Original by Philip Gibbs 21-September-1996
It is well known that the first derivative of position with respect to time is velocity and the second is acceleration. It is a little less well known that the third derivative, i.e. the rate of change of acceleration, is technically known as jerk.
The term impulse has sometimes been used instead of jerk, however, impulse is more commonly used in physics to mean a change of momentum imparted by a force, equal to the force times its duration. The term jerk is therefore preferred for rate of change of acceleration.
As its name suggests, jerk is important when evaluating the destructive effect of motion on a mechanism or the discomfort caused to passengers in a vehicle. The movement of delicate instruments needs to kept within specified limits of jerk as well as acceleration to avoid damage.
In the case of the Hubble space telescope, the engineers are said to have even gone as far as specifying limits on the magnitude of the fourth derivative. There is no universally accepted name for the fourth derivative, i.e. the rate of change of jerk, but the term jounce is said to have been used. Another less serious suggestion is snap, crackle and pop for the 4th, 5th and 6th derivatives respectively.