"Accelerations" as higher order derivatives

[member 753608]

TL;DR

Physical interpretations of higher order derivatives of time: velocity, acceleration, etc. ...

In physics, velocity (speed) is the "change of position (spacial location) per change of time" and acceleration is the "change of velocity per change of time". Mathematically this is first and second derivative. Do further derivatives exist that correspont physical quantities like "change of acceleration per change of time" ... etc.?

 

[Baluncore]

Yes.
Position, Velocity (speed), Acceleration, Jerk, Snap (jounce), Crackle, Pop.
https://en.wikipedia.org/wiki/Jerk_(physics)

 

[sophiecentaur]

TL;DR Summary: Physical interpretations of higher order derivatives of time: velocity, acceleration, etc. ...

Do further derivatives exist that correspont physical quantities like "change of acceleration per change of time" ... etc.?

There's no limit to how many orders of derivative - because it's Maths. But practically, you can easily 'see' how you can go further than acceleration (second derivative of time) because acceleration is proportional to Force and force can easily vary as an object changes its position. The force from a rubber band goes up as you stretch it. For small displacements about a position where the rubber is stretched 'a bit' the force will be proportional to the displacement (there's a third order of derivative) but rubber is very non-linear so the force won't be truly proportional to the displacement so that will take you into a fourth derivative of time. You can go further when the experiment is affected by even more variables.
Robert Hooke could be turning in his grave about this but I'd bet he thought about this a lot so maybe he wouldn;t have been too surprised the way things have gone. Round about his time (The Enlightenment) Maths was being developed and that helped with descriptions of processes where nothing was straight 'proportional' and describing that sort of thing without Maths could be very difficult.

 

[member 753608]

Yes.
Position, Velocity (speed), Acceleration, Jerk, Snap (jounce), Crackle, Pop.
https://en.wikipedia.org/wiki/Jerk_(physics)

Yes, thank you. While "Jerk" is described, what are the physical meaning and applications of "higher order accelerations"?

 

[Vanadium 50]

what are the physical meaning and applications of "higher order accelerations"?

There really aren't any. Just names. Because people demand names.

 

[sophiecentaur]

Those ‘names’ you want are short for ‘rate of change of rate of change of rate of change of etc…..’. Going further than a second derivative is easier described in Mathematical expressions. But that seems to be a general principle that Maths is a useful short form to describe most of Physics and Engineering.
Which is easier to communicate: s/t or metres travelled in 20 seconds?

 

[Baluncore]

While "Jerk" is described, what are the physical meaning and applications of "higher order accelerations"?

They do not need to have a physical meaning, and you will probably never need to use them all. They will have a different meaning, in each field of application.

Each is used in turn, to remove a step-discontinuity, to push it one further domain away, from where you are working with continuous functions. If you need them for your applied mathematics, they are available to you.

For me today, they are conveniently there, simply as an answer to your original question.

 

[sophiecentaur]

They do not need to have a physical meaning, and you will probably never need to use them all.

A point worth mentioning is that there are no practical situations in which the relationship between two variables is linear over the whole range. Speed is never uniform and nor is acceleration; there are always deviations from the straight line curve. Those higher order accelerations are always there.

 

[member 753608]

Those ‘names’ you want are short for ‘rate of change of rate of change of rate of change of etc…..’. Going further than a second derivative is easier described in Mathematical expressions. But that seems to be a general principle that Maths is a useful short form to describe most of Physics and Engineering.
Which is easier to communicate: s/t or metres travelled in 20 seconds?

Yes, absolutely with you. But there are no physical meaning and applications of thus further derivatives, right? They are just mathematical constructs?

 

[sophiecentaur]

Yes, absolutely with you. But there are no physical meaning and applications of thus further derivatives, right? They are just mathematical constructs?

IMO the expression “physical meaning” can only be applied to a familiar physical and very obvious experience. So a ‘jerk’ would be a physical feeling as the accelerator pedal is pressed a bit harder. Would you claim to be aware of variations in that sensation?
Your question takes us further from the theory and with less understanding of Physics.

 

[Baluncore]

But there are no physical meaning and applications of thus further derivatives, right? They are just mathematical constructs?

