12 ms·

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

181 points by EndXA 2y ago

koliber 2y ago
Someone once explained this to me in a very intuitive way. It goes like this: You’re sitting in the driver’s seat of a car. It is standing still. You push the gas pedal down 2 cm and hold it there. Your car begins accelerating. That’s the second derivative. You start pressing your foot further on the gas pedal. Your foot has a velocity on the gas pedal. It is causing your car’s acceleration to grow! That’s jerk. If you push your foot on the gas pedal faster and faster your foot accelerates on the gas pedal. That contributes to the cars snap.
Avlin67 2y ago
i remembrer using squaed sinus acceleration curves profile for robotique at school to minimise jerk
vinc 2y ago
A long time ago I wrote an engine for a newspaper that was helping journalists discover what was happening on social media. I was counting the number of times an URL was posted on Twitter and Facebook. I started with velocity and acceleration, but after I while I discovered that I could go one level higher and use jerk to understand when an URL was shared by an influencer. I have a hard time imagining another level above that.
- kevindamm 2y ago
  DDoS attacks, high inflection from a lot of disparate sources.
- Akronymus 2y ago
  Snap could be the acceleration of "influencers" sharing an article? Basically, how fast it spreads from one to many
  - frenchyatwork 2y ago
    That might be more exponential than polynomial.
- simpaticoder 2y ago
  When it comes to a measured time-series, the function is always discrete and arbitrary; there is no 'curve' like that generated by a function well-defined on the reals, and so there is no real closed-form derivative. In this context derivatives are not equations so much as derived data, reducing two points to one. And this process is recursive, such that you can take 4 points, reduce the two adjacent ones to 1 point, and then reduce those two into 1 point. In fact for 2^n points you can get the nth derivative in this way. The utility of this data is highly questionable in almost every context, but its available for every time-series. (One application that comes to mind is a kind of checksum, where you recursively derive a time series and stop when local neighbors go to 0, and you're left with a sparse list of high-order numbers that in some sense characterize the series.)
Rygian 2y ago
The proposed hierarchy is: - position - velocity - acceleration - jerk - snap - crackle - pop - "and so on" I'm good up to jerk, but not really sure for the remaining higher-order concepts.
- pestatije 2y ago
  this is the same as dimensions
DrNosferatu 2y ago
Lore has it that Snap, Crackle, and Pop are named after the three elves on Kellogg’s Rice Krispies cereal boxes. I use them in the context of N-Body Simulations. Curious to learn about other contexts for their use - anyone? https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv...
- ahazred8ta 2y ago
  The color printing industry has Snap, Gracol and Swop. Yes, the Gracol logo is a blackbird perched on CMYK dots. https://duckduckgo.com/?q=snap+gracol+swop https://duckduckgo.com/?q=snap+gracol+swop
  - demondemidi 2y ago
    Like grackle I presume.
- n4r9 2y ago
  > Lore has it that Snap, Crackle, and Pop are named after the three elves on Kellogg’s Rice Krispies cereal boxes. Surely this is true. Is there any likely alternative explanation?
marginalia_nu 2y ago
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
- azernik 2y ago
  Yes. That is the point of the article. > Jerk and snap can be observed in various areas of physics and engineering. In physics and engineering jerk and snap should always be considered when vibration occurs and particularly when this excitation induces multi-resonant modes of vibration. They should also be considered at all times when a transition occurs such as: start up and shutdown; take-off and landing; and accelerating and decelerating. > Acceleration without jerk is just a static load, and therefore constant acceleration alone could never cause vibration. In a machine shop, a toolmaker can damage the mill or the job if the setup starts vibrating. This vibration happens because of jerk and snap. > In mechanical engineering it is important in automotive design to ensure that the cam-follower does not jump off the camshaft. It is also important in manufacturing processes as rapid changes in acceleration of a cutting tool can lead to premature tool wear and result in an uneven and rough surface finish. > In civil engineering railway train tracks and roads should be designed for a smooth exit from a straight section into a curve, and it is common to use a transition called a clothoid, which is part of a Cornu spiral (also referred to as an Euler spiral). When a clothoid is implemented the change in acceleration is not abrupt and the levels of jerk and possibly snap are significantly reduced. If the transition between different radii of curvature is sudden, the transition is uncomfortable for passengers and potentially dangerous as it could cause the car or train to be thrown off the road or track. With good physics design engineers are attempting to produce a gradual jerk and constant snap, which gives a smooth increase in radial acceleration, or preferably a zero snap, constant jerk, and linear increase in radial acceleration. Just as road and railway engineers design out jerk and snap using the clothoid transition so, too, do roller coaster designers when they design loops and helices for the roller coasters [11, 12].
