What is the Significance of Multiple Time Derivatives in Physics?

[robert]

If the derivative of displacement if velocity, and the derivative of displacement is acceleration, does the derivative of acceleration give you anything? We were trying to think of something in class today but couldnt.

 

[chroot]

The time derivative of acceleration is called 'jerk.'

From wikipedia (http://en.wikipedia.org/wiki/Jerk):

In physics, jerk (in British English, jolt), also called surge, is the derivative of acceleration with respect to time (or the third derivative of displacement). Yank is mass times jerk, or equivalently, the derivative of force with respect to time. Jerk is a vector, and there is no generally used term to describe its scalar value.

The units of jerk are metres per second cubed (m/s3). There is no universal agreement on the symbol for jerk, but j is commonly used.

Jerk is used at times in engineering, especially when building roller coasters. Some precision or fragile objects—such as passengers, who need time to sense stress changes and adjust their muscle tension, or suffer e.g. whiplash—can be safely subjected not only to a maximum acceleration, but also to a maximum jerk. Jerk may be considered when the excitation of vibrations is a concern.

Higher derivatives of displacement than jerk also exist, but they are rarely necessary, and hence lack agreed names. Many suggestions have been made, such as jilt, jouse and jolt. In development of the Hubble Space Telescope's pointing control system, the fourth derivative of position was considered and the engineers used the word jounce in their publications.

- Warren

 

[whozum]

There are infinite time derivatives of position, but only the first six I think are actually named. The position function for constant jerk becomes

$$x(t) = x_0 + v_0 t + \frac{1}{2} at^2 + \frac{1}{6} j t^3$$

Also, the derivative of velocity is acceleration, you seem to have a little mix-up there.

 

[HallsofIvy]

The first six? I knew "jerk" but what are the other three?

 

[Galileo]

snap, crackle and pop presumably, according to http://math.ucr.edu/home/baez/physics/General/jerk.html

But they admit it's not standard.

 

[robert]

Also, the derivative of velocity is acceleration, you seem to have a little mix-up there.

ya i meant the derivative of velocity is acceleration. i didnt even notice i wrote it wrong though.

 

[dextercioby]

You know,more time derivatives on the position vector are not welcome for various reasons.Take the Lorentz-Dirac reaction force.It has the third time derivative.It poses problems with the causality.Newtonian physics,however,seems to accommodate the time varying acceleration.Thankfully,in quantum physics the problems generated by more than 2 time derivatives are absent.There's no such thing as force,nor acceleration.

Daniel.