The present thesis deals with inverse multibody dynamics problems. In particular, optimal control problems will be treated, which are governed by differential-algebraic equations. The main goal therein is the minimization of the control effort, which is necessary for moving a multibody system from one configuration to another. A basic task therefore is the formulation of the underlying equations of motion.
Main focus will be on the formulation of the equations of motion with natural coordinates, which facilitates the design of structure-preserving time-stepping schemes. It is well known that schemes preserving basic properties of the mechanical system algorithmically exhibit superior stability properties in comparison to standard integrators. The application of these schemes within optimal control problems requires a consistent incorporation of the control torques. A convincing way for the incorporation of the control torques will be proposed in this contribution. In addition to the schemes based on the rotationless formulation, also an energy-momentum conserving time-stepping scheme based on quaternions will be presented. Although the quaternion-based scheme turns out to be competitive in the forward dynamics of rigid bodies, the extension to multibody problems is not as straightforward and easy to handle as with the rotationless formulation in terms of natural coordinates. Therefore quaternions will not be applied within optimal control problems in this thesis. Regarding optimal control of multibody systems, new energy-momentum consistent direct transcription methods in terms of natural coordinates will be presented. In a first step, the equations of motion obtained by a reduction process via the discrete null space method will be applied. The arising results will be compared with those achieved by a formulation of the equations of motion with the widely used minimal coordinates. In a second step, the original equations of motion in form of differential-algebraic equations will serve as basis for the formulation of the optimal control problem. In addition to the direct transcription methods mentioned before, a novel optimal control method based on indirect transcription will be presented. The newly proposed method conserves the Hamiltonian corresponding to the optimal control problem. It is worth mentioning that this method is directly related to previously developed energy consistent schemes in forward dynamics.