# Are there any practical uses of position derivatives beyond Jerk?

Jerk, or the rate of change of acceleration and knowing it has important applications in manufacturing and in motion control (for instance automobiles).
For the life of me, I can’t recall ever reading about the derivatives beyond third order, except that they exist (wiki tells me they are called “snap”, “crackle” and “pop”).
Is there any practical application where the calculating of snap is necessary? Do SpaceX engineers worry about Falcon9 's crackle?

The quintessential example I’ve always heard is that the Hubble Space Telescope engineers set limits on snap/jounce. Wikipedia mentions this. However, their cite leads to this page, which is a dead end. They don’t cite any NASA documentation to support the claim.

I do have a personal theory as to what happened. Since a crucial aspect of Hubble is that it rotates to aim in a certain direction, it may make sense to put a limit on rotational jerk. But rotational derivatives are “one higher” than the equivalent linear derivative. A constant hub speed will have particles on the edge experiencing constant acceleration. An accelerating hub will have particles experiencing jerk. And a hub with non-zero jerk will have particles experiencing jounce/snap. So it may be that they didn’t explicitly limit jounce, but did so indirectly by limiting rotational jerk.

More on the HST, IIRC: they considered 11 orders of time derivative when designing it. I think that means position, velocity, acceleration, jerk, snap, crackle, pop, and 4 more.

The only way I could see that happening would be if they were producing a power-series expansion for some function or another (which may not necessarily have been a position function).

What’s after “Pop”?

Fee, Fie, Foe, and Fum ?

Jeez, I just add milk and maybe some cut fruit

Derivatives of higher order may not all have agreed-upon names, and not often have practical uses, but at least all the derivatives on one function, namely ex are easy to deal with.

The trig functions and the hyperbolic trig functions are nearly as easy.

(Aside)
A bunch of mathematical functions are at a party, and one says to another, “Hey, don’t talk to that guy over there. He’s the derivative operator. He’ll differentiate you!” And the other replies “I’m not afraid of any derivative operator, I’m e^x.” So he goes over and says “Hi, I’m e^x.”, and the other function says “Nice to meet you; I’m the derivative with respect to y.”.

Just so it be clear, what is the mechanical mechanism by which large values of 3rd, 4th, … derivatives fracture or destroy structural materials? How to figure out acceptable limits for my toaster or LEO rocket?