  Over the last decades quaternions have become a crucial and very successful
tool for attitude representation in robotics and aerospace. However, there is a
major problem that is continuously causing trouble in practice when it comes to
exchanging formulas or implementations: there are two quaternion
multiplications in common use, Hamilton's original multiplication and its
flipped version, which is often associated with NASA's Jet Propulsion
Laboratory. We believe that this particular issue is completely avoidable and
only exists today due to a lack of understanding. This paper explains the
underlying problem for the popular passive world to body usage of rotation
quaternions, and derives an alternative solution compatible with Hamilton's
multiplication. Furthermore, it argues for entirely discontinuing the flipped
multiplication. Additionally, it provides recipes for efficiently detecting
relevant conventions and migrating formulas or algorithms between them.
