Re: Ohne die Arbeit, part 3 (Long & wordy)

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Sun, 16 Nov 1997, Bob Sciamanda wrote:

> Read more carefully, John. You are correct that the MET exploits the 
> (pseudo)work of only external forces.  But in this example, I have
> chosen 
> my system as only the mass M1, so that F(|R|) is an external force.
> I am not interested in the motion of the CM of the dumbell, only in the
> behavior 
> of R(t), the motion of M1 relative to M2.

Bob,

I have carefully reread your derivation and I still see what I saw
before--the standard intermediate mechanics approach of reducing the two
body problem to an isomorphic, extended MET treatable one body problem
where the body has a different mass than either M1 or M2 and moves about a
fixed point in space with a different radius than either M1 or M2 followed
by the *interpretation* of the result as describing the location of M1
relative to M2 rather than relative to an inertial frame as would be
required by the MET/PET.

However, in thinking about your words, another thought occurred to me.  I
now see that the external force on M1 *is* in fact a conservative force
(as long as one restricts the analysis to the CM frame and does not allow
any other external forces to act on either M1 or M2.)  So one really *can*
look at M1 as the system and proceed as follows: 

First, write the force on M1 as a pure function of R1.  That is, for the
force law F(|R|), substitute the equivalent force law 

           F~(|R1|) = F( |R1|*(1 + M1/M2) ).

Now we have

           M1*R1'' = F~(|R1|)

and since F~(|R1|) is a conservative force, we can define a potential
energy function U~(|R1|) and proceed with the extended MET analysis.  The
result gives us, directly, the behavior of R1. 

Frankly, however, I don't think I'd consider either approach suitable for
use in an introductory course. 

John
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