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

(iopscience.iop.org)
181 points EndXA | 1 comments | 19 Jun 24 10:16 UTC | HN request time: 1.589s | source
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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

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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.
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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.

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1. 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).