Determination of optimal switching angles in the Dual‐Euler method based on round‐off error models

Abstract

Purpose

Optimal switching angles are investigated for minimizing accumulated numerical errors when the dual‐Euler method is used in the simulation of angular rotation.

Design/methodology/approach

First, round‐off errors are theoretically modeled with a simplified mathematical representation of rotation. Round‐off 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 (±π/4, ±3π/4) 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 (±π/4, ±3π/4) yield near minimum numerical errors in angular parameters of pitch, yaw, and roll if truncation errors are not dominant by using high‐order 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.

Originality/value

Optimal switching angles in the dual‐Euler method are identified based on the truncation error analysis. The mechanism of accumulated numerical errors in the dual‐Euler method, which depends on switching angles, is also revealed.

Citation

Yoon, S., Kong, J., Lee, K. and Hwang, H. (2005), "Determination of optimal switching angles in the Dual‐Euler method based on round‐off error models", Engineering Computations, Vol. 22 No. 3, pp. 286-296. https://doi.org/10.1108/02644400510588094