Modeling mechanical DAE using natural coordinates

An efficient modeling technique for multibody systems, which extends the concept of natural coordinates with closed kinematic loops is presented. By establishing a local coordinate system in each body a system with constant mass matrix is set up. The propagation of topological information into the model leads to the application of a block-oriented rational Cholesky decomposition of the system matrix. The overall algorithm shows linear complexity in the number of bodies for systems with a constant number of kinematic loops. To handle rank-deficient constraint Jacobians arising from loop closing conditions the concept of constraint partitioning during decomposition is outlined. Restriction of the partitioning decision based on the topology information minimizes the monitoring effort and avoids disadvantages experienced in other partitioning methods. Numerical results for the 6-bar-mechanism proof the algorithm to run efficiently with projection stabilized index-1 integration methods.