From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Fri, 6 Aug 1999 15:15:29 -0500
Hi Brian-
You make a choice of paths to understanding when you write:
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But, Jim, the calculations of work and the implied recourse to the
concept of work as the explanation for the (change of) motion is
certainly unnecessary and, therefore, irrelevant to the explanation of
what is going on. What is needed to change motion is force.
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The notion that force is a fundamental entity is part of the
Neewtonian approach to understanding dynamics. One should point out
to more advanced students (I tried this recently in a statics course)
that there is at least one alternative approach based upon the minimization
of certain quantities; we may conveniently refer to this as the
Lagrangian approach to dynamics. One can take Action as the fundamental
quantity, and all of Newton is exhibited as the consequence of minimizing
action. Force then appears merely as the gradient of a potential, which
is part of a Lagrangian.
This approach is crucial to an understanding of modern quantum
mechanics and field theory, and underlies much work in continuum mechanics and
, even, structural mechanics. It is also, in many cases, easier to use.
When I wanted to write down the equations for the mass on a string problem,
with two degrees of freedom, I found them quickly from the Euler-Lagrange
equations, rather than trying to start from Newton's law.
Moral: only to a confirmed Newtonian is it true that "what is needed
to change motion is force." For the rest of us, "force is a sufficient cause
of a change in motion."
Regards,
Jack
"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography