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RE: superposition



Thank you, thank you. I'm glad somebody made the point that =
superposition is a consequence of the linearity of the governing =
equations. Superposition works in regions where the governing equations =
can be approximated as linear. I've heard it said that all of =
engineering is the art of linearizing nonlinear physics.

That came out harsher than I intended. Sorry about that. The question =
about superposition is really a question about the validity of =
linearizing near critical points, unless you happen to be lucky enough =
that the governing equations turn out linear everywhere.

Ken Kousen
kousen@concentric.net

----------
From: "JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, =
ARGONNE, IL 60439" <JLU@hep.anl.gov>
Sent: Wednesday, January 15, 1997 3:02 PM
To: phys-l@atlantis.cc.uwf.edu
Cc: JLU@hep.anl.gov
Subject: Re: superposition

Hi all-
One of the points to be made in an elementary physics course is
that we deal with approximations to reality. This is because most =
problems
are too difficult for us humans to solve. The art of physics is largely
the art of finding viable approximations.
Nature is inherently non-linear. There are, however, linear
approximations that describe many phenomena with sufficient accuracy for
many practical purposes. An example is the set of Maxwell's equations =
in
a vacuum. These equations are linear and, as we know, useful for many
purposes.
Superposition is a consequence of linearity. The criterion for
superposition to work is that the phenomenon in question be subject to
linear equations. Superposition is then a trivial consequence.
One must, however, be careful, as John has reminded us. Linear
partial differential equations are generally subject to boundary =
conditions.
The superposition principle need not work when one is dealing with =
solutions
for two different sets of boundary conditions.
The interesting question, I suggest, is not to ask for examples
of situations where superposition does not work (it hardly ever does), =
but
to ask for the circumstances and reasons where it does appear to work.
Regards,
Jack

..