Postion -> Velocity -> Acceleration -> Jerk ->?

[tectactoe]

We all know that, assuming $$x(t) =$$ position as a function of time, then:

$$x'(t) = v(t) = velocity$$
$$x''(t) = v'(t) = a(t) = acceleration$$
$$x'''(t) = v''(t) = a'(t) = j(t) = jerk$$ (assuming j is the symbol for jerk).

But what does $$x''''(t) = j'(t)$$ come out to be? Is there a fourth derivative of position? And if so, is it ever practically used?

What about fifth, sixth, seventh, etc derivatives?

This is just something I've been extremely curious about since I learned of the third derivative, jerk (or jolt).

Thanks!

 

[h2oski1326]

The term ¨x¨[d4x/dt4 is the time derivative of the jerk,
which might be called a ‘‘spasm.’’ It has also been called a
‘‘jounce,’’ a ‘‘sprite,’’ a ‘‘surge,’’ or a ‘‘snap,’’ with its successive
derivatives, ‘‘crackle’’ and ‘‘pop.’’

http://sprott.physics.wisc.edu/pubs/paper229.pdf

'snap', 'crackle' and 'pop'...

 

[tectactoe]

Haha that's funny.

Does anyone happen to have a position/time graph in which you'd be able to calculate something like the fifth or sixth derivative of x? Would these ever even be needed? Hah.

 

[K.J.Healey]

Anything that is a harmonic function, like say a pendulum, will have a non zero nth order x^n derivative thing.

say, x = Sin(t)

 

[Hootenanny]

Derivatives of order 4 & 5 can be used to find and classify the maximum/minimum accelerations, for example.