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Ulrich Simon
12-21-2000, 05:02 AM
Dear all,

"Andrew Pinder (HSL)" wrote:
>> Also I personally still can't see any advantage in D'Alembert's approach

In my opinion there are some advantages in D'Alembert's
prinziple using inertial forces like every other force.

An Example:
When you build up the equations of motion for an gyroscope
you have to consider the gyroscopic moments. With Newton's
notation you will get at least two coupled equation in the
Form:

x'' * m = - Omega * g_xy * y' + f_x

y'' * m = + Omega * g_xy * x' + f_y

x'', y'' - angular acceleration,
Omega - rotational speed,
m - second moment of mass perpendicular to the axis of the
gyroscope,
g_xy - second moment of mass in the axis of the gyroscope.

Now there are two forces coming from inertial effects: (x''
* m) and (Omega * g_xy * y'). There is no difference between
this two forces (moments) in principal (Omega * x' is an
angular accelaration of the mass).
Hmm, witch one do you want to declare to be "not real" ?
Which one is part of the reason which one is the result ?

An other Example:
A satellite on a geo-stationary orbit with two forces:

m*a = m*g

When you like the idea of the space distorted from gravity,
then you say that there is NO force at all. The orbit is
then the forceless "straight" course. g is then a kind of
acceleration.
Is the weight then "not real"? Hmm, I feel my weight is much
real.
Both forces are "real" or not.

And last (again):
Forces are axiomatic in the mechanics.
Forces are a concept with no strong definition.
We're always measure only the results: displacements,
stains, piezo-voltage, ...

I have made good experiences in teaching it this way.
But don't ask my students. ;-)

Nice Days

Ulrich Simon

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