Correction of numerical error when two direction cosine columns are used as kinematical variables

Abstract

Abstract When more than three variables are used to characterize a rotation they must satisfy one or more algebraic constraints. Numerical errors in integrating the kinematical differential equations cause the constraints to be violated. Known correction procedures for four- and nine-variable parametrizations are reviewed. A new correction technique is developed for six-variable methods in which two columns of the direction cosine matrix provide the six variables. Results of numerical tests of the method are given. Baumgarte's method for constraint stabilization also is described briefly.