Rotation in Three Dimensions - 3D Math Primer for Graphics and Game Development - page 232

clockwise/counterclockwise for bank. If we look from the origin to the
positive end of the y-axis, then positive heading does rotate counter-
clockwise. Or if we look from the positive end of the z-axis towards
the origin (looking backward from in front of the object), then posi-
tive bank appears to rotate the object clockwise. In either case, the
left-hand rule prevails.

Now you have reached the orientation described by the Euler angles.
Notice the similarity of Steps 1-3 to the procedure used in Section 7.3.2 to
locate the direction described by the spherical coordinate angles. In other
words, we can think of heading and pitch as defining the basic direction
that the object is facing, and bank defining the amount of twist.

8.3.2 Other Euler Angle Conventions

The heading-pitch-bank system described in the previous section isn't the
only way to define a rotation using three angles about mutually perpen-
dicular axes. There are many variations on this theme. Some of these
differences turn out to be purely nomenclature; others are more meaning-
ful. Even if you like our conventions, we encourage you to not skip this
section, as some very important concepts are discussed; these topics are
the source of much confusion, which we hope to dispel.
First of all, there is the trivial issue of naming. The most common
variation you will find was made popular by the field of aerospace, the
yaw-pitch-roll method. 5 The term “roll” is completely synonymous with
bank, and for all purposes they are identical. Similarly, within the limited
context of yaw-pitch-roll, the term “yaw” is practically identical to the
term heading. (However, in a broader sense, the word “yaw” actually has
a subtly different meaning, and it is this subtle difference that drives our
preference for the term heading. We discuss this rather nit-picky distinction
in just a moment, but for the moment yaw and heading are the same.) So
essentially yaw-pitch-roll is the same system as heading-pitch-bank.
Other less common terms are often used. Heading also goes by the
name azimuth. The vertical angle that we call pitch is also called attitude
or elevation. The final angle of rotation, which we call “bank,” is sometimes
called tilt or twist.

5 It's probably a bit presumptuous of us to refer to yaw-pitch-roll as a variation. After
all, there is a Wikipedia article for yaw-pitch-roll, but none for heading-pitch-bank, so
who's to say our preference isn't the variation? We admit this presumption and are
prepared to defend our preference shortly.