londons_explore 2y ago
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.
- amelius 2y ago
  Do you have proof for that, or is this like audiophiles asking for gold connectors because "they make the sound better"?
  - analog31 2y ago
    Not proof, but jerk is a factor when bringing a car to a smooth stop. You have to learn how to brake smoothly in order to avoid the "drivers ed stop" where the car and its passengers lurch forward and then bounce back. But the controls for automated vehicles like airport trams have to be designed to avoid this. The underlying reason is that some components such as the tires and suspension are elastic. This is in fact an issue for the designers of controls for mechanical systems. I learned about it in Process Control class, albeit 40 years ago.
    - robertlagrant 2y ago
      Cars 20+ years ago vs more recent cars - I've definitely noticed them auto-doing what I was taught to do with older cars: ease off the brakes right at the end.
      - sokoloff 2y ago
        I wonder if this is a change in braking material, specifically a reduction in difference between dynamic coefficient of friction and static coefficient of friction between the pad and rotor (or equivalently, the shoe and drum). If older cars had a higher differential, you’d need to let up more as the brake finally locks up.
anymouse123456 2y ago
Serious, well-written, scientific information that also references children's breakfast cereal? Moar please!
- numbol 2y ago
  Here you go https://en.wikipedia.org/wiki/Cheerios_effect https://en.wikipedia.org/wiki/Cheerios_effect
Liftyee 2y ago
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 https://en.wikipedia.org/wiki/Absement
- VHRanger 2y ago
  This is breaking my brain a little, any eli5?
  - vasco 2y ago
    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.
  - kruczek 2y ago
    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.
  - basil-rash 2y ago
    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.
oldandtired 2y ago
Here in Victoria (Australia), we commonly see road signs stating that "speed kills" whereas the reality is that it is the jerk that kills.
- oldandtired 2y ago
  I didn't think my play on words would cause such controversy about acceleration and jerk. Mayhaps I should not be making "Dad jokes" here.
- Gooblebrai 2y ago
  If you want to be pedantic, you could argue that it is the collision that kills.
  - user_7832 2y ago
    Is it not life that kills?
    - account42 2y ago
      I'm pretty sure it's time.
  - samatman 2y ago
    It isn't, though. It's the jerk. The difference between falling from a height and landing on a trampoline, and landing on concrete from the same height, is that the trampoline smoothly accelerates you to a halt once you collide with it. The concrete does so much more rapidly: that's jerk. Both of these are collisions with the same amount of force behind them.
    - rcxdude 2y ago
      No, it's the acceleration. The forces are absolutely different between your two examples. The energy is the same, but in one case the energy is dissipated over a longer time, requiring less acceleration and thus force. Jerk and acceleration will tend to be correlated in collisions, but you can construct cases with very high jerk and low acceleration which are just fine and cases with very high acceleration and low jerk which are not at all safe, though the latter case will generally require a lot more energy (fighter jets and rockets, for example).
crabmusket 2y ago
> So, there must be some jerk involved. Me every day before checking git blame.
demondemidi 2y ago
Is there ever a higher order derivative that is a constant in the real world? And is every real world signal continuous in every higher order derivative?
- account42 2y ago
  Yes, the derivatives of time are relatively constant.
mensetmanusman 2y ago
Favorite economics quote: "In the fall of 1972, President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case fore reelection. - by Hugo Rossi"
zaps 2y ago
Jerks on roller coasters
PinguTS 2y ago
I know, this is an old paper, but I don't follow the this assumption: > The terms jerk and snap mean very little to most people, including physicists and engineers. Almost 20 years ago we defined jerk into our standards for lift applications. I know jerk is an important parameter for any modern rotating machine that includes gears. While in lift applications it is known as the roller coaster effect, people in different parts of the world have a different taste on when they want to use a lift. I know I over simplify when I say, that American people want to have the gut feeling when riding a lift, especially an express lift in those high buildings. In difference in Asian countries the lift ride must be smooth as possible. They don't like to have the feeling of riding a lift at all. In Europe it is something in between. Lift manufacturers have to respect those (end) costumers otherwise the are not chosen. The same in any rotating machine with some sort of gears. Because jerk and those higher orders contribute to the wear and tear of gears. As you want to have longer lasting gears many modern machine manufacturers limit those parameters to reduce wear and tear. So, with a little software change I can demand a higher price because service and maintenance can be reduced.
