As you can see, the projectiles post went out last weekend… well, last Monday evening, when technical posts usually go out. In a way, I’m sorry to have used my reserve post so quickly, and yet that is what it was for: to let me do mathematics almost all weekend.

I picked up quaternions as soon as I finished the diary post last Saturday… and I never put them down again, until I had finished what I set out to do.

And what was that? The newsgroup post I had seen triggered something: I decided that the easy way to find an Euler angle decomposition of a matrix was to use its quaternion representation rather than the matrix itself.

I was right. Of course, I didn’t know that until I had actually worked it out.

I expect that I will be writing a couple of posts about (3D) rotations. First, a rotation can be represented by a matrix, by its angle and axis of rotation, by a quaternion, and by Euler angles. Second, I wanted to be able to move between all four of those representations.

I spent a lot of time last weekend telling Mathematica® exactly what I wanted to do. And, all too aften, discovering that I didn’t really want to do that.

But we’ll start slowly. The first post in this set will be an introductory description of quaternions. Among other things, that will let me keep testing my code, refining it if necessary. (Actually, I already want to change three things.)

The second post will probably discuss rotations per se, and their representation by quaternions.

The third post will show how to move between the four representations.

On the other hand, I haven’t decided what I’ll do this weekend after I get the introductory quaternions post written.

But, as usual, we’ll see how it turns out.

Oh, this blog reached another milestone this morning: WordPress has now caught more than 10,000 spam comments. Good job.