Everyday life may be a stretch, however some higher-end quadrotors are able to navigate safely in complex indoor environments by generating trajectories that minimize the snap, the second derivative of acceleration.
Therefore, angular velocity is determined by jerk - the rate at which this thrust vector is changing.
The angular velocity cannot be changed instantaneously, because the quadrotor can only exert a finite torque about its rotational axes. So we need to design trajectories that do not attempt to change the angular velocity -- and hence, the jerk -- too quickly.
Therefore, we should try to minimize something like the maximum norm of the snap along the trajectory.
In practice we often minimize the integral of the squared norm of the snap, because it can be posed as a convex quadratic optimization problem with respect to the control points of a spline.
Just checking my understanding.
1st derivative = velocity
2nd derivative = acceleration
3rd derivative = jerk
4th derivative = snap
5th derivative = crackle
6th derivative = pop
I just learned the last 3 due to this discussion and Wikipedia[1][2].
[1]: https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv...
−7th: absop
−6th: absackle
−5th: absnap
−4th: abserk
−3rd: abseleration
−2nd: absity
−1st: absement
What are they used on?
(Very nice to think about)
Crackle and pop, I have no idea if you could tell the difference.
The Wikipedia page on Jerk also has a good explanation for the how people feel that: https://en.wikipedia.org/wiki/Jerk_(physics)
I'm unsure if we can really feel Snap and beyond.