Nonlinear Dynamics of Multibody Systems Using an Augmented Lagrangian Formulation

A class of multibody systems subject to bilateral scleronomic motion constraints is investigated. The formulation is based on a new set of equations of motion, expressed as a coupled system of strongly nonlinear second-order ordinary differential equations. After putting these equations in a weak form, the position, velocity, and momentum type quantities are assumed to be independent, leading to a three-field set of equations of motion. Next, an equivalent augmented Lagrangian formulation is set up by introducing a set of penalty terms. This final set of equations is then used as a basis for developing a new time integration scheme, which is applied to several example systems. In those examples, special emphasis is put on illustrating the advantages of the new method when applied to mechanical systems, involving redundant constraints or singular configurations.