Efficient conversion of Euler angles to quaternion for practical aerospace applications

Abstract Current methods for converting Euler angles to a rotation quaternion are computationally intensive and have limited practical applications in aerospace. This study introduces an efficient approach that directly converts Euler angles in any desired sequence to a rotation quaternion, eliminating the need for intermediate Euler angle transformation matrices, which leads to a significant improvement in computational efficiency. Moreover, it is general because it works with all 12 possible sequences of rotations. A case study is presented, demonstrating the application of the algorithm in converting between the launch frame and the missile frame of a vertical takeoff vertical landing (VTVL) rocket. The results show more than a ninefold improvement in computational efficiency compared to the classical Euler angle method while maintaining consistency of results.