations of this equilibrium. Necessary and sufficient conditions for completely damped systems are obtained.