Determination of optimal switching angles in the DualEuler method based on roundoff error models

Purpose Optimal switching angles are investigated for minimizing accumulated numerical errors when the dualEuler method is used in the simulation of angular rotation. Designmethodologyapproach First, roundoff errors are theoretically modeled with a simplified mathematical representation of rotation. Roundoff errors take critical roles in the vicinity of indefinite points because they cause major numerical inaccuracy in very large numerical values represented with limited binary numbers. Optimal switching angles of 4, 34 are derived and numerically examined. With a more practical and severe rotational model, the switching angles are numerically tested. Findings In conclusion, switching pitch angles of 4, 34 yield near minimum numerical errors in angular parameters of pitch, yaw, and roll if truncation errors are not dominant by using highorder integration algorithms and small step sizes. It is also noticed that accumulated numerical errors increase dramatically if pitch and roll angles are switched beyond the optimal angles with a little margin. Originalityvalue Optimal switching angles in the dualEuler method are identified based on the truncation error analysis. The mechanism of accumulated numerical errors in the dualEuler method, which depends on switching angles, is also revealed.