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Re: [Phys-l] non-conservative --> non-grady ???



Hi all-
Since the two statements are mathematically equivalent, as far as I can see, why is either one to be preferred?
Regards,
Jack

On Thu, 21 Feb 2008, John Denker wrote:

On 02/20/2008 09:57 AM, Alfredo Louro wrote:
"Piecewise time-independent" is not time-independent at all. And
whether a force is conservative cannot depend on what the particle is
doing. One way of defining a conservative force is to say the work
done by it around a closed path is zero. For any closed path. At all
times.


Do we really want to define "conservative force" that way?

I called attention to a situation
http://www.av8n.com/physics/img48/accelerator.png
where it was uniformly true that the field /applied to/ the
system was
a) independent of time, and
b) the gradient of some potential.

This is a statement about the field /applied to the system/
at the time and place where the system happens to be.


Do we really want to insist that the field be unchanging at
all other times and all other places as well? That seems
kinda strict. Forsooth, it guarantees that the suggested
definition is vacuous. That is, there cannot be any field
that satisfies the terms of this definition, because surely
there is a non-constant field somewhere in the universe.


This example seems to reinforce the point I was making at the
beginning of this thread: The whole business of "non-conservative"
force field is just begging to be misunderstood.

To summarize:
-- If you mean grady, say grady. Calling a non-grady field
"non-conservative" is asking for trouble.
-- Both grady and ungrady force-fields uphold conservation of
energy. No exceptions have ever been observed.
-- Conservation is not the same as constancy. Local conservation
of XX means that XX is constant /except/ insofar as it flows
across the boundary.
-- For an isolated system, conservation would be the same as
constancy, but that's an almost trivial subset of physics.
Physics relies on /local/ conservation laws that can be
applied to non-isolated systems and subsystems.


http://www.av8n.com/physics/conservative-flow.htm
http://www.av8n.com/physics/non-grady.htm

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