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Re: the energy



Jack Uretsky wrote:

A general remark on this thread. I think that people are relying too much
on Newton's laws as the foundation of mechanics. Newton provided only one
of many alternative foundations. Any argument that relies only on
Newton's laws is bound to be suspect.

Think instead of using variational principles (least action and least
time) formulations of mechanics.

snip


The downside to this way of proceeding is that nobody in its right
mind wants to introduce calculus of variations and functional thinking to
high school freshmen.


Hardly at the ninth grade level. Feynman's high school physics
teacher, Mr. Bader, did introduce him to the principle of least action.
Feynman tells about this in Chap. 19 of Vol. 2 of the _Feynman
Lectures_. Edwin Taylor and his associates have some articles about
teaching the Principle of Least Action as an introduction to mechanics
for students with only a knowledge of elementary calculus at
<http://www.eftaylor.com>. There are some Java applets which illustrate
the principle for vertical motion in a gravitational field -- a ball
projected upwards. They have also avoided the calculus of variations in
illustrating Feynman's book, _QED_, and similarly for the discussion of
geodesics in _Exploring Black Holes_ by Taylor and Wheeler.

Hugh Logan