Generalized correction of numerical errors in kinematical differential equations based on euler normalized parameters

Abstract

It is shown how to correct the solutions of kinematical differential equations for arbitrary two-axis rotations represented by Euler-Rodrigues parameters. Two methods are described: minimizing the errors in the Euler-Rodrigues parameters themselves and minimizing the errors in the Frobenius norm of the direction cosine matrix. Details of the former are developed and numerical experiments are done which show an average improvement of about 17% in the root mean square values of the Euler-Rodrigues parameters. This generalizes the method of [2] and completes the framework developed in [3] for the practical use of these parameters in multiboy dynamic simulation.