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Re: da/dt = jerk?



On Sat, 6 Nov 1999, Leigh Palmer wrote:

Now it is true that there is a jerk involved here, but it has
(ideally)infinite magnitude. The magnitude of the jolt felt is not
related directly to to the magnitude of the jerk; "jolt", if I may
coin a physical quantity, is the change in acceleration, delta a,
and is unrelated to the rate of change so long as the time interval
involved is sufficiently short.

Seems that "Jolt" as a term is already in use as a synonym for "Jerk"
(see below)



Interesting bit from the sci.phys FAQ:
http://math.ucr.edu/home/baez/physics/jerk.html


Updated 18-January-1998 by PEG
Original by Philip Gibbs 21-September-1996

What is the term used for the third derivative of position?

It is well known that the first derivative of position (symbol x) with
respect to time is velocity (symbol v) and the second is acceleration
(symbol a). It is a little less well known that the third derivative,
i.e. the rate of change of acceleration, is technically known as jerk
(symbol j). Jerk is a vector but may also be used loosely as a scalar
quantity because there is not a separate term for the magnitude of
jerk analogous to speed for magnitude of velocity.

In the UK jolt has sometimes been used instead of jerk and may be
equally acceptable.

Many other terms have appeared in individual cases for the third
derivative, including pulse, impulse, bounce, surge, shock and super
acceleration. These are generally less appropriate than jerk and jolt,
either because they are used in engineering to mean other things or
because the common English use of the word does not fit the meaning so
well. For example impulse is more commonly used in physics to mean a
change of momentum imparted by a force of limited duration [Belanger
1847] and surge is used by electricians to mean something like rate of
change of current or voltage. The terms jerk and jolt are therefore
preferred for rate of change of acceleration. Jerk appears to be the
more common of the two.

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 be kept within specified limits of jerk as well as acceleration to
avoid damage. When designing a train the engineers will typically be
required to keep the jerk less than 2 metres per second cubed for
passenger comfort. In the aerospace industry they even have such a
thing as a jerkmeter; an instrument for measuring jerk.

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, The term jounce
has been used but it has the drawback of using the same initial letter
as jerk so it is not clear which symbol to use. Another less serious
suggestion is snap (symbol s), crackle (symbol c) and pop (symbol p)
for the 4th, 5th and 6th derivatives respectively. Dork has also been
suggested for the sixth derivative. Although the reasons given were
less than entirely sincere, dork does have an appealing ring to it.
Higher derivatives do not yet have names because they do not come up
very often.

Since force (F = ma) is rate of change of momentum (p, symbol clashes
with pop) it seems necessary to find terms for higher derivatives of
force too. So far yank (symbol Y) has been suggested for rate of
change of force, tug (symbol T) for rate of change of yank, snatch
(symbol S) for rate of change of tug and shake (symbol Sh) for rate of
change of snatch.

Now class, repeat after me...
"Momentum equals mass times velocity!
Force equals mass times acceleration!
Yank equals mass times jerk!
Tug equals mass times snap!
Snatch equals mass times crackle!
Shake equals mass times pop!!

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