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Paolo De Leva
12-13-2000, 02:10 AM
Dear Biomch-L subscribers,

Ton van den Bogert, in his recent and interesting message wrote:

> Weather forecasting is done by solving large finite element
> models on a mesh that is attached to the earth. And since the earth is
> not an inertial reference frame, Coriolis forces and centrifugal forces
> (the latter are probably insignificant) must be added to the equations.
> This does not make the calculations more difficult; these "pseudo-forces"
> are very well known. One advantage of this is that it makes things
> easier to understand, for instance why the Coriolis force makes hurricanes
> spin counterclockwise in the northern hemisphere.

I see his point, and I agree. But I wouldn't write that "...this...
makes things easier to understand", because I give a different meaning to
the word "understand".

I believe that Ton used the word "understand" to say something different
from what I mean when I use that word: e.g. for me, in this case,
understanding means considering the relationship between the absolute
velocities of the molecules of air and:
- their height from earth surface, and
- their latitude
due to the rotation of the earth, which you can see only if you observe
everything from a fixed reference system. Thus, I wouldn't say that in this
case that "understanding" the phenomenon means to have some easy-to-use rule
to
know wether hurricanes spin ccw or cw.

And that's not just a terminological point: this kind of understanding
is
something that I always seek when I study a motion. For instance, I
need it even when I study the motion of a distal segment during a flail-like
action of the limb (e.g. a soccer kick, or a pitching action).

On the contrary, I completely agree on the statement: "This does not
make the calculations more difficult" (provided you can easily collect the
data, as Ton pointed out).

It is important to underline (as I did several times in previous
discussions on BIOMCH-L) that the calculations using inertial forces are
neither simpler nor more complex. Their complexity is perfectly equivalent.

You might argue that you can more easily write equations in non-inertial
frames, and that is not questionable. Indeed, for many top-level researchers
in our field this is true.
But in my opinion solving the equations involves the same number of
operations, whatever is your approach. Although I have not a mathematical
dimonstration of the above statement, I can show it in many examples.


With kind regards,


Paolo de LEVA

University Institute of Motor Sciences
Biomechanics Laboratory
P. Lauro De Bosis, 6
00194 ROME - ITALY

Telephone: (39) 06.367.33.522
FAX/AM: (39) 06.367.33.517
FAX: (39) 06.36.00.31.99

Home:

Tel./FAX/AM: (39) 06.336.10.218



----- Original Message -----
From: "Ton van den Bogert"
To:
Cc: "Dr. Chris Kirtley" ; "arnold mitnitski"
; "Paolo de Leva"
Sent: Tuesday, December 12, 2000 10:01 PM
Subject: Re: [BIOMCH-L] Centrifugal Force


> Dear Biomch-L subscribers,
>
> This is one of those academic discussions which make no real difference
> in the end, but they are fun and stimulating. So here is my two cents
> worth...
>
> "Dr. Chris Kirtley" wrote:
>
> > Incidentally, I've always wondered why there are no centrifugal forces
> > included David Winter's 2D inverse dynamics analysis (in Biomechanics
> > and motor control of human movement and elsewhere). Did David leave
> > these out because they are negligible in gait, or for soem other reason?
>
> I think the centrifugal force is not included in these equations because
> the equations of motion were written for motion measured in an inertial
> reference frame. Centrifugal force only appears in equations of motion
> written for movement in a rotating coordinate system.
>
> Knowing that Stalin did not allow non-inertial reference frames (thanks
> to Arnold Mitnitski for this interesting piece of information), I can't
> resist offering a few examples where using non-inertial frames seems to be
> a good way to do the calculations.
>
> Example 1: Weather forecasting is done by solving large finite element
> models on a mesh that is attached to the earth. And since the earth is
> not an inertial reference frame, Coriolis forces and centrifugal forces
> (the latter are probably insignificant) must be added to the equations.
> This does not make the calculations more difficult; these "pseudo-forces"
> are very well known. One advantage of this is that it makes things
> easier to understand, for instance why the Coriolis force makes hurricanes
> spin counterclockwise in the northern hemisphere. But the main reason is
> convenience in the computational work. Even though it is true that the
> solution would be the same when the equations are solved in an inertial
> frame, one can imagine the difficulties when weather forecasting would be
> done on a mesh attached to the sun, or the galaxy, or the center of mass
> of the universe...
>
> Example 2: Some years ago I was involved in a study on inverse dynamic
> analysis of downhill skiing. Because of the large volume needed for
> movement analysis, we considered using a system to measure only the motion
> of the body segments relative to the boot, definitely a non-inertial
frame.
> When transforming the equations of motion to this reference frame,
"pseudo-force"
> terms appear that include the state of acceleration (linear acceleration,
> angular acceleration, and angular velocity) and orientation of the
reference
> frame relative to the earth. It also appeared that these terms could be
> determined from a number of accelerometers rigidly attached to the
> non-inertial frame. So, inverse dynamics can theoretically be done in a
> non-inertial frame with a completely body-mounted instrumentation system.
> In this case, transforming all motion data to an inertial reference frame
> is not even possible, because we don't know the motion of the non-inertial
> frame. We only know its state of acceleration. We did the project
somewhat
> differently in the end, but at least I know that it is theoretically
possible
> and that it requires equations of motion to be written for the
non-inertial
> frame. And those equations include pseudo-force terms. I don't think this
> type of analysis can be done in an inertial reference frame.
>
> In both cases, I guess the reason for using a non-inertial frame is the
> difficulty of collecting movement data relative to an inertial frame.
It's
> fine to write the equations in an inertial frame, but what if you don't
have
> the data that is needed to do something with the equations?
>
> Finally, I fully agree with Chris Kirtley mentioning Einstein's principle
of
> general relativity. According to that principle, there is no way of
knowing
> whether a force that we measure (e.g. gravity) is "real", or "just a
pseudo-force"
> which is a consequence of doing measurements in a non-inertial reference
frame.
> General relativity treats gravity as a pseudo-force just like the
centrifugal
> force. Even Stalin would agree that gravity belongs in a free body
diagram,
> but in fact gravity is no more "real" than a centrifugal force.
>
> Ton van den Bogert
>
> P.S. For an explanation of the effect of Coriolis forces on the weather,
> and some critical comments on draining sinks, see
> http://www.ems.psu.edu/~fraser/Bad/BadCoriolis.html
>
> For an introduction to general relativity, see
> http://www.svsu.edu/~slaven/gr/index.html
>
> --
>
> A.J. (Ton) van den Bogert, PhD
> Department of Biomedical Engineering
> Cleveland Clinic Foundation
> 9500 Euclid Avenue (ND-20)
> Cleveland, OH 44195, USA
> Phone/Fax: (216) 444-5566/9198

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