Velocity, Acceleration, Jerk, Snap, Crackle, and Pop! — Derivatives of Distance

Here are more about velocity, acceleration, jerk, snap, crackle, and pop.

Humans are highly sensitive to jerk (rate of change of acceleration) and road and railroad curves are designed to minimise it. Minimising snap (rate of change of jerk) improves the performance of cutting tools in machining.


Which brings to mind my suspicion that G Harry Stine was responsible for “Silent weapons for quiet wars”. In particular notice the phrase “fourth law of motion”.


I vaguely recall learning that pop is the derivative of snap, but it just doesn’t stick in the brain. :man_shrugging:


According to Wikipedia, the derivatives are as follows. The quantity \mathbf{x} is bold face to indicate it is a vector: it has both a magnitude and direction.

\begin{array}{cl} \mathbf{x} & {\rm Distance/Position} \\ \frac{d\mathbf{x}}{dt} & {\rm Velocity} \\ \frac{d^2 \mathbf{x}}{dt^2} & {\rm Acceleration} \\ \frac{d^3 \mathbf{x}}{dt^3} & {\rm Jerk} \\ \frac{d^4 \mathbf{x}}{dt^4} & {\rm Snap} \\ \frac{d^5 \mathbf{x}}{dt^5} & {\rm Crackle} \\ \frac{d^6 \mathbf{x}}{dt^6} & {\rm Pop} \\ \end{array}

and adds that the names for the last three derivatives are used “sometimes somewhat facetiously”. Fortunately, there is a jingle to help remember them.



Ok, that’s funny.

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See also Ostrogradsky instability:

In applied mathematics, the Ostrogradsky instability is a feature of some solutions of theories having equations of motion with more than two time derivatives (higher-derivative theories).

Not a bug such as violation of conservation of momentum (hence energy) implied by reactionless drives.

And in the event people don’t get why I bring up G Harry Stine in this context, they need to read Jerry Pournelle’s article on “a very odd device called the Dean drive”:

I had my own encounter with something along these lines that is one of the more spooky things that has happened to me, coming as it did on my first day of employment as Vice President for Public Affairs at E’Prime Aerospace commercializing the MX missile as a launch system. I can’t find any of my prior writeups of this experience via google but I think I posted something about it at the arocket list. I’ll see if I can dig it up when I’m not so pressed for time.

Long story short – the day I arrived, the president got a call from some guy that he took in my presence. After talking with him a while he handed the guy off to me. The guy called E’Prime because he’d called NASA which referred him to E’Prime because E’Prime had experience getting a launch license and he had something he wanted to “let loose” and go into space. And… no… this wasn’t a “dean drive” kind of contraption with marginal thrust. It was a device built to stimulate vibration in yachts that had malfunctioned while being tested indoors and hit the ceiling and stuck there.

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Not endorsing but noticing the following appeared as I tracked down the emerging literature on relativistic Weber electrodynamics:

March 2023

cites the Mach 2022 paper on the jerk of a charged particle:

then April 2023:

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The only reason I don’t “like” some of your highly arcane posts is that they are far beyond my understanding. Thus, like most everyone, I must allocate my reading time which is in short supply, while demand - in the form of ever-increasing volume of available material for browsing - is increasing. Things I don’t understand, alas, I must skip over. That doesn’t imply I don’t like the fact that you make the effort to post them. If I “like” them individually, it dishonestly implies I have read them. As one dedicated to integrity (thought this is a small matter, indeed), I think you fully understand what I mean. I wish I could understand more of the arcane materials with which you and John are conversant.


And if I give the impression that I grok the papers I post in fullness then may this post dispense with such pretensions. This is more like a travel log through the literature related to tantalizing puzzles life has placed in my breadth-first search paths.