Rotation in Three Dimensions - 3D Math Primer for Graphics and Game Development - page 235

In contrast, when players navigating a first-person shooter move the
mouse from left to right, they are performing a heading rotation. The
rotation is always about the vertical axis (the upright y-axis). If players are
looking downward and move the mouse horizontally to perform a heading
rotation, they continue to look downward and spin in place. The point
is certainly not that heading is better than yaw because that's what we
do in first-person shooters. The point is that a yawing motion cannot be
accomplished by adjusting a single Euler angle, but a heading motion can.
That's why we think “heading” is a better term: it's the action that results
when you make an incremental change to the first Euler angle.
Alas, the same argument can be leveled against the term “pitch.” If
bank is nonzero, an incremental change to the middle Euler angle does
not produce a rotation about the object's lateral axis. But then, there
isn't really a simple, good word to describe the angle that the object's
longitudinal axis makes with the horizontal, which is what the middle Euler
angle really specifies. (“Inclination” is no good as it is specific to the right-
handed conventions.)
We hope you have read our opinions with the humility we intended,
and also have received the more important message: investigating (seem-
ingly cosmetic) differences in convention can sometimes lead us to a deeper
understanding of the finer points. And then sometimes it's just plain nit-
picking. Generations of aerospace engineers have been putting men on the
moon and robots on Mars, and building airplanes that safely shuttle the
authors to and from distant cities, all the while using the terms yaw and
roll. Would you believe that some of these guys don't even know who we
are!? Given the choice to pick your own terminology, we say to use the
word “heading” when you can, but if you hear the word “yaw,” then for
goodness sake don't make as big of a deal out of it as we have in these
pages, especially if the person you are talking to is smarter than you.
Although in this topic we do not follow the right-handed aerospace co-
ordinate conventions (and we have a minor quibble about terminology),
when it comes to the basic strategy of Euler angles, in a physical sense, we
believe complete compliance with the wisdom of the aerospace forefathers
is the only way to go, at least if your universe has some notion of “ground.”
Remember that, in theory, any three axes can be used as the axes of ro-
tation, in any order. But really, the conventions they chose are the only
ones that make any practical sense, if you want the individual angles to be
useful and meaningful. No matter how you label your axes, the first angle
needs to rotate about the vertical, the second about the body lateral axis,
and the third about the body longitudinal axis.
As if these weren't enough complications, let us throw in a few more.
In the system we have been describing, each rotation occurs about a differ-
ent body axes. However, Euler's own original system was a “symmetric”