Derivation of Dynamics Equations for Body Components in the Reduced Multibody System Transfer Matrix Method

Dynamics equations serve as both a fundamental and an essential component within a multibody system dynamics methodology, as they govern the solution procedures and critically impact the computational efficiency of the approach. In the context of the reduced multibody system transfer matrix method, the dynamics equations for body components including internal connecting forces, rather than the global dynamics equations characterized by the generalized mass matrix of the system, are desired to be established, enabling the recursive solution of the forward dynamics problem. The dynamics equations of rigid body and flexible body components, as well as their reduced transfer equations, are derived in this paper respectively by utilizing the virtual power principle, which contributes to the theoretical foundation for the establishment of the recursive solution procedures. Finally, the derived dynamics equations are verified through a numerical example. It can be concluded that the derived dynamics equations are capable of being incorporated into the recursive solution procedures for the forward dynamics problem.