Abstract
In this paper, the quaternion, the dual Euler, and the direction cosine methods are numerically compared using a non-aerodynamic 6 degree-of-freedom rigid model at all-attitude angles of an aircraft. The dual Euler method turns out to be superior to the others in the applications because it shows better numerical accuracy, stability, and robustness in integration step sizes. The dual Euler method is affordably less efficient than the quaternion method in terms of computational cost. Numerical accuracy and stability, which allow larger integration step sizes, are more critical in modern real-time applications than computational efficiency because of today's increased computational power. If the quaternion method is required because of constraints in computation time, then a suppression mechanism should be provided for algebraic constraint errors which will eventually add computational burden.