Contributions to the Method of Coordinate Splitting for Solving Differential Algebraic Equations

Abstract

The Coordinate Splitting method is a numerical technique which was developed to aid in solving constrained multibody dynamic systems modelled as differential algebraic equations (DAEs). This paper presents a discussion about the implementation of this technique, analyzing what happens to the structure of the DAEs and how the quantity called the annihilation matrix is utilized to compute a solution. Also, an explicit formula is described for computing the Jacobian of the DAE formulation of the Coordinate Splitting method when using QR-factorization to determine the annihilation matrix. Finally, an illustrative example is used to demonstrate that the Coordinate Splitting method can be successfully applied to systems involving a singular inertia matrix.