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I don't know if the header corresponds to my actual quest but i will explain.
In quadcopter dynamic equations of Newton-Euler formation that I have encountered in all academic publications,
torque equation is like this: enter image description here

The cause of gyroscopic effect is from the spinning of the four propellers
but i am confused about gyroscopic part of this equation, because, as you know,
in gyroscopic effect torque causes precession angular velocity perpendicular to spinning and torque vector.
In the equation above, it is written down as if the angular velocity [p,q,r] of the body frame is produced completely from gyroscopic torque caused by the spinning of propellers however, the torque applied to the rigid body itself also contributes to the angular velocity.

  • Is it assumed that angular velocity created by gyroscopic effect is much higher than the ones created by other factors so do they assume that precession is equal to the body frame a.v. ?
  • Gyroscopic torque is subtracted from total torque produced by propellers and the relation between movement of the body and applied torque to the body is established, but why is not generated angular velocity from the gyro effect considered because it will not be same with the situation where the same torque is applied but any gyro effect is not observed.
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  • $\begingroup$ Please use MathJax for formulae. $\endgroup$
    – Vincent Thacker
    Commented May 6 at 13:49
  • $\begingroup$ It is understandable that you want to cover the subject widely, but the result is that you compounded several question together. The design of Stackexchange is such that the question needs to be a focused question. I recommend that you find an entry point, an aspect of the problem that allows you to submit a focused question, one that allows/invites a focused answer. (And if need be, follow-up questioning) There is a 2012 answer by me specifically about gyroscopic precession $\endgroup$
    – Cleonis
    Commented May 9 at 4:54
  • $\begingroup$ @Cleonis Then, let me ask the question like this: In the famous wheel experiment to demonstrate gyroscopic effect, if we make this experiment in the space and weight of the axle of the wheel is much higher than the spinning wheel and if torque was applied perpendicular to spinning axis, how would behavior of the axle be in the axle frame $\endgroup$
    – pysicsuser
    Commented May 9 at 20:58
  • $\begingroup$ This isn't working out. You write: 'how would behavior of the axle be in the axle frame?' The phrasing 'the axle frame' means: the coordinate system that is co-oriented with the axle. So: by definition the axle does not change orientation wrt the axle frame. I believe the answer I linked to earlier (gyroscopic precession ) contains the information that you need to make progress. I recommend you submit your line of questioning on a threaded forum, such as physicsforums. Stackexchange is by design not threaded. $\endgroup$
    – Cleonis
    Commented May 10 at 9:38
  • $\begingroup$ @Cleonis I mean, if there is an observer that is assumed to be static, couldn't angular velocity and acceleration of the object be defined with respect to the object frame. $\endgroup$
    – pysicsuser
    Commented May 10 at 12:58

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