And here's another one about Euler angles. I want to ensure I'm understanding it right.
I had a really hard time getting how and why gimbal lock is possible, because the most common explanation is "loosing one degree of freedom" or something like "two axes are in the same plate". Explanations like "map from Euler angles is not a covering map for rotation space" sounds good, but still doesn't reveal the reason.
Then, I've read wikipedia once again and saw this:
"Euler rotations are never expressed in terms of the external frame, or in terms of the co-moving rotated body frame, but in a mixture.
They constitute a mixed axes of rotation system, where the first angle moves the line of nodes around the external axis z, the second rotates around the line of nodes and the third one is an intrinsic rotation around an axis fixed in the body that moves."
And then it hit me. When I was looking at all the pictures from all the articles and books, I saw something like this:
And I thought, that Euler angles are based on co-moving frame (so did a couple of my friends I asked, for that matter). But they are not! And from that moment everything seemed obvious!
If one axes is global and two others are co-moving, then they can become aligned and we have a gimbal lock.
So, here are my questions:
Am I right at all, and this is the basic reason for gimbal lock in Euler angles?
Will any rotation representation based on 3 orthogonal axes from one frame be gimbal-lock-free? Not only quaternions, but rotational matrices for example?
WHY OH WHY did Euler used those, let's say, strange set of axes?!
WHY OH WHY isn't it written in capsbold in every article about Euler angles, why all the pictures are so confusing?! Or maybe I'm the only one who didn't know that?
P.S. I'm sorry for my bad english.