While reading from various sources about Euler angles, and the concept of Pitch, Roll, Yaw, I have come across some inconsistencies.
In one source,
- yaw is a rotation about the rigid body's $y$ axis (pointing up),
- pitch is a rotation about the rigid body's $x$ axis
- roll is a rotation about the rigid body's $z$ axis
However, in the wikipedia entry on Euler angle here in the Conventions section,
they give an intrinsic rotation z-y'-x'' and write that these are referred
to as yaw, pitch, and roll.
I suppose my question is what is the most common convention of which axis each of the three words pitch, roll, and yaw are rotating around, and is there discrepancies between the choices in different texts, or have I made an error.
Best Answer
The conventions are relatively arbitrary. Axes labeled $x,$ $y,$ and $z$ are abstract mathematical concepts; aircraft and ships are real-world objects. There's no label on the nose of the aircraft to say what letter ($x,$ $y,$ or $z$) is the name of the axis that points forward.
There are some standards in industry, but I would not guarantee that they will be consistent across all possible applications of the words roll, pitch, and yaw. Also, some might be surprising. For example, the yaw axis illustrated in the Wikipedia article is pointing downward. (This has the effect that positive yaw is toward the right.)
Provided your first source used a right-handed set of axes, if the positive $z$ axis is forward then the $x$ axis is pointing to the body's left and a positive pitch will push the front of the body down.