- account42 2y ago
  > American people want to have the gut feeling when riding a lift, especially an express lift in those high buildings. In difference in Asian countries the lift ride must be smooth as possible. They don't like to have the feeling of riding a lift at all. In Europe it is something in between How representative are these stated preferences actually of the population. I'd imagine that the individual preferences vary greatly from person to person and also change with age.
  - xxpor 2y ago
    They're the preferences of the buying managers.
    - amelius 2y ago
      If I were buying, I'd ask for a sensation of horizontal force when going up/down and see what they'd come up with.
godber 2y ago
Great find EndXA!! You melted my brain a bit.
zokier 2y ago
Another similar "hidden but intuitive" property is higher order geometric curvature continuity. For example squircles/superellipses have more smoothly changing curve than naive rounded rectangle, or industrial design using Gn continuity/class A surfaces: https://en.wikipedia.org/wiki/Class_A_surface https://en.wikipedia.org/wiki/Class_A_surface https://www.johndcook.com/blog/2018/02/13/squircle-curvature/ https://www.johndcook.com/blog/2018/02/13/squircle-curvature... I do see quite clear parallels between higher order time derivates and these higher order curvature measures, although I don't know if there is any formal relation here
debo_ 2y ago
Careful, you will give the agile people more measurements to fudge. "No no, we don't estimate jerk directly. We compute it from our acceleration."
01100011 2y ago
Bob Pease brought this into the discussion space over 30 years ago: https://www.electronicdesign.com/technologies/embedded/digital-ics/article/21757343/whats-all-this-fuzzy-logic-stuff-anyhow https://www.electronicdesign.com/technologies/embedded/digit...
djtango 2y ago
For people who understand sound - how much can acceleration, jerk and snap affect the tone a piano creates? A (mis)conception of the piano is that it is purely percussive and velocity is the only parameter you control for voicing on the piano but professionals would beg to differ...
- ssl-3 2y ago
  For playing a note on a piano and doing nothing more, I'd like to suggest that the velocity of the hammer as it strikes a string is the only variable that can be adjusted by the player. A hammer in a piano always moves on a fixed path. It always strikes the same part of the string, and it always does so in the same orientation. And after it strikes that string, it always falls away from it. That's how that part works. Striking a percussion instrument with a stick (such as a wooden block) has more variables to toy around with than playing a note on a piano does. But there's a lot more going on in a piano than striking strings: Strings are also muted, and the degree of muting can be manipulated. It is not binary. And, of course, pianos are polyphonic: With ten fingers, we can strike ten different [sets of] strings at different velocities and at different times, and we can even mute them to individually-different degrees. And then, there's also the pedals...
sehugg 2y ago
Jerk (time derivative of acceleration) had an important role in the Apollo missions. It was used to compute TGO (Time-To-Go) for the lunar module's landing program. TGO is the primary variable for the quadratic function, and it is combined with the current/desired state vectors to compute the throttle setting and thrust vector.
Zobat 2y ago
Matt Parker, calling himself Stand up Maths has an excellent (and mildly amusing) video about this. Spoiler, he get's a ride on a motorcycle around a race track, logs some data and tries to find the higher orders of derivatives from that data. https://www.youtube.com/watch?v=sB2X5l5CsNs https://www.youtube.com/watch?v=sB2X5l5CsNs
hbarka 2y ago
It’s very common to say that a car has acceleration but since the introduction of powerful electric cars like Tesla, that quickness you feel is the third derivative called jerk, or the acceleration of acceleration. Jerk is a little strange to think of because it feels a lot like acceleration but for you electric car owners who know about that quick 0-60, it’s jerk which makes you gasp and smile.
aaaronic 2y ago
Jerk, Snap, Crackle, and Pop are the only ones I thought had agreed upon names. But my understanding is probably 20 years out of date at this point. However, the paper says they’re not commonly taught, but jerk is taught in many high school (AP) Physics classes — we have to keep our balance by noticing the change in acceleration.
kazinator 2y ago
Jerk is why you don't want a straight track to abruptly turn into a circular arc. Unless, perhaps, it's for a roller coaster.
midjji 2y ago
What value is gained from using these terms over just saying nth derivative?
nullc 2y ago
How about some software for jerk limited trajectory computation: https://github.com/pantor/ruckig https://github.com/pantor/ruckig too bad it uses an odd cloud-based model for waypoint handling. Anyone know of any software for jerk limited planning which allows position constraints? Whats the fastest jerk limited path from A to B the doesn't pass though the forbidden zone. The jerk limited path may deviate from a straight line. So even when the A to B line is admissible, a straightforwardly constructed jerk limited path may not be.

