# Are there any practical uses of position derivatives beyond Jerk? **URL:** \ **Category:** Factual Questions\ **Created:** [November 24, 2021, 8:42am UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855 "2021-11-24T08:42:16Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![AK84](https://avatars.discourse-cdn.com/v4/letter/a/85e7bf/32.png) [@AK84](https://boards.straightdope.com/u/AK84)\ **Post date:** [November 24, 2021, 8:42am UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855/1 "2021-11-24T08:42:16Z")
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? ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [November 24, 2021, 9:06am UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855/2 "2021-11-24T09:06:38Z")
The quintessential example I’ve always heard is that the Hubble Space Telescope engineers set limits on snap/jounce. Wikipedia [mentions this](https://en.wikipedia.org/wiki/Jerk_(physics)#Force,_acceleration,_and_jerk). However, their cite leads to [this page](https://math.ucr.edu/home/baez/physics/General/jerk.html), 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. ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [November 24, 2021, 3:47pm UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855/3 "2021-11-24T15:47:07Z")
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. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 24, 2021, 3:51pm UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855/4 "2021-11-24T15:51:38Z")
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). ---
**Author:** ![AK84](https://avatars.discourse-cdn.com/v4/letter/a/85e7bf/32.png) [@AK84](https://boards.straightdope.com/u/AK84)\ **Post date:** [November 25, 2021, 3:55am UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855/5 "2021-11-25T03:55:06Z")
What’s after “Pop”? ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [November 25, 2021, 4:11am UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855/6 "2021-11-25T04:11:16Z")
> [@AK84](#): > > What’s after “Pop”?   Fee, Fie, Foe, and Fum ? ---
**Author:** ![superwombat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/superwombat/32/16616_2.png) [@superwombat](https://boards.straightdope.com/u/superwombat)\ **Post date:** [November 25, 2021, 4:57am UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855/7 "2021-11-25T04:57:45Z")
Jeez, I just add milk and maybe some cut fruit ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [November 25, 2021, 6:52am UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855/8 "2021-11-25T06:52:35Z")
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. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 25, 2021, 1:37pm UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855/9 "2021-11-25T13:37:10Z")
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.”. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [November 25, 2021, 3:13pm UTC](https://boards.straightdope.com/t/are-there-any-practical-uses-of-position-derivatives-beyond-jerk/954855/10 "2021-11-25T15:13:20Z")
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?