Documentation should clarify that the quaternions are defined using an active rotation convention about quaternion HOT 2 CLOSED

I strenuously object to using "conventional" names for identifying any conventions, because even the names are ambiguous, uninformative, and very easy to misinterpret. My advice, as always, is to understand the relationships between different quantities, which is what I actually try to document. For example, see the docstrings of as_rotation_matrix and from_rotation_matrix, which specify that the rotation matrix m acts in the same way as the quaternion q such that

m @ v.vec == q * v * q.conjugate()

Or the docstring of rotate_vectors, which specifies that a quaternion R acts on a vector v to produce a new vector as

vprime = R * v * R.conjugate()

But the meaning of that relationship depends on what R represents: a change of basis or a physical rotation. Therefore, fundamentally and unavoidably, the way you think of those relationships — and how you name them — is up to you.

Moreover, most of this package doesn't actually deal with rotations. In fact, off the top of my head, those are the only three functions that actually deal with applying rotations per se. The Euler-angle functions, for example, only produce quaternions from a set of angles; they don't apply any quaternions. And again in those cases, all I do is document the relationship between those angles and the quaternion. And of course, that's another example where people have repeatedly asked me to identify the convention with names including "active" and "passive" — though with completely different meaning to your usages above.

IMO, using names like these only misleads, and makes the complete and utter mess of conventions combinatorically worse.

from quaternion.

Point taken on the mathematical definitions being the source of truth, but for all the verbiage about Euler angles being bad some language on anticipating this (IMO rather more insidious) footgun would be much appreciated. I'll also note that the Shuster convention talked about in those papers changes the definition of quaternion multiplication itself, so that i * j = -k rather than +k. I don't see the multiplication definition called out in the docs right now.
(discussed a bit previously in #96)

from quaternion.