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

(iopscience.iop.org)
181 points EndXA | 12 comments | 19 Jun 24 10:16 UTC | HN request time: 0s | source | bottom
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londons_explore ◴[19 Jun 24 11:39 UTC] No.40727286[source]▶
I wish designers of vehicles - particularly cars, trains and busses, would work to minimize jerk, snap and crackle.

Turns out if you minimize those, you get a far more comfortable ride. It matters far more than acceleration.

Finite element models of the whole system (tyres and suspension components and flexing elements of the vehicle body and road/track) can quickly allow analysis of the jerk, snap and crackle, and allow tuning of damping and drive system control loops to make a far more comfortable ride.

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amelius ◴[19 Jun 24 11:42 UTC] No.40727304[source]▶
Do you have proof for that, or is this like audiophiles asking for gold connectors because "they make the sound better"?
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1. setopt ◴[19 Jun 24 11:53 UTC] No.40727380[source]▶
Anecdotal evidence:

Ever experienced that a bus is braking (near-constant deacceleration), and people seem fine; but then the bus comes to a halt and thus stops deaccelerating, and people suddenly fall on the floor?

I think at least the derivative or acceleration is important for how well people can compensate. Not sure about higher derivatives though.

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2. amelius ◴[19 Jun 24 12:26 UTC] No.40727607[source]▶
Acceleration equals force, so yeah, if you abruptly change acceleration then this equals abruptly changing the force on people in the bus. Acceleration should thus be continuous (not necessarily differentiable). I don't know how you would justify constraints on higher derivatives. Perhaps they mess with our own internal control mechanism?
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3. ccccccc1 ◴[19 Jun 24 12:48 UTC] No.40727774[source]▶
is it physically possible to have non-continuous acceleration?
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4. shagie ◴[19 Jun 24 13:14 UTC] No.40727994{3}[source]▶
Imagine a multistage rocket and the changes in acceleration.

Figure 4-3 in https://www.ibiblio.org/apollo/Documents/lvfea-AS506-Apollo1... shows this for Apollo 11.

replies(1): >>40728398 #
5. zardo ◴[19 Jun 24 14:01 UTC] No.40728398{4}[source]▶
I imagine if you zoom in far enough on those points you have the acceleration continuously changing as pressure slowly builds in the engines over several microseconds.
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6. shagie ◴[19 Jun 24 14:11 UTC] No.40728487{5}[source]▶
I was thinking more of the instant you shut off engines and disconnect 130,000 kg of mass of stage one.

There is an interesting Δa/Δt while fuel is consumed and mass changes.

There are discontinuities to the graph when engines are shut down and stages decoupled.

replies(1): >>40729669 #
7. setopt ◴[19 Jun 24 14:31 UTC] No.40728677{3}[source]▶
If we zoom in on a single electron absorbing the momentum of a single photon, it will accelerate “instantly”. The same goes for e.g. an unstable atomic nucleus that ”splits”.

At macroscopic scales, I’m not aware of exactly instantaneous acceleration, since you would need some time to “sync” the movement of each atom in the object. But some processes will of course look instantaneous at any given time scale.

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8. amelius ◴[19 Jun 24 15:29 UTC] No.40729197{3}[source]▶
Voltages can change abruptly. Therefore, forces can change abruptly, and hence acceleration as well.
9. sokoloff ◴[19 Jun 24 16:16 UTC] No.40729669{6}[source]▶
That’s the essence of a legitimate question: over small enough time periods (as the bolts explode over a non-zero period of time), is it continuous or discontinuous?

Over a macro scale, it’s discontinuous, of course.

replies(1): >>40731312 #
10. tomek_ycomb ◴[19 Jun 24 18:52 UTC] No.40731289[source]▶
I think bus is braking with a constant breaking force.

But, the bus has a non-constant kinetic energy (going up with the velocity*velocity, down as velocity goes down.)

So, you're actually producing a non-linear acceleration. This is jerk, but you can also think of it as just a non-linear acceleration and people are reacting to the fact it's not at all near constant deacceleration, and this is most noticable as velocity hits zero.

So, yes, it's jerk, but no, I think it can be intuitively better understood with pure acceleration terms and no jerk needed

11. tomek_ycomb ◴[19 Jun 24 18:54 UTC] No.40731312{7}[source]▶
It's nature, it's continuous at small enough scales.

But, checkout Zeno's paradox for more on your philosophical questions

12. circuit10 ◴[21 Jun 24 15:10 UTC] No.40750441{4}[source]▶
Aren’t you describing infinite acceleration, or discontinuous velocity?