"Darwin123" escreveu na mensagem
...
On May 8, 1:34 pm, "El Enrrabadore-mor"
wrote:

Do you think you know top/gyroscopes?
Do you know eigenvalues and eignevectors? The moment of inertia
is a tensor matrix. If you perform an eigenanalysis on the moment of
inertia, which is called diagonalization, you will get the the
symmetric axes of the object and the moment of inertia around each
body.
For a spherical body, the solution is three orthogonal axis with an
equal moment of inertia. However, this solution is degenerate. You can
chose any three orthogonal axis and it will be an axis of symmetry for
the sphere. I suspect that may be related to your problem. The
equations you are using are ill-conditioned due to the degeneracy of
the eigenvector solution. This is a math problem, not a physics
problem.

My equations don't have any trouble to predict the sphere
behaviour, for instant (the usual torque/precession for a
gyroscope moment I3w3):
T1 = I1 dw1/dt + I3 w3 w2 sin(theta) +
+ (I3-I2) w2^2 sin(theta) cos(theta)

So, I guess I could fortunately get out of that degeneracy
you've been talking about.
So, you agree that Euler's equations of motion don't
qualify for a sphere?


Plugging in numbers into an equation where the solution is
degenerate causes problems. When this happens to me, I go back to the
physics. I look for degeneracy, a place where there is too much
symmetry. In your case, I would look at the spherical body more
closely. Try to make a spherical top, or simulate a spherical top
using your hand. You may find a physical restriction that you weren't
aware of.

The best gyroscopes are spherical.
Gravity Probe B gyroscope is the most perfect sphere ever made.


Read "Classical mechanics" by Goldberg
Read "Classical mechanics" by Korben and Stehele.
This is not Einsteinian relativity, this is Newtonian mechanics. In
relativity, there is no such thing as a completely rigid body. This
creates problems you may not be completely aware of. However, they
have been solved. Look up "Thomas precession" and "right-angled
lever". In any case, the top problem has be solved even under
relativistic conditions. The key is realizing that the "Thomas
precession" and the "right angled lever" are related. The "right-
angled lever" provides the torque for "the Thomas precession." Have
fun.

Many thanks.
Can you point out any solutions besides Euler's equation
of motion? They look like this:
T1 = I1 dw1/dt + (I3-I2) W2 W3
T2 = I2 dw2/dt + (I1-I3) W3 W1
T3 = I3 dw3/dt + (I2-I1) W1 W2