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

Summary

The problem concerns rotation with two degrees of freedom about known axes, the rotation described by normalized Euler parameters. Traditional kinematic correction of these parameters has been to renormalize them periodically by dividing each by their euclidean norm. This work develops a correction method which utilizes knowledge about the two-degree-of-freedom character of the rotation to correct a second constraint on the parameters. Numerical trials of 1000 random cases show that the present method reduces the error norm in the Euler parameters on the average to about 55% of it uncorrected value. Correction by the traditional method in the same cases reduces the error norm in the Euler parameters to about 31% of its uncorrected value. Thus the larger part of the total correction is done by traditional method, but the new method, with fairly modest computational requirements, gives a worthwhile improvement if maximal correction is desired.