I What does jounce help us to do in physics?

[Physics4Eva]

TL;DR Summary

How is jounce used in physics and does it have any useful applications?

I understand how jounce is the fourth derivative of position vector, but I don't understand is how it is actually used in physics. I know it differentiates jerk, but what does this help physicists to understand? The following is an equation that explains jounce:

So how exactly is this equation applied to a graph in terms of acceleration and jerk? And what does jounce truly help us to understand other than differentiation?
Thanks guys!

 

[anorlunda]

We can differentiate position an infinite number of times. There is no need to stay awake nights thinking of a unique physics principle associated with each.

See http://wearcam.org/absement/Derivatives_of_displacement.htm

derivative	terminology	SI unit	meaning
-5	absounce	m·s5	time integral of abserk
-4	abserk	m·s4	time integral of abseleration
-3	abseleration	m·s³	time integral of absity
-2	absity	m·s²	time integral of absement
-1	absement (absition)	m·s	time integral of position
0	position (displacement)	m	position
1	velocity	m·s-1	rate-of-change of position
2	acceleration	m·s-2	rate of change of velocity
3	jerk	m·s-3	rate of change of acceleration
4	jounce (snap)	m·s-4	rate of change of jerk
5	crackle	m·s-5	rate of change of jounce
6	pop	m·s-6	rate of change of crackle
7	lock	m·s-7	rate of change of pop
8	drop	m·s-8	rate of change of lock

 

[FactChecker]

We can differentiate position an infinite number of times. There is no need to stay awake nights thinking of a unique physics principle associated with each.

But there is a definite intuitive meaning all the way up to and including jerk, so I think it is a good question.

 

[anorlunda]

I think that is abserk.

 

[A.T.]

But there is a definite intuitive meaning all the way up to and including jerk, so I think it is a good question.

"Definite intuitive" is an oxymoron.

 

[Ibix]

There's a direct observable related to acceleration, which is how hard you are pushed into your seat or the wall or whatever. Derivatives of acceleration just tell you how it is changing. That it changes is interesting (have you ever tried to stand on a train or bus when the acceleration is changing?), but I'm not sure that higher derivatives are particularly physically significant. They quantify how fast you have to react to changes in acceleration, I suppose, but that's more of an engineering interest than a physics one.

 

[anorlunda]

I would like to nominate "occupy" as an alternative to "abasement" from the table above.

I occupied the hotel room at x1,y1 for one day. It cost me $100.
I occupied the apartment at x2y2 for a month. It cost me $2000
I occupied a campsite on the island for a week. It was free.
Follow these GPS waypoints and you'll occupy the Appalachian Trail from end to end.

That suggests hike (as in rent hike) instead of "absity."

@Physics4Eva , I apologize for making light of your question. It's Saturday morning.

 

[Dr.D]

This quantity, jounce, is better known in the area of cam design as snap. There are some cam designers who think it is important (usually meaning to insist on continuity in snap), while others say it does not matter. The folks I work with in cam design are of the latter school, and say it really does not matter. They do insist on continuity in the first 3 derivatives.

 

[Physics4Eva]

Thanks guys very helpful!

 

[cosmik debris]

Cam shafts utilise higher derivatives of position. If you think about a valve in an ordinary internal combustion engine, as the valve changes direction at the top (or bottom) of the cycle the acceleration of the valve is changing. Higher derivatives are also involved as the whole shape of the cam determines an acceleration profile to ensure maximum area under the valve with the least stresses.

Also worth mentioning is that absition is the integral in a PID controller.

Cheers

 

[Swamp Thing]

I would like to nominate "occupy" as an alternative to "abasement" from the table above.

I think you'll find the table says "absement".

Personally, though, I think abasement would have been way more interesting.

But this whole discussion reminds me of that funny-collective-nouns thing. What would be a nice name for a collection of derivatives?

 

[Swamp Thing]

"A body experiences a crackle of 2.718 yottameters per attosecond to the fifth power"
<** Cackle! **>

But to address the OP, here's how I see it. Terms like jounce are more relevant to applied physics or engineering. A mechanical system can easily have a frequency response that amplifies higher frequencies much more than lower ones, so that certain parts of the mechanism vibrate a lot more than the applied displacement if that displacement is rapid.

Mathematically, boosting higher frequencies is very much akin to differentiation. And if the system is complex (higher order) then higher derivatives can be generated / amplified.

The "jounce" in the applied stimulus is roughly a measure of how much higher frequency energy is present (especially in a transient) as opposed to lower frequencies, which in turn gives a qualitative indication of how much amplification-related stresses and strains would then be generated.

 

[Dr.D]

This quest for words that mean absolutely nothing in reality should really be beneath this site.

"A body experiences a crackle of 2.718 yottameters per attosecond to the fifth power"

Look at the example from Swamp Thing. Does that say anything meaningful to anyone? The only place I have ever seen any of these terms arise in in the area of cam design, and area where I still do some work. Most of these terms would mean nothing at all to a cam designer.

 

[sophiecentaur]

But there is a definite intuitive meaning all the way up to and including jerk, so I think it is a good question.

If you subject a structure to varying acceleration (every car that was ever designed) then the variation with time of distortion of the components will depend on the Jerk.
It's how we manage to get sticky nuts and bolts apart with a bit of brute (jerk) force.

 

[anorlunda]

I think you'll find the table says "absement".

LOL, I tried again and again to override the spell checker. In the end, the spell checker won and I lost. :-)

 

[Dr.D]

If you really want to communicate, it is far more clear to refer to the 3rd, 4th, 5th, ... derivative of displacement. If on the other hand, the appearance of erudition is the goal, then these strange terms are hard to beat.

 

[vanhees71]

I've no clue what all these derivatives should do in physics except trouble ;-)). The only example, where $\dot{a}$ occurs is in the infamous (still not satisfactorily solved) radiation-reaction problem in the connection with classical point particles and electromagnetism. It's only cured in an ad-hoc way by eliminating this $\dot{a}$ term again by eliminating it, using the Landau-Lifshitz version of the Abraham-Lorentz-Dirac equation.