Transcript

MARCUS DU SAUTOY

There’s nothing like trying things out for yourself to really understand new concepts. In this case, we’re going to try to understand whether the order of operations matters if we’re doing rotations around different axes. So, let’s try this out. I’ve got a handy object here which we’re going to experiment on. We’ll keep it really simple, and I’m just going to do two operations: a rotation around the x-axis, and a rotation around the z-axis. So, here’s the starting position. Imagine we’ve got the axes, so: here’s the x-axis, the y-axis, and then the z-axis.

So I’m going to start by doing a rotation of 90 degrees around the x-axis. And then I’m going to do a 90 degree rotation around the z-axis. That leaves the book looking like this. But what happens if I do those rotations in the other order? So let’s start with the book in the same position. So now I’m going to do a rotation of 90 degrees around the z-axis, followed by a 90 degree rotation along the x-axis. Now the book looks like this.

So, when it comes to rotations around different axes, it really matters what order you do them in.