Aircraft Kinematic Equations with Full-Angle Quaternion to Euler Conversion
Aircraft attitude kinematic equations represented by Euler angles exhibit singularity at large angles, whereas quaternion representation avoids this issue. Therefore, quaternions are universally adopted for aircraft kinematic equations. However, control laws predominantly use Euler angles due to their intuitive visualization of attitude, making them more comprehensible for human interpretation. Consequently, aircraft control system simulations require bidirectional conversion between quaternions and Euler angles. While converting Euler angles to quaternions is straightforward with a one-to-one correspondence, the reverse conversion is complex due to non-unique mapping where one quaternion may correspond to one or two Euler angle sets. This necessitates robust algorithmic implementation for full-angle range coverage.