Re: Energy, etc

[Brian McInnes <bmcinnes@PNC.COM.AU>]

Hi Jack,
I note your pertinent comment about the Newtonian and Lagrangian
approaches to mechanics.

> 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.


It certainly is easier to use in many cases such as the one you
mention.  Is it easier for extended articulated bodies such as the
skater pushing off the wall?  It may well be.  I have a blank on it.


>        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."

I plead guilty to being a confirmed Newtonian.  However, I would say
that minimizing action is a consequence of an non-zero net force on an
object.  We can also look at approaches such as the minimization of
free energy.  We use different techniques for the elucidation of
different problems.  The techniques are neither contradictory nor
exclusive.

Regards,
Brian McInnes