Abstract
We propose a method of correction for the direction cosine matrix in the process of integrating kinematics equations. Corrections that are constructed for two vectors of the rotation matrix are selected from the conditions of minimization of the sum of the squares of their moduli, provided that adjusted vector orthonormality is fulfilled. We obtain the exact solution for the optimization problem as well as analytical equations for use in applied problems during the process of integrating equations of kinematics.
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