181 points by EndXA 2y ago

Someone once explained this to me in a very intuitive way. It goes like this: You’re sitting in the driver’s seat of a car. It is standing still. You push the gas pedal down 2 cm and hold it there. Your car begins accelerating. That’s the second derivative. You start pressing your foot further on the gas pedal. Your foot has a velocity on the gas pedal. It is causing your car’s acceleration to grow! That’s jerk. If you push your foot on the gas pedal faster and faster your foot accelerates on the gas pedal. That contributes to the cars snap.

Avlin67 2y ago

i remembrer using squaed sinus acceleration curves profile for robotique at school to minimise jerk

vinc 2y ago

A long time ago I wrote an engine for a newspaper that was helping journalists discover what was happening on social media. I was counting the number of times an URL was posted on Twitter and Facebook. I started with velocity and acceleration, but after I while I discovered that I could go one level higher and use jerk to understand when an URL was shared by an influencer. I have a hard time imagining another level above that.

kevindamm 2y ago
DDoS attacks, high inflection from a lot of disparate sources.
Akronymus 2y ago
Snap could be the acceleration of "influencers" sharing an article? Basically, how fast it spreads from one to many
- frenchyatwork 2y ago
  That might be more exponential than polynomial.
simpaticoder 2y ago
When it comes to a measured time-series, the function is always discrete and arbitrary; there is no 'curve' like that generated by a function well-defined on the reals, and so there is no real closed-form derivative. In this context derivatives are not equations so much as derived data, reducing two points to one. And this process is recursive, such that you can take 4 points, reduce the two adjacent ones to 1 point, and then reduce those two into 1 point. In fact for 2^n points you can get the nth derivative in this way. The utility of this data is highly questionable in almost every context, but its available for every time-series. (One application that comes to mind is a kind of checksum, where you recursively derive a time series and stop when local neighbors go to 0, and you're left with a sparse list of high-order numbers that in some sense characterize the series.)

