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The axis definition affect the roll, pitch and yaw definition in a quadcopter?

Image I have the axis defined this way:

enter image description here

then to roll I have to put a higher velocity in (1) than in (3) (turn around the $x$ axis), and to pitch I have to put a higher velocity in (2) than in (4) (turn around the $y$ axis), for example. But what if I have the axis defined like this:

enter image description here

the turn around the $x$ axis will happen when 1 and 4 have one velocity and 2 and 3 another one, and the turn around the $y$ axis will occur when the velocity in 1 and 2 is $v_1$ and the velocity in 3 and 4 is $v_2$, for example.

Is that correct? How are the kinematics equations in this case?

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    $\begingroup$ Your reasoning is correct. The kinematic equations, however, will not change. They are static representations of Newton's laws of motion. $\endgroup$
    – koverman47
    Feb 25, 2020 at 22:30
  • $\begingroup$ Do you know any book or thesis or paper where the dynamics and kinematics are explained step by step? $\endgroup$
    – Unnamed
    Feb 27, 2020 at 12:40
  • $\begingroup$ (The dynamics and kinematics of a quadcopter) $\endgroup$
    – Unnamed
    Feb 27, 2020 at 12:49
  • $\begingroup$ Unfortunately no, but I recommend doing some exploring of your own. You will likely learn quite a bit more than you'd expect that way. $\endgroup$
    – koverman47
    Feb 28, 2020 at 21:49

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