Correction of numerical error in kinematical differential equations when one direction cosine is known

Abstract

If a direction cosine matrix represents a two-axis rotation, one of the direction cosines remains zero. It is shown how one can take advantage of this knowledge to improve the correction of numerical errors in the parametrizing variables of the matrix. The cases of Euler parameters and six-parameter representations are considered, as well as Euler-Rodrigues parameters for which there is no traditional correction process because they normally do not satisfy any kinematical constraint. Improvement in the matrix estimates can be gotten in all cases, but only for the six-parameter method is it substantial.