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.
Jerk is also very important for road or rail track design. If you imagine needing to make a 90 degree bend, the "obvious" way to do it is by rounding off the corner with a circular radius.
But if you do that, it means the vehicle goes from having 0 sideways acceleration to experiencing 100% of the centripetal acceleration to move an object on a circular path (a = v^2 / r) instantaneously.
As an occupant of the car, that means you go from sitting comfortably to suddenly being thrown sideways.
It's much more comfortable if you ease into the turn, with the track design considering the rate of change of acceleration. If the designer didn't consider jerk you would definitely notice.
One thing that is strange is that we can easily imagine the first two derivatives: position we can just imagine a static point, velocity we can imagine a constant speed i.e. a straight line on a position-time graph, acceleration we just imagine a parabola, but jerk is somehow conceptually indistinguishable. The difference between a point, a line, and a parabola are stark, the third order jerk is not so easy to distinguish, instead still just looking like the parabola.
I've always wondered why this is, why curves in general are perceptually similar if scaled correctly, while a straight line is so clearly different. Perhaps it is because our perceptions developed to distinguish between inertial and non inertial reference frames?
> 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.
The terms jerk and snap while perhaps known in the rare space of elevator purchasing aren’t generally used terms in most fields. I’m surprised that’s in any way controversial ?
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
Why bother with giving words for something which is longer than their mathemathical definition? The word can be unknown, but if the function is unknown the word is useless?
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.
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.)
"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"
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:
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
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.
>I wish designers of vehicles - particularly cars, trains and busses, would work to minimize jerk, snap and crackle.
They do.
>Turns out if you minimize those, you get a far more comfortable ride. It matters far more than acceleration.
They know that this is the case. And put a lot of effort into making sure your car has the desired feel.
Besides your comfort these considerations are extremely important for the durability analysis for the vehicle.
>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.
Finite element simulations are undesirable, they are extremely calculation expensive for those kind of large models and somewhat unsuitable. They are used in crash tests.
For the application you described multi body systems are used, where the car is decomposed into its functional components, which can be modeled either as stiff or flexible. With that you have a reasonably accurate model of a car which you can use to test on a virtual test track.
Basically every competent car manufacturer is doing this.
It's designed for in the road/track, not the vehicle. For train tracks in the UK the recommended max jerk is 0.35 mm/s/s/s. The jerk is limited by using 'Euler spiral' sections to join up the straights and the curves. Travelling along an Euler spiral at constant speed means you feel constant jerk laterally, so can be scaled to keep the jerk below any arbitrary value.
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
> 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].
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.
Here is a video of a guy that tried to automate a grinding machine by installing an electric motor. Initially the movement was very unsatisfactory, it was not smooth, or very jerky. He then received an upgraded motor that included a “jerk control” feature and the movement of his machine became smooth.
It came as a surprise to me but it seems like jerk is something that can be felt in real life.
If you're driving along and want to stop for the traffic lights, you start decelerating. The car in front of you slams the brakes and leaves less space then you anticipated. You now need to decelerate faster. That's negative jerk. If you apply the change in deceleration instantaneously, you will also experience jerkiness in your braking (= way to remember what this derivative is called).
Yes. The higher derivates are useful in many cases, both as sought properties and observations. The invariances implied by relativity,(the trivial notion that the universe behaves the same regardless of where you select the center), mean that most laws are defined on the second derivative. Taylor approximations are useful to approximate something locally, but properties of the system over wider regions generally need to account for the higher derivatives. You can see this in e.g. simulating a system over time requires that the derivatives at the borders of the valid taylor approximation region to be included as diracs.
Or in other words, you can approximate exp(x) as a set of first order taylor approximations that each covers a small window to arbitrary precision, but the combination of them is still has well defined higher derivatives that are not 0.
I believe they have applications in missle guidance systems.
I cannot remember what it's called but essentially given a target position in space the missle uses parametric data about its current position/orientation/speed and their higher derivatives to dead reckon about where it is in regards to the target.
Anyone remember what that's called? I went on a rabbit hole with it a few years ago, it's really interesting math and programming. Everything works basically stateless except for current instrument data, last position and target position from what I remember.
> Do these higher order derivatives say anything meaningful?
I'm becoming seasick due to a jerkiness of a car. Not due to a speed or a acceleration, but it is jerk that does it for me. I watched it from my childhood, I hated trolleybuses for that: they are electric and they tend to change acceleration instantly. But I didn't understood how it works until much later.
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.
No, it's the acceleration. That's what produces the forces. But there is usually a correlation between jerk and acceleration in a collision, given a certain amount of energy (speed^2)
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.
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.
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.
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.
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...
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?
[+] [-] PinguTS|1 year ago|reply
> 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.
[+] [-] wlesieutre|1 year ago|reply
But if you do that, it means the vehicle goes from having 0 sideways acceleration to experiencing 100% of the centripetal acceleration to move an object on a circular path (a = v^2 / r) instantaneously.
