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

[Bob Sciamanda <sciamanda@worldnet.att.net>]

John Mallinckrodt wrote:
> . . . 
> 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

My introduction to part 1 clearly stated that this is a review;  there
is nothing new here.

> 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.

Are you saying it is forbidden to use the MET in this way?  I simply
used a traditional method to attack a problem which was ostensibly not
suited to the MET (because I was asking for the relative displacement
R), by showing that the desired quantity R is also the solution of a
different, MET solvable problem.  Why not? 
 
> 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.

Bravo! It will come to an equivalent result.

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

Agreed!  I only brought up this example to soften your testimony to the
uselessness of the MET:

	> As Bob was careful to note, this can be done only when one or more of 
	> the external forces is a function only of the system CM position.  
	> I can think of only two situations in which this can be the case: 
	> 1) the system is a point particle or a rigid, non-rotating body 
	> that behaves like a point particle (in which case the extended 
	> MET/PET reduces to its most elementary form) or 2) the force is 
	> constant.  
	> 
	> Using the extended MET/PET we can do roller coaster problems (as 
	> long as we can ignore the minor up and down motions of the earth 
	> that result from its interaction with the roller coaster), but we 
	> cannot perform any significant analysis of the interaction of two 
	> or more large gravitating masses.

> John
> -----------------------------------------------------------------
>  A. John Mallinckrodt      http://www.intranet.csupomona.edu/~ajm
>  Professor of Physics    mailto:ajmallinckro@csupomona.edu
>  Physics Department       voice:909-869-4054
>  Cal Poly Pomona            fax:909-869-5090
>  Pomona, CA 91768-4031   office:Building 8, Room 223

-Bob
-- 
Bob Sciamanda				sciamanda@edinboro.edu
Dept of Physics				sciamanda@worldnet.att.net
Edinboro Univ of PA			http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA				(814)838-7185