Ton Van Den Bogert

12-12-2000, 07:01 AM

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

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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

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