Equations of motion for arbitrary rigid-body systems with application examples

In connection with the solution of problems in the area of dynamics, it is often necessary to derive nonlinear equations of motion for systems which, in the context of the problem, can be considered as systems of rigid bodies that are flexibly connected with each other. In the reported investigation, it is assumed that the bodies are rigid and that all linkages provided by the joints are ideal. This means that linkage forces do not perform virtual work. The number of bodies, the coupling structure, and the form of the joint linkages are arbitrary. A reduced system is formed and equations of motion are developed for this system in three steps on the basis of the d'Alembert principle. Attention is given to the kinematics of the relative motion of two adjacent bodies connected by joints and the kinematics of the motion of the individual bodies with respect to the inertial space.