Quaternions these days are used for 1 thing: 3D rotations. My goals go beyond rocket science and gaming, so I run http://quaternions.com to show what can be done with quaternions in physics.

I went to the Harvard library once to find all the books that had quaternions in the title. There were only a dozen that were written after 1950. The reason is that quaternions are the house where scalars and vectors where born (Hamilton coined those names, along with dot, cross, curl, and gradient). Hamilton thought they could do everything. When he did not deliver the goods, quaternions got sent to the history books by math dudes as bitter as that fight over complex numbers. There are thousands of books with "vector" in the title, their victory is so complete few people have heard of quaternions.

With books that have quaternions and some other physics thing in the title, they explain the basic algebra, then as soon as the going gets tough, they toss in an extra factor of i (although a quaternion already has an i, j, and a k), and use complex-valued quaternions. In my technical opinion, that blows.

I have spent little effort on the rotation stuff. It is used in rocket ship rotation calculations because errors are easier to keep under control than with Euler angles.

To get a sense of how cold this area of research is, I went to the second meeting on quaternions in Rome in 1999, five years after the first one. They did not have a meeting in 2004. I was bummed, because I have pictures of a quaternion sine function that I'm sure that crowd would be interested in.

doug