Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)

For those interested, it's also worth taking a look at the time-integrals (or "lower derivatives") past displacement: absement, absity, abseleration, etc. https://en.wikipedia.org/wiki/Absement

This is breaking my brain a little, any eli5?

There's some good examples in the wiki link, I liked: "A vehicle's distance travelled results from its throttle's absement. The further the throttle has been opened, and the longer it's been open, the more the vehicle's travelled." Plus the fact that the units are m*s instead of m/s.

Velocity measures how fast displacement changes. In the same way, displacement measures how fast absement changes. This means if displacement is small, then absement will grow slowly; if displacement is large, then absement will grow quickly.

I think in the linked article there's a good real-world example of that with a valve:

> opening the gate of a gate valve (of rectangular cross section) by 1 mm for 10 seconds yields the same absement of 10 mm·s as opening it by 5 mm for 2 seconds. The amount of water having flowed through it is linearly proportional to the absement of the gate, so it is also the same in both cases.

The first one comes up in control systems: you have two displacements, the target position and the real position. You subtract them to get the error, also a displacement. You can then integrate that error term to get the total error over the course of the control period. That would be “absement”, measured in m*s. You might then tune your control algorithms to optimize that value.

I’m not sure how to think about the lower orders. You might, for instance, have a learning control system you expect to come to a lower error state over time. The integral of the absement would be a decent way to capture that phenomena.

I did a bunch of stuff with PID back in the day, but honestly this is the first time I'm forcing my brain to look at the word "absement" to describe the integral portion. Looking back, I must have encountered the word many times in the past, but my brain just didn't process the label. I mentally knew and fully understood the concept, and did code / systems implementation involving it, but never really knew the term.

I also distinctly remember being about to go into an exam in undergrad EE, and having a decades-older MechE ask if I knew about "jerk". I had a temporary panic because I didn't know the term - but then when they started explaining it, I already knew it all, I just had never been exposed to the term "jerk" as the word to use for it.

So maybe it's just a terminology thing? I've been in situations where I definitely knew the concept thoroughly, both absement and jerk, but didn't know those labels.

Why bother with giving words for something which is longer than their mathemathical definition? The word can be unknown, but if the function is unknown the word is useless?

Reaching your hand into an oven (for some reason), you not only care about how far it is into the over, its position, you also care about how long it's been at its current position.

The funny thing is I’m almost certain everyone here has been exposed to the term “jerk”, in the exact technical meaning, but didn’t make the relation that the colloquial meaning and the technical meaning are the same.

Acceleration feels like a constant force (because… it is). When that force changes, you feel “jerked”.