As an occupant of the car, that means you go from sitting comfortably to suddenly being thrown sideways.
It's much more comfortable if you ease into the turn, with the track design considering the rate of change of acceleration. If the designer didn't consider jerk you would definitely notice.
[+] [-] bowsamic|1 year ago|reply
I've always wondered why this is, why curves in general are perceptually similar if scaled correctly, while a straight line is so clearly different. Perhaps it is because our perceptions developed to distinguish between inertial and non inertial reference frames?
[+] [-] account42|1 year ago|reply
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.
[+] [-] fnordpiglet|1 year ago|reply
[+] [-] kovezd|1 year ago|reply
[+] [-] codexb|1 year ago|reply
[+] [-] Liftyee|1 year ago|reply
[+] [-] VHRanger|1 year ago|reply
[+] [-] midjji|1 year ago|reply
[+] [-] vinc|1 year ago|reply
I have a hard time imagining another level above that.
[+] [-] simpaticoder|1 year ago|reply
[+] [-] Akronymus|1 year ago|reply
[+] [-] kevindamm|1 year ago|reply
[+] [-] mensetmanusman|1 year ago|reply
"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"
[+] [-] zokier|1 year ago|reply
https://en.wikipedia.org/wiki/Class_A_surface
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
[+] [-] londons_explore|1 year ago|reply
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.
[+] [-] constantcrying|1 year ago|reply
They do.
>Turns out if you minimize those, you get a far more comfortable ride. It matters far more than acceleration.
They know that this is the case. And put a lot of effort into making sure your car has the desired feel.
Besides your comfort these considerations are extremely important for the durability analysis for the vehicle.
>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.
Finite element simulations are undesirable, they are extremely calculation expensive for those kind of large models and somewhat unsuitable. They are used in crash tests.
For the application you described multi body systems are used, where the car is decomposed into its functional components, which can be modeled either as stiff or flexible. With that you have a reasonably accurate model of a car which you can use to test on a virtual test track.
Basically every competent car manufacturer is doing this.
[+] [-] owisd|1 year ago|reply
[+] [-] amelius|1 year ago|reply
[+] [-] DrNosferatu|1 year ago|reply
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_deriv...
[+] [-] Rygian|1 year ago|reply
[+] [-] pestatije|1 year ago|reply
[+] [-] marginalia_nu|1 year ago|reply
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|1 year ago|reply
> 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].
[+] [-] fellerts|1 year ago|reply
[+] [-] hristov|1 year ago|reply
It came as a surprise to me but it seems like jerk is something that can be felt in real life.
https://youtu.be/FPhNc6GwX1o?si=8cf7wU14puB8lsaa
[+] [-] bux93|1 year ago|reply
[+] [-] midjji|1 year ago|reply
Or in other words, you can approximate exp(x) as a set of first order taylor approximations that each covers a small window to arbitrary precision, but the combination of them is still has well defined higher derivatives that are not 0.
[+] [-] ImPleadThe5th|1 year ago|reply
I cannot remember what it's called but essentially given a target position in space the missle uses parametric data about its current position/orientation/speed and their higher derivatives to dead reckon about where it is in regards to the target.
Anyone remember what that's called? I went on a rabbit hole with it a few years ago, it's really interesting math and programming. Everything works basically stateless except for current instrument data, last position and target position from what I remember.
[+] [-] ordu|1 year ago|reply
I'm becoming seasick due to a jerkiness of a car. Not due to a speed or a acceleration, but it is jerk that does it for me. I watched it from my childhood, I hated trolleybuses for that: they are electric and they tend to change acceleration instantly. But I didn't understood how it works until much later.
[+] [-] glitchc|1 year ago|reply
Only true for small x (less than 1).
[+] [-] 01100011|1 year ago|reply
[+] [-] aaaronic|1 year ago|reply
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.
[+] [-] oldandtired|1 year ago|reply
[+] [-] rcxdude|1 year ago|reply
[+] [-] oldandtired|1 year ago|reply
[+] [-] selimthegrim|1 year ago|reply
I’m not sure anyone noticed the difference between the two
[+] [-] mauvehaus|1 year ago|reply
[+] [-] selimthegrim|1 year ago|reply
[+] [-] Gooblebrai|1 year ago|reply
[+] [-] Zobat|1 year ago|reply
https://www.youtube.com/watch?v=sB2X5l5CsNs
[+] [-] sehugg|1 year ago|reply
[+] [-] nullc|1 year ago|reply
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.
[+] [-] koliber|1 year ago|reply
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.
[+] [-] djtango|1 year ago|reply
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...
[+] [-] anymouse123456|1 year ago|reply
Moar please!
[+] [-] demondemidi|1 year ago|reply
[+] [-] account42|1 year ago|reply
[+] [-] kazinator|1 year ago|reply