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Small Unmanned Aircraft by Timothy W. McLain, Randal W. Beard

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APPENDIX B

Quaternions

B.1 Quaternion Rotations

Quaternions provide an alternative way to represent the attitude of an aircraft. While it could be argued that it is more difficult to visualize the angular motion of a vehicle specified by quaternions instead of Euler angles, there are mathematical advantages to the quaternion representation that make it the method of choice for many aircraft simulations. Most significantly, the Euler angle representation has a singularity when the pitch angle θ is ±90 deg. Physically, when the pitch angle is 90 deg, the roll and yaw angles are indistinguishable. Mathematically, the attitude kinematics specified by equation (3.3) are indeterminate since cos θ = 0 when θ = 90 deg. The quaternion representation of ...

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