RE: Models, etc.

[Hugh Haskell <hhaskell@mindspring.com>]

> Can anybody think of a process in nature (excepting quantum mechanical
> phenomina) which can be modeled by an equation which is not continuous
> and which does not have continuous derivitives of all orders?
> -
> What is the highest order derivitive which has physical significance?
> (ex acelleration, a second order derivitive undoubtedly has significance.
>    jerk, a third order derivitive has debatable or only minor
> significance, I am sure that the fouth order derivitive has been
> named but I can think of no place where it is used.)

Is my mathematical recollection incorrect, or it it true that when the nth
derivative of a function is zero for all values of the independent
variable, that the derivative process stops? In other words, doesn't a
quadratic function have only two derivatives, and not "derivative of all
orders"?

If that is true, then any natural process modeled using a positive integer
power law would not satisfy the "all orders" condition, but any other
function used to model the process would. Is the statement about "all
orders" meant to imply that correct modeling of nature should never take
the form of a power law?

With regard to the third and fourth dervs. of position. Jerk is important
in engineering practice since, among other things, it plays an important
role in material fatigue. The deriv. of jerk may also play a role in
engineering but I don't know of any. Since most physicists are not
concerned with jerk (until it happens to them) they may be justified in
ignoring it, but it certainly seems worthwhile to mention it in physics
classes, since, if nothing else, students experience it almost every time
they start or stop their car. It accounts for that little extra "jolt" you
feel just as your car comes to a complete stop. And pilots who fly off
aircraft carriers know a lot about jerk because catapaults are most
definitely not constant acceleration devices. On the other hand, the
arresting cables that stop the planes on landing are more nearly constant
acceleration devices.

Hugh

************************************************************
Hugh Haskell
<mailto://hhaskell@mindspring.com>

The box said "Requires Windows 95 or better." So I bought a Macintosh.
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