The discrete null space method for the energy consistent integration of constrained mechanical systems

The present work deals with energy consistent time stepping schemes for finite-dimensional mechanical systems with holonomic constraints. The proposed procedure is essentially based upon the following steps: Firstly, the index three differential-algebraic equations corresponding to the constrained mechanical system are directly discretized. Secondly, the discrete Lagrange multipliers are eliminated by using a discrete null space matrix. In many cases it is feasible to further reduce the number of unknowns by employing specific reparametrizations. The proposed method entails a number of advantageous features such as size-reduction and improved conditioning of the resulting system of algebraic equations. It is shown that the newly developed method is well-suited for both open-loop and closed-loop multibody systems.