[basil-rash]

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.

[dmoy]

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.

[basil-rash]

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”.