Steady precession of a gyroscope

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  • #26
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PS... the spinning/flipping nuts in Zero G you can see linked bottom right in that first video to is also fabulous; makes a very unintuitive topic quite reachable
 
  • #27
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My credentials for the gyroscope problem are very good. I have simulated the motion of the gyroscope, called the symmetric top in a uniform field with reaction force at the base. I used elliptic functions and theta functions a la Landau and Lifshitz or Whittaker.
I have looked at many elementary treatments at the freshman/ sophomore level and found them unsatisfying as well. I confess I do not remember Feynman's argument and I may read them tonight if I am not too tired. After reading several elementary treatments, I came to the conclusion, that if I were teaching an freshman/sophomores, I would never test them on the gyroscope.
The bad news is I do not know of any good treatment of the gyroscope that doesn't involve the Lagrangian, the Hamiltonian treatment, and roots of the cubic equation. (I'll get back to you if I like Feynman's treatment) That is why I wouldn't ask a question of anyone but very good physics undergraduates (Junior/Senior) at a strong college/university.

One professor, perhaps Ed Purcell was asked what the hardest things physics undergraduates learn. The questioner expected Purcell to say Quantum mechanics, or Relativity. The professor agreed these are the most novel areas, but in his experience the hardest things undergraduates are expected to learn is rigid body mechanics. After working with many physics, math and engineering graduates, I agree. (I might get back to you to the link to this article)
 
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  • #28
vanhees71
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The message is that learning Hamilton's principle of least action and analytical mechanics is well worth the effort for two reasons: (a) mechanics becomes much easier than when sticking to pure Newtonian methods and forces (for me Hamilton's principle was a revelation when I first learnt about); (b) Hamilton's principle underlies all fundamental physics, and Newtonian mechanics is the most simple example to learn about it. The most important feature is that it makes Noether's theorems on symmetries and conservation laws possible, which is the most important and most beautiful concept of physics.:bow:
 
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  • #29
A.T.
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Hey A.T. - I've watched plenty of Gyroscope vids in my time and I have to say that first one is superb
Yes, I have seen this type of explanation in some books, but for a long type there was no animation of it. I was very happy when this one appeared, so I didn't have to make one myself.

The book "Thinking Physics" uses a rectangular pipe loop, in which a heavy fluid circulates. If you try to rotate the pipe loop around one axis Z, it is obvious that fluid on opposite sides along Z will react against the pipe in opposite directions perpendicular to Z, because it is moving in opposite directions in these segments.
 
  • #31
learning Hamilton's principle of least action and analytical mechanics is well worth the effort
I had a moment of epiphany while reading your mention of the least action principle. It connected nicely with a way of thinking about gyroscope behavior that I have sometimes found useful.

Those who have actually played with a bicycle wheel gyro will remember that it actually takes some extra effort to turn the wheel steadily around a strictly vertical axis, because it desperately wants to tip over to one side. (I'm talking about the case where you support one end of the axle with each hand). On the other hand, it takes a lot less effort to rotate it around the vertical axis if you also permit it to tip over by just the right amount. (In this case we only need to support the weight of the wheel, and we don't need to counteract its tipping action). So by experimenting with different combinations of turning and tipping, you can learn what it would like to do if left to its own devices with no external torque, once a precession has been set up.

Well, when we experiment manually with different trajectories, we are in a sense trying to find the one that complies with the Hamiltonian law, i.e. the trajectory that it would follow if no external torque were applied.
 
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  • #32
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I'm not sure, but I may be ruining your epiphany moment. On the other hand, you may get another one when you grapple with the thoughts I am about to address. You mention "a trajectory that it would follow if no external torque were applied", and you played with a gyroscope and got a physical feeling for the torques, and forces involved.

Unless you did your experiments in free fall (like in orbit) the gyro had torques acting on it. Typically when you spin the gyroscope on the floor, the reaction force from the floor is providing a torque about the center of mass up through the symmetry axis of the gyroscope. In your case, your hands are exerting reaction forces to the gyro, so the gyro is not free (unless you're not holding it at all and it is just dropping)

As Feynman points out in his lectures, the general motion of the gyro can nod (or aka nutate) as well as precess. This is true for a gyro with a reaction force (like the floor or a stand). A "free" gyro, (a gyro freely falling) like in the space shuttle (as long as it is symmetrical about the axis), will not nutate (nod). It will still precess. Hence, you were not really experimenting with a "free" gyro (with no external forques), unless you were in space or a falling elevator.
 
  • #34
dyn
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One professor, perhaps Ed Purcell was asked what the hardest things physics undergraduates learn. The questioner expected Purcell to say Quantum mechanics, or Relativity. The professor agreed these are the most novel areas, but in his experience the hardest things undergraduates are expected to learn is rigid body mechanics. After working with many physics, math and engineering graduates, I agree. (I might get back to you to the link to this article)
From a learning perspective i also totally agree with this statement
 
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