Rygian 2y ago

The proposed hierarchy is: - position - velocity - acceleration - jerk - snap - crackle - pop - "and so on" I'm good up to jerk, but not really sure for the remaining higher-order concepts.

pestatije 2y ago
this is the same as dimensions

DrNosferatu 2y ago

Lore has it that Snap, Crackle, and Pop are named after the three elves on Kellogg’s Rice Krispies cereal boxes. I use them in the context of N-Body Simulations. Curious to learn about other contexts for their use - anyone? https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv...

ahazred8ta 2y ago
The color printing industry has Snap, Gracol and Swop. Yes, the Gracol logo is a blackbird perched on CMYK dots. https://duckduckgo.com/?q=snap+gracol+swop https://duckduckgo.com/?q=snap+gracol+swop
- demondemidi 2y ago
  Like grackle I presume.
n4r9 2y ago
> Lore has it that Snap, Crackle, and Pop are named after the three elves on Kellogg’s Rice Krispies cereal boxes. Surely this is true. Is there any likely alternative explanation?

marginalia_nu 2y ago

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

azernik 2y ago
Yes. That is the point of the article. > Jerk and snap can be observed in various areas of physics and engineering. In physics and engineering jerk and snap should always be considered when vibration occurs and particularly when this excitation induces multi-resonant modes of vibration. They should also be considered at all times when a transition occurs such as: start up and shutdown; take-off and landing; and accelerating and decelerating. > Acceleration without jerk is just a static load, and therefore constant acceleration alone could never cause vibration. In a machine shop, a toolmaker can damage the mill or the job if the setup starts vibrating. This vibration happens because of jerk and snap. > In mechanical engineering it is important in automotive design to ensure that the cam-follower does not jump off the camshaft. It is also important in manufacturing processes as rapid changes in acceleration of a cutting tool can lead to premature tool wear and result in an uneven and rough surface finish. > In civil engineering railway train tracks and roads should be designed for a smooth exit from a straight section into a curve, and it is common to use a transition called a clothoid, which is part of a Cornu spiral (also referred to as an Euler spiral). When a clothoid is implemented the change in acceleration is not abrupt and the levels of jerk and possibly snap are significantly reduced. If the transition between different radii of curvature is sudden, the transition is uncomfortable for passengers and potentially dangerous as it could cause the car or train to be thrown off the road or track. With good physics design engineers are attempting to produce a gradual jerk and constant snap, which gives a smooth increase in radial acceleration, or preferably a zero snap, constant jerk, and linear increase in radial acceleration. Just as road and railway engineers design out jerk and snap using the clothoid transition so, too, do roller coaster designers when they design loops and helices for the roller coasters [11, 12].

londons_explore 2y ago

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.

amelius 2y ago
Do you have proof for that, or is this like audiophiles asking for gold connectors because "they make the sound better"?
- analog31 2y ago
  Not proof, but jerk is a factor when bringing a car to a smooth stop. You have to learn how to brake smoothly in order to avoid the "drivers ed stop" where the car and its passengers lurch forward and then bounce back. But the controls for automated vehicles like airport trams have to be designed to avoid this. The underlying reason is that some components such as the tires and suspension are elastic. This is in fact an issue for the designers of controls for mechanical systems. I learned about it in Process Control class, albeit 40 years ago.
  - robertlagrant 2y ago
    Cars 20+ years ago vs more recent cars - I've definitely noticed them auto-doing what I was taught to do with older cars: ease off the brakes right at the end.
    - sokoloff 2y ago
      I wonder if this is a change in braking material, specifically a reduction in difference between dynamic coefficient of friction and static coefficient of friction between the pad and rotor (or equivalently, the shoe and drum). If older cars had a higher differential, you’d need to let up more as the brake finally locks up.

anymouse123456 2y ago

Serious, well-written, scientific information that also references children's breakfast cereal? Moar please!

