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At Hof
12-12-2000, 09:03 PM
Dear Biomch-l discussiants,
Funny that this topic immedeately gives such a strong response!
Although all sensible points have been raised already, I cannot but
add my own viewpoint.
In fact both those pro- and contra virtual forces have their point:
1) These virtual forces are not needed when you stick to an inertial
reference frame. That is why they are not in the book af Winter. His
analysis is based op optokinetic recordings. It is then natural to refer to an inertial
laboratory frame.
2) They can come in very handy in some calculations.

My point is: how to teach this to students? My experience is that
they can quite easily learn to do the calculations, but some
simple insights are very difficult. A main point is Newton's third
law, and the concept of a free body diagram. On what body is the
force working? Most students are very inclined to draw both the force
on the body and the force from the free body on the outside world (to
happily conclude that both are equal and opposite and thus cancel).
This is why I very carefully avoid to introduce 'virtual forces',
because I expect that would increase confusion to an all-times high.
The best is thus to stick to a laboratory frame of reference, and
give some arguments why it is to be preferred.
All the same, d'Alembert's principle can be very handy. It gives you
the immedeate solution of the moment equation for a set of coupled
rigid bodies. I found this out some years ago, J. Biomechanics 25:
1209-1211, 1992. (Interestingly, neither I nor my reviewers saw at
the time that it was in fact a formulation of 'Alembert's principle
of 1740.) In short:
For a static system we have the equilibrium equations:
sum(F) = 0
sum(M) = 0, around an arbitrary point
According to d'Alembert for the dynamic case this becomes only
slightly more complicated:
sum(F) = sum(ma)
sum(M) = sum(r x ma) + sum( I*alpha)
moments again around an ARBITRARY point.
I try to teach this to the students. It is not easy, but at least
somewhat more conveniently arranged than the Newton-Euler approach,
going from segment to segment, and with moments always around the
centres of mass.
The entries at the left hand side of these equations are 'real'
forces and moments. Those at the right hand side I just call 'terms
ma , r x ma, and I*alpha', never suggesting that they, or their
opposites, are real forces or moments.
I wonder whether this approach will allways work, even in the case of
Ton's meteorologic problems.
But centrifugal forces... no way.
Best wishes,
************************************************** *****
At Hof
Department of Medical Physiology &
Laboratory of Human Movement Analysis AZG
University of Groningen
A. Deusinglaan 1, room 769

PO Box 196
NL-9700 AD GRONINGEN
THE NETHERLANDS
Tel: (31) 50 3632645
Fax: (31) 50 3632751
e-mail: a.l.hof@med.rug.nl
************************************************** *******

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