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

1. Feb 8, 2008

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!!

2. Feb 8, 2008

h2oski1326

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

'snap', 'crackle' and 'pop'.....:rofl:

3. Feb 8, 2008

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.

4. Feb 8, 2008

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)

5. Feb 9, 2008

Hootenanny

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