numbol 2y ago
Here you go https://en.wikipedia.org/wiki/Cheerios_effect https://en.wikipedia.org/wiki/Cheerios_effect

Liftyee 2y ago

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 https://en.wikipedia.org/wiki/Absement

VHRanger 2y ago
This is breaking my brain a little, any eli5?
- vasco 2y ago
  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.
- kruczek 2y ago
  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.
- basil-rash 2y ago
  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.

oldandtired 2y ago

Here in Victoria (Australia), we commonly see road signs stating that "speed kills" whereas the reality is that it is the jerk that kills.

oldandtired 2y ago
I didn't think my play on words would cause such controversy about acceleration and jerk. Mayhaps I should not be making "Dad jokes" here.
Gooblebrai 2y ago
If you want to be pedantic, you could argue that it is the collision that kills.
- user_7832 2y ago
  Is it not life that kills?
  - account42 2y ago
    I'm pretty sure it's time.
- samatman 2y ago
  It isn't, though. It's the jerk. The difference between falling from a height and landing on a trampoline, and landing on concrete from the same height, is that the trampoline smoothly accelerates you to a halt once you collide with it. The concrete does so much more rapidly: that's jerk. Both of these are collisions with the same amount of force behind them.
  - rcxdude 2y ago
    No, it's the acceleration. The forces are absolutely different between your two examples. The energy is the same, but in one case the energy is dissipated over a longer time, requiring less acceleration and thus force. Jerk and acceleration will tend to be correlated in collisions, but you can construct cases with very high jerk and low acceleration which are just fine and cases with very high acceleration and low jerk which are not at all safe, though the latter case will generally require a lot more energy (fighter jets and rockets, for example).

crabmusket 2y ago

> So, there must be some jerk involved. Me every day before checking git blame.

demondemidi 2y ago

Is there ever a higher order derivative that is a constant in the real world? And is every real world signal continuous in every higher order derivative?

account42 2y ago
Yes, the derivatives of time are relatively constant.

mensetmanusman 2y ago

Favorite economics quote: "In the fall of 1972, President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case fore reelection. - by Hugo Rossi"

zaps 2y ago

Jerks on roller coasters

PinguTS 2y ago

I know, this is an old paper, but I don't follow the this assumption: > The terms jerk and snap mean very little to most people, including physicists and engineers. Almost 20 years ago we defined jerk into our standards for lift applications. I know jerk is an important parameter for any modern rotating machine that includes gears. While in lift applications it is known as the roller coaster effect, people in different parts of the world have a different taste on when they want to use a lift. I know I over simplify when I say, that American people want to have the gut feeling when riding a lift, especially an express lift in those high buildings. In difference in Asian countries the lift ride must be smooth as possible. They don't like to have the feeling of riding a lift at all. In Europe it is something in between. Lift manufacturers have to respect those (end) costumers otherwise the are not chosen. The same in any rotating machine with some sort of gears. Because jerk and those higher orders contribute to the wear and tear of gears. As you want to have longer lasting gears many modern machine manufacturers limit those parameters to reduce wear and tear. So, with a little software change I can demand a higher price because service and maintenance can be reduced.

account42 2y ago
> American people want to have the gut feeling when riding a lift, especially an express lift in those high buildings. In difference in Asian countries the lift ride must be smooth as possible. They don't like to have the feeling of riding a lift at all. In Europe it is something in between How representative are these stated preferences actually of the population. I'd imagine that the individual preferences vary greatly from person to person and also change with age.
- xxpor 2y ago
  They're the preferences of the buying managers.
  - amelius 2y ago
    If I were buying, I'd ask for a sensation of horizontal force when going up/down and see what they'd come up with.

godber 2y ago

Great find EndXA!! You melted my brain a bit.

