Michael Schwartz

12-13-2000, 03:09 AM

I cannot resist adding my thoughts (perhaps there

should be an entire listserv dedicated to inertial

forces).

My thoughts are not unique, but rather adapted

(stolen) from the brilliant work

"The Variational Principles of Mechanics" by

Cornelius Lanczos (Dover Inc., New York).

I would strongly urge anyone involved in mechanics

to read as much of this as possible. It is fairly

dense material but gives amazing insight. In Ch.

IV, Lanczos deals exclusively with d'Alembert's

Principle. When I first saw this, I was

confused. I had always thought (been taught) that

this "principle" was merely algebraic shuffling.

However, it is noted by Lanczos that "it is

exactly this apparent triviality which makes

d'Alembert's principle such an ingenious invention

and at the same time so open to distortion and

misunderstanding.".

This current "debate" is a great example of how

prophetic Lanczos was!!!

The most important point is that by transforming a

non-equilibrium problem to an equilibrium problem

by the addition of the inertial forces, the

Principal of Virtual Work now holds (the virtual

work of all forces vanishes). This then means

that the PVW and all of it's consequuences can be

directly applied to a "dynamic" problem.

One of these consequences, related to gait

analysis, is to allow the use of "kinematical

variables", that is, velocities that are not the

derivatives of actual position coordinates. The

example cited by Lanczos is the spin of a top

about its axis of symmetry, however one could

extend this to think of the angular velocities of

Euler angles.

Finally, d'Alembert's principle makes clear the

exact origin and nature of the different apparent

forces arising from moving reference frames

whether in translation, rotation or change in rate

or direction of rotation (mass * omega_dot X R),

which Lanczos dubs the "Euler force".

Well that's my $0.02 as we say on this side of the

pond. Thanks to all contributors for the

stimulating discussion.

--

Michael Schwartz, Ph.D.

Director of Bioengineering Research

Gillette Children's Specialty Healthcare

Assistant Professor

Orthopaedic Surgery, Biomedical Engineering

University of Minnesota

Phone:(651)229-3929 Fax:(651)229-3867

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

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

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

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

should be an entire listserv dedicated to inertial

forces).

My thoughts are not unique, but rather adapted

(stolen) from the brilliant work

"The Variational Principles of Mechanics" by

Cornelius Lanczos (Dover Inc., New York).

I would strongly urge anyone involved in mechanics

to read as much of this as possible. It is fairly

dense material but gives amazing insight. In Ch.

IV, Lanczos deals exclusively with d'Alembert's

Principle. When I first saw this, I was

confused. I had always thought (been taught) that

this "principle" was merely algebraic shuffling.

However, it is noted by Lanczos that "it is

exactly this apparent triviality which makes

d'Alembert's principle such an ingenious invention

and at the same time so open to distortion and

misunderstanding.".

This current "debate" is a great example of how

prophetic Lanczos was!!!

The most important point is that by transforming a

non-equilibrium problem to an equilibrium problem

by the addition of the inertial forces, the

Principal of Virtual Work now holds (the virtual

work of all forces vanishes). This then means

that the PVW and all of it's consequuences can be

directly applied to a "dynamic" problem.

One of these consequences, related to gait

analysis, is to allow the use of "kinematical

variables", that is, velocities that are not the

derivatives of actual position coordinates. The

example cited by Lanczos is the spin of a top

about its axis of symmetry, however one could

extend this to think of the angular velocities of

Euler angles.

Finally, d'Alembert's principle makes clear the

exact origin and nature of the different apparent

forces arising from moving reference frames

whether in translation, rotation or change in rate

or direction of rotation (mass * omega_dot X R),

which Lanczos dubs the "Euler force".

Well that's my $0.02 as we say on this side of the

pond. Thanks to all contributors for the

stimulating discussion.

--

Michael Schwartz, Ph.D.

Director of Bioengineering Research

Gillette Children's Specialty Healthcare

Assistant Professor

Orthopaedic Surgery, Biomedical Engineering

University of Minnesota

Phone:(651)229-3929 Fax:(651)229-3867

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

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

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

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