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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---------------------------------------------------------------

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

---------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------