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

On May 8, 6:21 am, "El Enrrabadore-mor"
wrote:
I've been claiming for Years that nobody ever fully explained
the top/gyroscope by means of Classic Mechanics, including
in this thread. (relativity not even has a clue).
This is not true. The precession of spinning objects is fully
explained both in Newtonian and relativistic physics. It is you who
don't know the necessary physics involved. It seems to me that you
haven't even tried.

Do you think you know top/gyroscopes?
I've already faced tens of sharks around here with that
challenge and I'm fishing right now (why you think I've
changed my name - I'm fishing).

Do you want to try some basic general questions yourself?

Wait, you know something about precession.
(And only precession of an horizontal gyroscope for sure).
What about a tilted gyroscope, 360 degrees around?
Mathematically, the periodicity of the trigonometric functions
creates a bit of a problem because the inverse solution of the
equations isn't unique. I can't see what you are doing. However, I'll
bet your problem is with solving the mathematics rather than a real
problem with the physics.
What about nutation?
What about nutation under precession?
What about precession under nutation?
In the case spherical "top" resting on a flat surface, which is
orthogonal to the gravitational field, there is no nutation or
precession. You can't get the axis of rotation to face in a different
direction than the gravitational field, not without breaking the
surface. I am not using mathematics, I am merely resting a ball on a
surface and trying to roll it. If you try to use mathematics to
describe nutation or precession here, you will probably get
pathological solutions.
This is not a problem in physics. You have to pay close attention
to those trigonometric functions. They are tricky. You may be getting
a perfectly good description of a broken surface. Look up "holonomic
trajectories."
I suspect that such behavior is possible on a surface that tilts
with respect to the gravitational field, or with an object that isn't
really rigid. However, that will take real analysis and I don't really
have the time.

Actually I not interested in spheres.
My gyroscope is the following:
http://www.gyroscope.com/d.asp?product=SUPER2
with gimbals:
http://www.gyroscope.com/d.asp?product=GIMBALS

Spheres are just a funny case, that one can use as a gyroscopic
mass, instead of a disk.
Torque is to be applied around the horizontal axis - T1
(a suspended mass for instance) and the gyro will precess
around the vertical - w2.
You can also force the precession motion, by means of
a second external torque T2, and you will get nutation - w1.

A ball on a flat surface cannot have external torques
applied, hence it's just a ball, not a gyroscope.


What about energy conservation?
What about it? Work-energy theorems show when and where mechanical
energy is preserved. As far as I can tell, there is no fundamental
violation of it. Or did you tilt that surface? You know, when a
spinning object falls, potential energy is changed to kinetic energy.

Yes I agree. Energy must be conserved.


I've already spent more then 4,000 hours in the past 3 Years,
looking for gyroscope equations that could predict
basic experimental results.
How sure are you of the experimental measurements? I mean, are
you really sure about the moment of inertia of your rotators? How do
you calculate them?

I'm not doing fine tuned measurements.
I understand the setup, also the forces involved, I know
the masses, radius, torque and inertia moments.
Basically I measure the time it takes to fall and I count the
number of precession turns given.
I've the gyroscope permanently feed by a motor, or else
I leave it free.
Time is in order of tens of seconds, up to 2 minutes.
The number of turns around 10 to 60.
Precession speeds up to 6 rad/s can be achieved.
It is very easy to draw conclusions and see if equations
fit, or not.
I've it mounted on a head of video cassette recorder,
which has a nice inertia moment for torque T2 and
spins with very small friction.
The centrifugal force is clear: m r w^2
When I change the term "m r", that causes force over
the bearings (with constant friction/torque) I got a nutation
that matches a precession speed square term.
So, the centrifugal force is real. You increase it and
the gyro will fall faster, according to *m r w^2*.


And I'm not doing this as a hobby. I really need then.
I got:
- Newton method done (T=dL/dt)
- Lagrangian method done
Already available in classical mechanics textbooks.

Do you have any with the Lagrange method solved ?


- Vectorial method done
You do know that moment of inertia of a nonspherical body is a
matrix. And that the matrix has to be differentiated?

Yes, but I use principal axis.


All them full solutions done by myself, zero simplification.
(I did that because couldn't find a book, link, whatever).
What I need is a genius that could explain me
how to get energy conservation out of it.
Try Goldstein, "Classical Mechanics," or Korben and Stehle,
"Classical Mechanics." A world of wonder awaits you.

I've already discussed Goldstein with Eric Gisse.
It's Euler's equations of motion and it give up nothing.
More on this below.



Euler's equations of motion don't qualify.
Just try them for I1 = I2 = I3 (sphere).
I learned Newtonian mechanics from
"Classical Mechanics" 2nd ed. by H. C. Corben and Philip Stehle
(Krieger 1960). I looked up nutation in the index. In chapter 9, page
149, it qualitatively describes both precession and nutation of a free
rotator.
On page 150, it shows the Euler equations related to a rotator
(equation 52.6). I can't write the equations in the text format, but
they are well known. When I substitute I1=I2=I3, I get a simple spin
with all three axis uncoupled. Basically, it looks like there is no
rotation or nutation for a spherical object.

There is nothing wrong with spheres.
Spheres do precess and nutate like any disk does.
I can make the disk to precess around a circle so that,
more or less, I have I1 = I2 = I3 and nothing strange happens.
I can have I1 = I2 = m r^2 much larger then the main inertia
moment I3 of the spin. Again nothing to notice.

I'm to suppose Euler's equation of motion are good
for nothing. Maybe, not even fully right after all.
At least, for spheres they don't qualify.
Only if I1=I2 much smaller then I3 they can predict anything.


Why should a spherical
object without friction show precession or nutation?

Why?
Why not?
Spheres do precess. Look at Gravity Probe B.


From your complaints, I have a suspicion that you have a problem
both with the physics and the mathematics. Physically: Nutation and
precession are not required in each and every rigid body. They are the
results of different degrees of motion being coupled together. Think
of coupled harmonic oscillators. For some symmetries, the motions are
decoupled. You can't get beats from two pendulums that aren't
connected in some way. Mathematically: you have to analyze
trigonometric functions very carefully. The inverse of a trigonometric
function isn't unique. For instance, consider differentiation. The
derivative of an inverse doesn't have to be the inverse of the
derivative since the function isn't unique.
I don't have my copy of Goldstein available. Someone borrowed it
and didn't return it. Try "Classical Mechanics" by Goldberg. It may
help you.