CONTRIBUTIONS TO THE METHOD OF COORDINATE SPLITTING FOR SOLVING DIFFERENTIAL ALGEBRAIC EQUATIONS

Jason P. Frye and Brian C. Fabien

Keywords

Differential algebraic equations, modelling and simulation, Lagrangian dynamics

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.

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