The reason many people have trouble understanding quaternions is that they reason about them incorrectly.
Quaternions are actually a separate 'thing' when compared to vectors (which is why their multiplication seems off and the square is a negative number).
Quaternions should be considered a versor (a rotation around great circles), that is a change in direction which is different from a vector.
Quaternions are actually a separate 'thing' when compared to vectors (which is why their multiplication seems off and the square is a negative number).
Quaternions should be considered a versor (a rotation around great circles), that is a change in direction which is different from a vector.
See this work: https://archive.org/details/cu31924001506769/