I found this example by Steven Wittens to be remarkably well done: http://acko.net/blog/animate-your-way-to-glory-pt2/

See the section "Blowing up the Death Star" and note that there are 100 parts total.

"So that's quaternions, the magical rotation vectors."

Take a look at geometric algebra.

http://www.geometricalgebra.net/

http://en.m.wikipedia.org/wiki/Geometric_algebra

That's not quite the same, but worth reading up on anyway.

The quaternions are a subalgebra of geometric algebra. It's not quite the same in that it's strictly more general and, therefore, more broadly applicable.