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

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.

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

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.

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"

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://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

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.

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_deriv...

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.

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

Bob Pease brought this into the discussion space over 30 years ago: https://www.electronicdesign.com/technologies/embedded/digit...

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.

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

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

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.

How about some software for jerk limited trajectory computation: 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.

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...

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

Moar please!

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?

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.

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

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

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.

Jerks on roller coasters

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

> So, there must be some jerk involved.

Me every day before checking git blame.

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."