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26 January 2014 @ 12:17 pm
Thing that I learned yesterday (one among many, but this is the most memorable):  
The first derivative of distance related to time (change in distance over time) (dx/dt) is velocity.

The second derivative (change in velocity over time) (d2x/dt2) is acceleration.

The third derivative (change in acceleration over time) (d3x/dt3) is jerk.

I knew all of those.

The fourth derivative is jounce.

The fifth, sixth, and seventh derivatives are snap, crackle, and pop.

This makes me very happy.
Ayesha: Seshat (found online)browngirl on January 26th, 2014 05:30 pm (UTC)
*smiling, takes notes*
Shadow/Brookekengr on January 26th, 2014 07:41 pm (UTC)
I have trouble seeing situations where those would be relevant (or measurable).

Well, not jerk, but...

Don't sup[pose you have the formulas for distance versus time for each of them. I have the one for jerk somewhere. Without checking my notes, I think it's

d = 1/6 * jerk * t^3
Janet Miles, CAP-OMjanetmiles on January 26th, 2014 09:53 pm (UTC)
I don't know if there are practical applications, either, but it pleases me that the names exist. Oh, wait, I think he said jounce is used in rocketry, something to do with directional boosts.

I don't have the equations you're looking for, and I'm no longer sure how I'd go about deriving them. It's been too long since I took differential equations.
The Renaissance Manunixronin on January 27th, 2014 12:34 am (UTC)
Velocity and acceleration are easy of course, and jerk is a pretty simple concept. I'm not sure I can come up with a practically usable understanding of jounce, let alone the remaining three.
The Renaissance Manunixronin on January 27th, 2014 12:36 am (UTC)
I don't think you can just go from jerk and time directly to distance. You'd have to integrate under the curve.
Shadow/Brookekengr on January 27th, 2014 02:29 am (UTC)
If it's *constant* jerk, then you can. Just like you can get distance from constant acceleration. My calculus isn't up to it, but someone whose calculus was up to it worked out the formula for me.

You *do* realize that derivatives and integrals can be calculated for various curves?

anyway, look at these formulas.

For constant velocity:

For constant acceleration

for constant jerk
d=(j*t^3)/6 (I looked up the formula in my notes)

The Renaissance Manunixronin on January 27th, 2014 05:39 am (UTC)
Don't you think constant jerk is a bit of a special case though? When are you ever going to encounter it in the real world at any value other than zero?
Shadow/Brookekengr on January 27th, 2014 11:36 am (UTC)
Constant *anything* is a special case.

But jerk is apparently constant enough in some situations for engineering types to have named it.
Tom the Alien Cat: arresting tomtac on January 27th, 2014 01:27 pm (UTC)
Thanks for posting this. Just this past weekend, I was throwing together a simulation of the first three, but accidentally put in a fourth and now have a simulation of jerk-acc-vel and position.

I have been using a program like that for decade, and always thought of jerk-jounce and snap as what happens to the throttle of a rocket engine. (But did not know the names.)

So "constant jerk" is where one advances the throttle at a constant rate, so the acceleration gets stronger and stronger as it builds. (My program only allows increments and decrements of one.) The astronaut might first feel just 2G, then it can build to much higher. "Jounce" could be the pressure one puts on the moving throttle to get it to move faster toward full throttle or back to zero throttle or reverse.

And, by the way, an example of positive jerk is what happens when the rocket thrust is constant, but mass of the rocket gets smaller as the fuel is used up -- the acceleration increases. And that is usually a "non-constant jerk". So this is a practical example of jounce.
Janet Miles, CAP-OMjanetmiles on January 27th, 2014 01:49 pm (UTC)
Thank you! That's very cool.