March 6 Information

So the third derivative of position, if you need it, is jerk.
I just discovered we've got an article jounce on the fourth derivative.
But that's where things start getting a little hinky.
At jounce there's an image (citing a reference) suggesting that the fifth and sixth derivatives are called flounce and pounce.
But there's also an (attributed) quote saying "The not so common names for the next three derivatives are snap, crackle, and pop", and indeed we've actually got articles, citing multiple references, on crackle and pop.
I realize it's a pretty academic question, but does anyone know whether jounce/flounce/pounce, or snap/crackle/pop, are more "official", and deserving of having their names on articles here? I've chased the linked references about as far as I can, without finding much in the way of definitivity. — Steve Summit ( talk) 19:21, 6 March 2020 (UTC) reply
P.S. And if this intrigues you, you can also look into absement, absity, abseleration, and abserk, or the somewhat related actergy.

While these are quite jovial terms, I don't think I've seen them seriously used in any physics or engineering context. It's much more appropriate, and a lot more common, to clearly describe the n^th derivative of position with respect to time.

As a point of note, when we use kinematic equations that actually do use the n^th derivative - for example, in complicated situations of mechanical control theory, robotics, vehicle dynamics, and so on... well,... when things are very simple, we only need to use second-order equations (hence, the omnipresent PID controller); and when we actually need more than two terms, then we're usually controlling a state-space matrix, or some other transform-domain; and so - if there were three or five or k-thousand terms, we are not typically controlling (or even caring about) the time-derivatives. Rather, we simply refer to the k-th element of the vector of control-variables, which may - for some special cases - be defined by some computable relationship to one or more time-derivatives. What we do have, in terms of standard terminologies, are specific names for specific methods to generate those computable relationships.

And therefore, every proper roboticist worth their salt has memorized every variant of those horrible A-B-C-D matrix methods, which are a formalization of the linearized relationships between all n-th order derivatives, and we can all solve them on paper, and do not actually have to resort to using MATLAB.

...So, we don't really need names for those higher-order derivatives of motion. As such, I tend to disbelieve anyone who claims to report an authoritative, widely-used nomenclature for them.

A great reference is the Nise book on Control Systems Engineering; that book is kind of the "canonical source of truth" for the "standard" terminology - at least among the community of engineers who design and study the dynamic control of mechanical systems. There are plenty of other great resources, too - I can dig some out if you want more...

Nimur ( talk) 19:47, 6 March 2020 (UTC) reply

Oh, I get it about whether we need an "authoritative, widely-used nomenclature for them" -- and that's kind of why asked, since our articles Crackle (physics) and Pop (physics) could seem to lend the ol' "undue weight".

(Ironically, I am a roboticist, although evidently not one worth my salt. :-) )

— Steve Summit ( talk) 03:27, 7 March 2020 (UTC) reply

A practical everyday example where jerk is important is holding onto a pole while standing aboard a bus or subway train. You can handle more acceleration if you know it's coming and have time to tighten your grip, and the way you know is that the jerk is low. -- 69.159.8.46 ( talk) 03:30, 7 March 2020 (UTC) reply

• Up to jounce is quite widely used. Above this I've only heard snap, crackle and pop.

High-order derivatives are used in cases where there's some other process acting as an integrator. Most commonly this is the human body: the organs flapping around inside can be sensed by their force on the abdominal wall and that can best be predicted by calculating these high derivatives for the vehicle the human is in. So the main application areas for this are rollercoaster physics (I think it was Disney who originally imagineered snap, crackle and pop), fighter aircraft pilot ergonomics and motor racing. F1 drivers experience small-dimension forces but of much higher acceleration (and jounce) far greater than fighter pilots do (More high-order impulse from concrete kerbs than aerodynamics).

Years ago, I made instrumented driving shoes with an accelerometer, to try and tie this to uncommanded throttle surges that were happening. Jounce was moving the ankle up and down and the high-precision throttle sensor was reacting so quickly that it was detecting these bounces. The fix was to low-pass filter the throttle control input. Andy Dingley ( talk) 20:23, 6 March 2020 (UTC) reply

Btw, rollercoaster physics should redirect to Physics of roller coasters. — 2606:A000:1126:28D:2D45:4564:93:B822 ( talk) 23:13, 6 March 2020 (UTC) ... thx, User:scs reply

And now it does. (You're welcome! :-) ) — Steve Summit ( talk) 03:27, 7 March 2020 (UTC) reply