A simultaneous space-time discretization approach to the inverse dynamics of geometrically exact strings

A continuous space-time Galerkin method is newly proposed for the numerical solution of inverse dynamics problems. The proposed space-time finite element method is combined with servo-constraints to partially prescribe the motion of the underlying mechanical system. The new approach to the feedforward control of infinite-dimensional mechanical systems is motivated by the classical method of characteristics. In particular, it is shown that the simultaneous space-time discretization is much better suited to solve the inverse dynamics problem than the semi-discretization approach commonly applied in structural dynamics. Representative numerical examples dealing with elastic strings undergoing large deformations demonstrate the capabilities of the newly devised space-time finite element method.