The physics is defined by the mathematics. Your inability to see "physical meaning" does not invalidate the mathematics, nor should it deny the understanding by others, those who can see physical meaning in the higher derivatives.

 

[member 753608]

Thank you. Right, "physical meaning" does not just refer to human's sensorial perceptions, but to applications on explaing physical concepts (simlar to gravitationl waves for example, where humans connot sens it but it explains phyisics). So the inquiry is about in which concepts those higher oder dirivatatives are applied in physics?

 

[sophiecentaur]

“Physical Meanings”? You would need to explain to me how they could be anything more than concepts which happen to be familiar enough to you for you to treat them, in your mind, the same way as hot and cold or pull and push etc..
Everything is part of an internal model in your brain and, when you feel familiar enough with something, you treat it as ‘understood’. There is no absolute distinction between mental and ‘physical’.
Maths is usually the best way to communicate and figure things out.

 

[member 753608]

Indeed, math is the best vehicle we have (and I love it btw - as a sidenote). So back to the point: In which physics concepts are "higher oder accelerations" applied? Thank you.

 

[gmax137]

I think the first few higher derivatives are used in designing camshafts. The shape of a cam (say in an engine valve train) is designed to prevent or minimize valve float or bounce. A hundred or eighty years ago cam design was by trial and error (ie, art), today it's done mathematically.

 

[Vanadium 50]

This thread is isomorphic to the 5 year old tugging at your sleeve and repeatedly asking "ut what's after that?"i

If I told you the 34th derivative was called glorbleschnorz, how would that help you solve any actual problem?

 

[member 753608]

This thread is isomorphic to the 5 year old tugging at your sleeve and repeatedly asking "ut what's after that?"i

If I told you the 34th derivative was called glorbleschnorz, how would that help you solve any actual problem?

names are not relevant; what's interesting is the applications of those concepts

 

[Baluncore]

I think the first few higher derivatives are used in designing camshafts.

In a world where second order polynomials rule, the higher derivative terms are lost, or rapidly become zero.
In the Fourier world, such as in camshaft design or signal processing, the higher derivatives roll onwards, and so seem to make more sense.

 

[Vanadium 50]

what's interesting is the applications of those concepts

And when is the 34th derivative useful in this regard?

 

[Baluncore]

If I told you the 34th derivative was called glorbleschnorz, how would that help you solve any actual problem?

"Glorbleschnorz"! Do you have a reference? I could go way back into the old German literature to follow the citations and investigate the origin of the term, who invented it, and why it was needed. That would be a real adventure, better than any holiday.

Touring the century old scientific libraries, and second hand bookshops of Europe, is something I really miss. Reading second hand books, while drinking coffee in the pavement cafés of Paris, has unfortunately been replaced by the internet. Ah, that brings back the aroma of old books and coffee.

 

[sophiecentaur]

So back to the point: In which physics concepts are "higher oder accelerations" applied?

The "concept" is included by the differential calculus which is applied to situations in which the higher orders are significance. Discussing them and giving them names is pointless - except for the private thoughts and pictures of an individual or when two individuals find a mutual pleasure in that line of thought.

 

[SammyS]

Yes, thank you. While "Jerk" is described, what are the physical meaning and applications of "higher order accelerations"?

@Baluncore provided a link to a Wikipedia page about "Jerk", which included quite a few applications of these higher order (time) derivatives of Position. If you had read it over, you would know that. The Wikipedia page also has many references as well as links to related Wikipedia pages.

 

[sophiecentaur]

In a world where second order polynomials rule,

In a microscopic world (which ours certainly is), descriptions in terms of polynomials would need some very high order terms. Polynomial descriptions of processes are actually quite arbitrary with built-in errors; they just happen to work well enough in most cases.
There's certainly one place where higher order variations are essential to get things right. The Rayleigh Jeans calculation of the spectrum of radiation from a hot body uses a simple classical model with a 'smooth curve' but it predicts an impossible 'Ultraviolet Catastrophe'. Planck had to introduce the idea of a far-from smooth (Quantum) relationship on the small scale to rescue us. Very high order relationships are essential to describe our real world and we can't reduce what goes on by a smoother and smoother graph.