Can someone explain to me in the following example where it mentioned '' the first angle - alpha is the pitch.....'' why is alpha the angle of first rotation, shouldn't it ba gamma as we apply the last rotation first? Also, alpha is rotation around the x-axis, should that be called a roll instead of a pitch?
Thank you in advance.
I think it depends on the alignment of the body-fixed coordinate frame. If $x$ is out the nose of the aircraft, and $y$ out the right wing, (typical in aerospace literature) then yes, $\alpha$ would be a roll. If instead $x$ was out the right wing, (more common in robotics literature) then $\alpha$ would be a pitch.
I don't know why they say that $\alpha$ is the angle of first rotation. You're right, in X-Y-Z euler angle convention, yaw is applied first. That is syntax I've never heard before, perhaps it refers to the way we refer to is as "roll pitch yaw", or the way we read it, from left to right