Why is it so much easier to lift a spinning gyro than if stationary?

[jbriggs444]

Perhaps we are speaking past each other. The word "define" does not mean the same thing as "calculate", "measure", "predict" or even "determine". I use it in the sense of a mathematical definition. To define the center of mass is to explain what the words "center of mass" mean.

The center of mass of a Chaotic Pendulum is perfectly well defined at all times. By that I mean that we know the meaning of the words "center of mass of a Chaotic Pendulum" at all times and further, that there is no ambiguity -- there is, in principle, exactly one position that is the "center of mass".

What is missing in the case of a Chaotic Pendulum is method for making a precise prediction of that center of mass, given a set of measurements, no matter how precise, of the initial conditions. It is, of course, possible to determine both the position and speed of the center of mass of the pendulum at any given time while it is spinning. It's just not possible to predict this position very far in advance.

 

[A.T.]

Maybe a revolving can full of marbles is not the best example of a spinning object

And neither is your chaotic pendulum, as there is nothing chaotic about a mounted gyro. And as jbriggs noted, you are confusing defining and predicting. And on top of that, your example is contradicting your own claim, that the CoM moves over the support point when the gyro precesses, because that would be very predictable and not chaotic all.

 

[Buckleymanor]

Perhaps we are speaking past each other. The word "define" does not mean the same thing as "calculate", "measure", "predict" or even "determine". I use it in the sense of a mathematical definition. To define the center of mass is to explain what the words "center of mass" mean.

The center of mass of a Chaotic Pendulum is perfectly well defined at all times. By that I mean that we know the meaning of the words "center of mass of a Chaotic Pendulum" at all times and further, that there is no ambiguity -- there is, in principle, exactly one position that is the "center of mass".

What is missing in the case of a Chaotic Pendulum is method for making a precise prediction of that center of mass, given a set of measurements, no matter how precise, of the initial conditions. It is, of course, possible to determine both the position and speed of the center of mass of the pendulum at any given time while it is spinning. It's just not possible to predict this position very far in advance.

I don't recognise that we are speaking past each other it's just that there is a probably a misunderstanding between the mathematical definition you propose and the experimental evidence that I try to explain.Mathematicaly it's obviouse that the CoM should be where it's calculated to be within a chaotic system but expermentaly it is obviouse it's not.Otherwise you would have a pendulum moveing in completely predicatable way.

 

[jbriggs444]

This is not a disagreement about physics. This is a disagreement about linguistics -- about the meaning of words. I did not propose a mathematical definition. I tried to explain what a "definition" (mathematical or otherwise) is.

The CoM of any system is always where it is defined to be. That is true by definition. No possible experiment can demonstrate otherwise. The fact that the CoM of a chaotic system cannot be predicted reliably far into the future is completely irrelevant. You persist in confusing "define" with "predict".

 

[A.T.]

The fact that the CoM of a chaotic system cannot be predicted reliably far into the future is completely irrelevant.

Especially since Buckleymanor proposes that the gyro's CoM changes in a very predictable way, as soon as the precession starts. Nothing chaotic about that.

 

[Buckleymanor]

This is not a disagreement about physics. This is a disagreement about linguistics -- about the meaning of words. I did not propose a mathematical definition. I tried to explain what a "definition" (mathematical or otherwise) is.

The CoM of any system is always where it is defined to be. That is true by definition. No possible experiment can demonstrate otherwise. The fact that the CoM of a chaotic system cannot be predicted reliably far into the future is completely irrelevant. You persist in confusing "define" with "predict".

Well I can't really argue past that as you recently posted this,." I use it in the sense of a mathematical definition"You have to make your mind up.

 

[A.T.]

You have to make your mind up.

Seems to me like almost everyone is pretty clear here, including the thread starter, who already acknowledged that his question was answered on the first page.

 

[PeterDonis]

Thread closed for moderation.