Yaw, pitch, and roll
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Yaw, pitch, and roll, also known as Tait–Bryan rotations, named after Peter Guthrie Tait and George Bryan, are a specific type of angle very often used in aerospace applications. The three angles specified in this formulation are defined as the roll angle, pitch angle, and yaw angle.
Tait-Bryan rotations are used in aerospace to define a rotation between a reference axis system and a vehicle-fixed axis system. Consider an aircraft-body coordinate (ABC) system which is fixed to the vehicle (rotates and translates with the vehicle). The origin of the ABC system is located at the vehicle's center of gravity, the x-axis points forward along some convenient reference line along the body, the y-axis points to the right of the vehicle along the wing, and the z-axis points downward to form an orthogonal right-handed system. Consider a world reference frame (WRF) that shares the same origin as the ABC system but is always aligned with x pointing in the direction of true north, y-axis pointing to true east, and the z-axis pointing down towards the center of gravity of the earth.
Given this definition, the rotation sequence is defined as follows: (Stevens, 26)
1. Right-handed rotation about the z-axis by the yaw angle.
2. Right-handed rotation about the new (once-rotated) y-axis by the pitch angle.
3. Right-handed rotation about the new (twice-rotate) x-axis by the roll angle.
The rotation from WRF to abc is defined as follows: (Stevens, 26)
- Rwrf to abc = Rz(yaw) × Ry(pitch) × Rx(roll)
where Rx(a), Ry(a), and Rz(a), is shorthand notation for the planar rotation matrices of a positive rotation by angle a about x-, y-, and z-axes, respectively. The inverse rotation, from ABC to WRF, is defined as the transpose of this matrix. The final rotation matrix can be referenced in the literature (Stevens, 26).
