Derivatives of distance -> velocity, acceleration, jerk... ?
Unknown
Then:
f'(t) = velocity
f''(t) = acceleration
f'''(t) = jerk
f^4(t) = ?
f^5(t) = ?
etcetera.
Is there any nomenclature for derivatives higher than the third for
this function? If so, what are they called? Thanks for your time.
--
Dave Typinski
da...@atlantic.net
Sam Wormley
[Physics FAQ] - [Copyright]
Updated 15-November-1998 by Stephanie Gragert
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.
It is also recognised in international standards:
In ISO 2041 (1990), Vibration and shock - Vocabulary, page 2:
"1.5 jerk: A vector that specifies the time-derivative of acceleration."
Note that the symbol j for jerk is not in the standard and is probably only
one of many symbols used.
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.
Needless to say, none of these are in any kind of standards, yet. We just
made them up on usenet.
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!!
-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 80,000 Newsgroups - 16 Different Servers! =-----
Uncle Al
>
> Given the function d=f(t) where d=distance and t=time,
>
> Then:
> f'(t) = velocity
> f''(t) = acceleration
> f'''(t) = jerk
> f^4(t) = ?
> f^5(t) = ?
> etcetera.
>
> Is there any nomenclature for derivatives higher than the third for
> this function? If so, what are they called? Thanks for your time.
This surfaces every quarter. The next three derivatives are snap,
crackle, and pop. Look up past postings in http://www.deja.com/
--
Uncle Al
http://www.mazepath.com/uncleal/
http://www.ultra.net.au/~wisby/uncleal/
(Toxic URLs! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
Unknown
<swor...@cnde.iastate.edu> wrote:
>Ref: http://math.ucr.edu/home/baez/physics/jerk.html
>
>[Physics FAQ] - [Copyright]
>
>Updated 15-November-1998 by Stephanie Gragert
>Updated 18-January-1998 by PEG
>Original by Philip Gibbs 21-September-1996
>What is the term used for the third derivative
>of position?
<snip>
>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.
<snip>
Thanks. I should have checked there first.
--
Dave Typinski
da...@atlantic.net
Unknown
wrote:
>Dave Typinski wrote:
>>
>> Given the function d=f(t) where d=distance and t=time,
>>
>> Then:
>> f'(t) = velocity
>> f''(t) = acceleration
>> f'''(t) = jerk
>> f^4(t) = ?
>> f^5(t) = ?
>> etcetera.
>>
>> Is there any nomenclature for derivatives higher than the third for
>> this function? If so, what are they called? Thanks for your time.
>
>This surfaces every quarter. The next three derivatives are snap,
>crackle, and pop. Look up past postings in http://www.deja.com/
Thanks. As Mr. Wormley pointed out, I should have searched the FAQ.
--
Dave Typinski
da...@atlantic.net
ran.dll
Uncle Al <Uncl...@hate.spam.net> wrote:
> Dave Typinski wrote:
> >
> > Given the function d=f(t) where d=distance and t=time,
> >
> > Then:
> > f'(t) = velocity
> > f''(t) = acceleration
> > f'''(t) = jerk
> > f^4(t) = ?
> > f^5(t) = ?
> > etcetera.
> >
> > Is there any nomenclature for derivatives higher than the third for
> > this function? If so, what are they called? Thanks for your time.
>
> This surfaces every quarter. The next three derivatives are snap,
> crackle, and pop. Look up past postings in http://www.deja.com/
>
http://math.ucr.edu/home/baez/physics/faq.html
Snap, crackle and pop are discussed also, as well as the problems
in adopting them.
The question of names for higher time derivatives for momentum
(force being the first) is also considered. - ran.dll
Sent via Deja.com
http://www.deja.com/