# Names of higher-order derivatives

Specific derivatives have specific names. First order is often called tangency/velocity, second order is curvature/acceleration. I've also come across words like Jerk, Yank, Jounce, Jolt, Surge and Lurch for 3rd and 4th order derivatives. Is there a widely agreed list of names for these? How many orders have specific names?

In this case, I'm dealing with NURBs curves, so the "tangency" and "curvature" related words are to be preferred over "velocity" and "acceleration" words.

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These are less common than the names velocity and acceleration for the first and second derivative of position with respect to time, but if we write $x$ for position, $m$ for mass and $p=m\times dx/dt$ for momentum, then

• $dx/dt$ is velocity
• $d^2x/dt^2$ is acceleration
• $d^3x/dt^3$ is jerk (also known as jolt, surge and lurch)
• $d^4x/dt^4$ is jounce

and for the momentum derivatives:

• $dp/dt$ is force
• $d^2p/dt^2$ is yank
• $d^3p/dt^3$ is tug

I've never seen a similar list for tangency/curvature style terminology (however, note that the curvature is not the same thing as the second derivative!)

Note that all of these names are very uncommon, and you shouldn't expect people to understand what you mean when you use them. My guess would be that the word 'jerk' when used to refer to the third derivative of position, is most commonly uses in the sentence "Hey, did you know that the third derivative of position is called jerk?"

Slightly related: in finance, if a derivative contract is valued at $V$ when the underlying is valued at $S$, then it is common to refer to

• $\partial V/\partial S$ as delta
• $\partial^2 V/\partial S^2$ as gamma
• $\partial^3 V/\partial S^3$ as speed
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Don't forget Snap, Crackle and Pop! –  anon May 11 '12 at 11:09

My contribution to this subject can be found here: http://www.thespectrumofriemannium.com/?p=4206

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