←back to thread

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

(iopscience.iop.org)
181 points EndXA | 4 comments | 19 Jun 24 10:16 UTC | HN request time: 0.437s | source
Show context
marginalia_nu ◴[19 Jun 24 11:14 UTC] No.40727129[source]▶
Do these higher order derivatives say anything meaningful?

I always got the sense from physics that outside of purely mathematical constructions such as Taylor series, higher order time derivatives aren't providing much interesting information. Though I'm not sure whether this is the inherent laziness of physicist math[1] or a property of the forces in nature.

[1] since e^x = 1 + x is generally true, why'd you even need a second order derivative

replies(8): >>40727177 #>>40727207 #>>40727251 #>>40727544 #>>40728112 #>>40730807 #>>40734568 #>>40735594 #
fellerts ◴[19 Jun 24 11:26 UTC] No.40727207[source]▶
Jerk (how fast acceleration changes) is useful. I've found being a passenger in newer electric buses to pose more challenges than ICE buses because EVs can change their acceleration so rapidly. While their maximum acceleration isn't very high, they can go from standstill to accelerating in a split second, toppling anyone standing unless they hold on to something. ICEs need more time to reach maximum acceleration. In other words, EVs jerk more.
replies(3): >>40727396 #>>40727411 #>>40727540 #
1. playingalong ◴[19 Jun 24 11:56 UTC] No.40727396[source]▶
How do you know this is not second derivative (acceleration), but the third or higher?

Genuinely curious.

replies(3): >>40728329 #>>40728502 #>>40737550 #
2. fellerts ◴[19 Jun 24 13:54 UTC] No.40728329[source]▶
I know it is the third derivative specifically because a rapid _change_ in acceleration easily puts you off-balance. A change in acceleration effects a change in the forces acting on you (F=ma). When those changes happen slowly, it's easy to adapt and change your stance to neutralize those forces, thus preventing your body from accelerating relative to your frame of reference (the bus).
3. myrmidon ◴[19 Jun 24 14:13 UTC] No.40728502[source]▶
Constant acceleration as bus passenger can be fully compensated by just leaning at an angle. This is not unpleasant.

But if the jerk (or higher derivatives) are non-zero, you have to change your "lean angle" quickly to avoid getting jerked around (which is obviously much more disruptive).

4. rcxdude ◴[20 Jun 24 11:45 UTC] No.40737550[source]▶
You can work it out from the principles of the engines (electric motor can produce their maximum torque at zero speed, combustion engines generally produce very little torque at zero speed, especially when modulated through a clutch or torque converter which you need in practice. And that's before looking at turbo-lag), but it's also something you can feel fairly viscerally: jerk is how quickly the feeling of acceleration changes. In a fast accelerating ICE car you might find yourself sinking more into the back of the seat as the car picks up speed. In an EV you basically just go from still to pressed all the way back, and then you start to pick up speed (and in fact the feeling of acceleration slackens off as the EV reaches a certain speed, though this will also happen with an ICE once they reach their peak acceleration point).