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unknown user
09-10-1996, 02:11 AM
Dear Dr. Cavanagh, President of the ISB,
and BIOMCH-L subscribers,

I believe that the following is a major topic for
standardization in data processing and presentation. I discussed
it already either personally or by e-mail with some of you.
This is a summary of my conclusions.

I will use Aristotelian logic structures to try and show
that the widely used Jean D'Alembert's approach (inertial forces)
is an hystorical mistake.
My rationale is based on the following thesis, which may
surprise some of you but is absolutely true, as you can find yourself
by solving any specific accelerated-motion problem using both:
- classical Newtonian mechanics (inertial reference system)
and
- D'Alembert's approach (non-inertial reference system
attached to the system),
and comparing the two methods.

THESIS
|-------------------------------------------------------------------|
| "D'Alembert's mechanics" does not simplify or make shorter |
| data processing and analysis (it does not make it more complex |
| or longer either). |
|-------------------------------------------------------------------|
For proving the above proposition I use to compute with the
two methods the tilt angle of a runner along a curved trajectory,
and simply count the number of multiplications, divisions and
additions needed.
Hence, two equivalent approaches to mechanics exist:
the "mechanics by D'Alembert", which introduces VIRTUAL FORCES, and
the classical mechanics according to Newton, which does not use
virtual forces.

ANTITHESIS 1
The use of virtual forces is a major drawback (see further
theoretical probing below). Thus, you can choose between two
"equivalent" approaches, one of which involving the crooked and
artful concept of VIRTUAL forces.

ANTITHESIS 2 (to the same thesis)
The mechanics according to Newton is widely known. People
teaches Newtonian mechanics. Almost no biomechanics professor teaches
D'Alembert's approach. Even biomechanists who use inertial (virtual)
forces confessed to me that they prefer not to teach D'Alembert's approach
to their undergraduates.

SYNTHESIS
Why should we force the readers of a paper who know only Newtonian
mechanics to learn and master a second thought system, artful and tricky
as Dalembert's one? This second system has two drawbacks (antitheses)
and no advantage (thesis). [forgive me for the use of adjectives such
as artful and tricky; what I mean will be clear later].
For many people it is already difficult to fully understand
Newtonian mechanics. WHY SHOULD WE GIVE THEM THE ILLUSION THAT A SIMPLER
"MECHANICS" EXISTS? (yes, it is an illusion; those who use D'Alembert's
approach just deceive and delude themselves about the contrary).
D'Alembert's mechanics keeps mixing many readers up. Some of you
use it by habit without any effort or confusion or medley, thanks to your
deep knowledge and professional preparation. There's enough space in
your minds for two different approaches. But your readers are not
supposed to be that clever.

FURTHER THEORETICAL PROBING
---------------------------

INTRODUCTION
Notice that I am not stating here that D'alembert approach is
wrong or gives incorrect results. On the contrary, results are the
same as those obtained with Newtonian mechanics. I will try now to
describe the problem from a student's viewpoint.

THESIS 1
When we teach Newton's third law we have to clearly stress that
the action is applied by body A ON BODY B, whilst the respective reaction
is applied ON BODY A.

ANTITHESIS 1
On the contrary, virtual forces (which are used in non-inertial
reference systems in place of the reaction forces) are applied to the
same body as the actual (non-virtual) action forces. Both centrifugal and
centripetal forces are applied to the same body. Inertial
forces are applied to the same body acted upon by the respective
equal and opposite force.

THESIS 2
Similarly, Newton's first law implies that a body
does not need forces to keep constant its vectorial velocity, and we
have to spend time to convince students that this is true
>>>>> with no exception