Regarding Euler angles

Hi all!

I was reading this article on Euler angles and gimbal lock:

Now, what i do not understand is this:
In any coordinate space(Cartesian) aren’t the three basis vectors need to be perpendicular to each other? So, i don’t understand when the article says something like two axes are aligned.

So, the article suggests that what was a roll, is now a heading for the plane.

My understanding is that the pilot still has all degrees of freedom of rotation, but the axes are just differently named. But, i fail to understand where there is a “loss of degree of rotation” here, since at any orientation, the object is still free to move in all directions, only that the meaning of rotations change.

Can anyone please explain this?


This is a maths problem but a physical one. Gimbal locks occur as a result of how the 3 angles are converted to rotation matrices and then those matrices are combined into a single rotation matrix. If you understand the maths you will understand the problem,
if you don’t then trust the guys - it happens so you can’t use all 3 euler angles without creating a Gimbal lock with some combinations.