Consider an object moving along a straight line. One might say something about its displacement, velocity or acceleration. These are the 0th, 1st and 2nd derivatives of the object's displacement. However, there are an infinite number of derivatives although we may rarely talk about the 1001st derivative.

Is there a name for the infinite set: {0th derivative of displacement, 1st derivative of displacement, 2st derivative of displacement, ......... }?

I've come across the problem of trying to describe this set in writing a mathematical piece of work related to the Maclaurin/Taylor series.

So far, I describe it as "derivatives of the object's motion" although I'm not too sure if this is quite right.

  • $\begingroup$ Position, velocity and acceleration are names of physical quantities, originating from classical mechanics, esp. Newtonian second order differential equations for forces. In mathematics one just calls the derivatives derivatives. $\endgroup$ – mvw Feb 24 '16 at 16:37
  • $\begingroup$ If that is the case, then would: "an object's derivatives" be generally understood? $\endgroup$ – Shuri2060 Feb 24 '16 at 16:42
  • 1
    $\begingroup$ An object has no derivatives. The object's position has. $\endgroup$ – mvw Feb 24 '16 at 16:44
  • $\begingroup$ Yes - and I'm looking for the particular word which describes those ones (if there is such a word). $\endgroup$ – Shuri2060 Feb 24 '16 at 16:45
  • $\begingroup$ Just $n$-th order derivatives or derivatives IMHO. $\endgroup$ – mvw Feb 24 '16 at 16:46

Here is a common convention for position derivatives

  • 0th Derivative : Position
  • 1st Derivative : Speed
  • 2nd Derivative : Acceleration
  • 3rd Derivative : Jerk [1]
  • 4th Derivative : Snap/Jounce [2]
  • 5th Derivative : Crackle
  • 6th Derivative : Pop
  • 7th Derivative : Lock [3]
  • 8th Derivative : Drop
  • 9th Derivative : ???

Beyond that, it is just an academic exercise in naming as it way beyond any practical use.


  1. Names of higher-order derivatives
  2. https://en.wikipedia.org/wiki/Jounce
  3. https://www.researchgate.net/post/What_are_the_physical_names_for_third_fourth_and_higher_order_derivatives_of_position

  • $\begingroup$ Thank you for your answer. However, I was looking for the general term to describe these derivatives, not the specific ones. $\endgroup$ – Shuri2060 Feb 24 '16 at 17:08
  • $\begingroup$ I think I have heard the collection of vectors $\vec{r}', \vec{r}'', \cdots$ referred to as the "osculating frame" or "osculating flag", assuming they are all linearly independent. $\endgroup$ – Nick Feb 24 '16 at 17:15

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