On the equations of motion in constrained multibody dynamics

The equations of motion for a constrained multibody system are derived from a continuum mechanical point of view. This will allow for the presence of rigid, as well as deformable, parts in the multibody system together with kinematical constraints. The approach leads to the classical Lagrange–d’Alembert equations of motion under constraint conditions. The generalized forces appearing in the equations of motion are given as expressions involving contact, internal and body forces in the sense of continuum mechanics. A detailed analysis of physical constraint conditions and their implication for the equations of motion is presented. A precise distinction is made between constraints on the motion on the one hand and resistance to the motion on the other. Transformation properties – covariance and invariance under changes of configuration coordinates – are elucidated. The elimination and calculation of the so-called Lagrangian multipliers is discussed and some useful reformulations of the equations of motion are presented. Finally a Power theorem for the constrained multibody system is proved.