zokier 2y ago

Another similar "hidden but intuitive" property is higher order geometric curvature continuity. For example squircles/superellipses have more smoothly changing curve than naive rounded rectangle, or industrial design using Gn continuity/class A surfaces: https://en.wikipedia.org/wiki/Class_A_surface https://en.wikipedia.org/wiki/Class_A_surface https://www.johndcook.com/blog/2018/02/13/squircle-curvature/ https://www.johndcook.com/blog/2018/02/13/squircle-curvature... I do see quite clear parallels between higher order time derivates and these higher order curvature measures, although I don't know if there is any formal relation here

debo_ 2y ago

Careful, you will give the agile people more measurements to fudge. "No no, we don't estimate jerk directly. We compute it from our acceleration."

01100011 2y ago

Bob Pease brought this into the discussion space over 30 years ago: https://www.electronicdesign.com/technologies/embedded/digital-ics/article/21757343/whats-all-this-fuzzy-logic-stuff-anyhow https://www.electronicdesign.com/technologies/embedded/digit...

djtango 2y ago

For people who understand sound - how much can acceleration, jerk and snap affect the tone a piano creates? A (mis)conception of the piano is that it is purely percussive and velocity is the only parameter you control for voicing on the piano but professionals would beg to differ...

ssl-3 2y ago
For playing a note on a piano and doing nothing more, I'd like to suggest that the velocity of the hammer as it strikes a string is the only variable that can be adjusted by the player. A hammer in a piano always moves on a fixed path. It always strikes the same part of the string, and it always does so in the same orientation. And after it strikes that string, it always falls away from it. That's how that part works. Striking a percussion instrument with a stick (such as a wooden block) has more variables to toy around with than playing a note on a piano does. But there's a lot more going on in a piano than striking strings: Strings are also muted, and the degree of muting can be manipulated. It is not binary. And, of course, pianos are polyphonic: With ten fingers, we can strike ten different [sets of] strings at different velocities and at different times, and we can even mute them to individually-different degrees. And then, there's also the pedals...

sehugg 2y ago

Jerk (time derivative of acceleration) had an important role in the Apollo missions. It was used to compute TGO (Time-To-Go) for the lunar module's landing program. TGO is the primary variable for the quadratic function, and it is combined with the current/desired state vectors to compute the throttle setting and thrust vector.

Zobat 2y ago

Matt Parker, calling himself Stand up Maths has an excellent (and mildly amusing) video about this. Spoiler, he get's a ride on a motorcycle around a race track, logs some data and tries to find the higher orders of derivatives from that data. https://www.youtube.com/watch?v=sB2X5l5CsNs https://www.youtube.com/watch?v=sB2X5l5CsNs

hbarka 2y ago

It’s very common to say that a car has acceleration but since the introduction of powerful electric cars like Tesla, that quickness you feel is the third derivative called jerk, or the acceleration of acceleration. Jerk is a little strange to think of because it feels a lot like acceleration but for you electric car owners who know about that quick 0-60, it’s jerk which makes you gasp and smile.

aaaronic 2y ago

Jerk, Snap, Crackle, and Pop are the only ones I thought had agreed upon names. But my understanding is probably 20 years out of date at this point. However, the paper says they’re not commonly taught, but jerk is taught in many high school (AP) Physics classes — we have to keep our balance by noticing the change in acceleration.

kazinator 2y ago

Jerk is why you don't want a straight track to abruptly turn into a circular arc. Unless, perhaps, it's for a roller coaster.

midjji 2y ago

What value is gained from using these terms over just saying nth derivative?

nullc 2y ago

How about some software for jerk limited trajectory computation: https://github.com/pantor/ruckig https://github.com/pantor/ruckig too bad it uses an odd cloud-based model for waypoint handling. Anyone know of any software for jerk limited planning which allows position constraints? Whats the fastest jerk limited path from A to B the doesn't pass though the forbidden zone. The jerk limited path may deviate from a straight line. So even when the A to B line is admissible, a straightforwardly constructed jerk limited path may not be.