View Full Version : Re: Centrifugal Force & Inverse Dynamics

12-21-2000, 11:03 PM
I would like to start by complimenting Ton and Paolo on the tone and
high level of debate in which they have engaged. It sets a standard
for us all.

My second point is to state the obvious. Given a set of measurements
and a specified set of forces, both of them would compute the same
trajectory of an object. In other words, they are using the same
physical principals but are disagreeing about which is the right
coordinate system and what are the names and interpretations of the
terms that appear in the equations.

It seems to me that the responders fall into two groups; the dualists
who contend that there are REAL forces and PSEUDO (or inertial or
imaginary) forces and they are not the same thing; and the monists
who reply that a force is a force (of course of course). This might
be easily settled if we knew what "real" is and I think we all feel
we do, although we do not all think the same. So let me pursue some

Real forces are associated with the interaction between two physical
objects. Muscles, rockets and contact between objects are examples.
So are the fields created by masses, charges and moving charges.

If the forces on an abject do not sum to zero, motion results and for
that we require a coordinate system. The dualists think reality
exists is in an inertial frame of reference while the monists are
equally comfortable in either. Now as a computational issue,
practicality takes precedence. Not even dualists would want to
discuss weather patterns in an inertial frame (The weather today will
be warm and sunny with light winds from the east of 600-610 miles
per hour.) So we are content to explain cyclones in terms of Coriolis
forces but we know that is just a convenience. It is the same
convenience that lets us say that the sun also rises and sets. It is
not the atmosphere that moves west, the earth moves east (I seem to
be getting a lot of Hemmingway references here.) Every problem that
can be described in a non-inertial frame of reference, can also be
described in an inertial frame (i.e. the earth rotates relative to

So what are real forces? I think (because I have not been able to
think of a counter example but if I am wrong, it should not be long
before someone provides one), that real forces are the same in all
coordinate systems and pseudo forces are not. Two examples:
Non-inertial frames have Coriolis forces, inertial frames do not.
When I hold a ball on a merry-go-round, in an inertial frame, my hand
provides a (real) centripetal force to accelerate the ball inward and
feels (pseudo) d'Alembert's force as resistance. In the rotating
frame, my hand resists the centrifugal force. Same equations,
different names. But regardless of the coordinate system in which the
motion is described, my muscles are generating the same real forces.

Since we get the same kinematic answers either way, does it matter?
As a matter of pedagogy I think it does but we need to teach it both
ways. Our students come in to our classes with centrifugal force well
established in their vocabulary but without a clear definition. So if
we can disagree like this, what can we ask of them? I think a more
profound issue is one of causality. On the merry-go-round, I prefer
to say that the force of my hand causes to ball to rotate around the
center. I do not like to say that centrifugal force causes my hand to
resist the ball. Maybe there is some other way to say it but I do not
see a "cause" for centrifugal force and so it is not real to me.
Notions of causality are important because they shape the way we
think about things.

PART 2 - Inverse dynamics.

Chris Kirtley asked if the CNS could do inverse dynamics to control
the motor system. My first response was the same as Ton's but having
thought about it some more, let me offer a different perspective. The
CNS not only can do that but does do that. But it does not do it
explicitly, the way we do it with our equations and Matlab. It does
it implicitly in the patterns of forces it generates in the muscles.

Think back, those of you old enough, to the time of analog computers
when a few amplifiers, diodes, resistors and capacitors and wires
could generate the solution to any nonlinear equation. Could not one
do that with a few million neurons? And I suggest that that is how
one should look at the force pattern generators in my schemes, the
forward models in Shadmehr's, the force fields of
Mussa-Ivaldi and Giszter and the dynamic forces of Ghez, Sainburg,
Bastian and others (This is my opinion and I am not speaking for any
of the above).
The joint torques are the solutions to the inverse dynamic equations,
even if we never explicitly write them out.

The immediate objection to this is that even (or especially) analog
computer solutions are only as accurate as their ability to integrate
accurately which always is difficult and especially in a noisy
environment. They drift and require frequent calibration. That is not
a problem because we can recalibrate every time we make contact with
an object or look at our limbs. Just as importantly, our
neuromuscular system is not an ideal force generator but one with
intrinsic elastic properties created especially by muscle
co-contraction and also by reflex action. If you look at the block
diagrams (or consider the implications of a converging force field),
there are two inputs; the force input (the solution to the ID
equations) and a position input that combines with length feedback.
If the force input is well planned, that second input does nothing.
But this elastic property makes the endpoint insensitive to errors in
that dynamic force input.

So I think Chris's question ties in very nicely with the issues of
what are real forces. If you think that there is a fundamental
difference between classes of forces, that some are real and some are
reactions to real forces, then you come to a different conclusion
about control and about pathology than you do if you think all force
components have similar stature. This is another long and potentially
interesting discussion but not this year.

CONSUMER WARNING: The above views express the opinions of the writer
and are not universally shared. Some of this was discussed here a
couple of years ago and we ended up agreeing to disagree. That has
not changed.

However, the evidence from this discussion is that educated people
can make careers in this line of work on either side of the fence so
I will just wish all you monists and dualists out there, Happy
Chanukah, Merry Christmas and May the Force be with you.
__________________________________________________ _________________
| Gerald Gottlieb (617) 358-0719
| NeuroMuscular Research Center 353-9757
| Boston University fax 353-5737
| 19 Deerfield St.
| Boston MA 02215

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