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Resizing the diagram |
Tait-Bryan at the end |
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\end{bmatrix}</math>
==== Conversion ====▼
===Relationship with Tait-Bryan angles===▼
[[Image:Flight dynamics with text.png|right|thumb]]▼
Similarly for Euler angles, we use the [[Tait-Bryan angles]] (in terms of [[flight dynamics]]):▼
* Roll - <math>\phi</math>: rotation about the X-axis▼
* Pitch - <math>\theta</math>: rotation about the Y-axis▼
* Yaw - <math>\psi</math>: rotation about the Z-axis▼
where the X-axis points forward, Y-axis to the right and Z-axis downward and in the example to follow the rotation occurs in the order yaw, pitch, roll (about body-fixed axes).▼
Nevertheless, it is not easy to find a matrix expression with Tait-Bryan angles because its final expression depends on how the rotations are applied.▼
▲== Conversion ==
By comparing the terms in the two matrices, we get
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\mbox{arctan} \frac {2(q_0 q_3 + q_1 q_2)} {1 - 2(q_2^2 + q_3^2)}
\end{bmatrix} </math>
▲[[Image:Flight dynamics with text.png|right|thumb]]
▲Similarly for Euler angles, we use the [[Tait-Bryan angles]] (in terms of [[flight dynamics]]):
▲* Roll - <math>\phi</math>: rotation about the X-axis
▲* Pitch - <math>\theta</math>: rotation about the Y-axis
▲* Yaw - <math>\psi</math>: rotation about the Z-axis
▲where the X-axis points forward, Y-axis to the right and Z-axis downward and in the example to follow the rotation occurs in the order yaw, pitch, roll (about body-fixed axes).
▲Nevertheless, it is not easy to find a matrix expression with Tait-Bryan angles because its final expression depends on how the rotations are applied.
== Singularities ==
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