Consider a gyroscope which is hanging by a string. Is it possible to flip the orientation of the gyroscope by oscillating the point of suspension? How does it come out mathematically?
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3$\begingroup$ A best first step to finding an answer is to try it. Get a gyroscope at the toy store and play with it. $\endgroup$– S. McGrewApr 15, 2018 at 18:33
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$\begingroup$ Here is a place to start on the math: [ocw.mit.edu/courses/physics/… and [ocw.mit.edu/courses/aeronautics-and-astronautics/…. You'll need to add a time-dependent torque aligned in the vertical direction (that is, a horizontal force at the outer end of the gyro axis), whose direction rotates as the gyro precesses) to have all the math you need. Also useful:;ftp.nmr.mgh.harvard.edu/pub/docs/MRI_Hanson/… $\endgroup$– S. McGrewApr 16, 2018 at 14:21
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Short answer: flip not possible.
Take a gimbal mounted gyroscope, spinning fast. And now you want to reorient it, so that in the end position the angular momentum vector is reversed (orientation flipped). That is possible with precisely the right torque, and you stop supplying that torque when the desired end position is reached.
You get the kind of control you need only with a torque.
(To remove any possible ambiguity: Here I mean by 'torque' a narrowed-down case: a moment of force such that the torque vector goes through the center of mass of the gyroscope wheel. Also called a 'couple'.)
I don't see any applied oscillation having the effect of flipping the orientation. On the contrary: an oscillation goes back and forth, I expect its overall effects to cancel out. For instance, if you apply an oscillation, with gradual buildup of the amplitude, and you also go out gradually, then I expect that the before and after orientation will be the same.
So: for flipping the orientation an oscillation is pretty much the method most certain to be unsuccesful.
This raises the question, why did you even consider the idea that some oscillation might possibly flip the orientation of a gyroscope?
Perhaps, I don't know, your thinking was that given that gyroscopic precession seems very counter-intuitive, maybe there is also a very counter-intuitive response to an applied oscillation?
Further reading: discussion by me of gyroscopic precession in a physics.stackexchange question from 2012
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$\begingroup$ The flip does take place if you rotate the point of suspension. The gyroscope will either flip up or down depending whether you rotate the point of suspension clockwise or counter-clockwise. $\endgroup$ Apr 18, 2018 at 6:00
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$\begingroup$ @user149973 In your original question you wrote 'oscillation'. It's not clear why you suddenly introduce 'rotation of the suspension point' here. I was hoping you would clarify your orginal question but I guess that's not going to happen. $\endgroup$– CleonisApr 18, 2018 at 20:00
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$\begingroup$ Would it be possible to flip the gyroscope's flywheel upside down without reversing the angular momentum vector? $\endgroup$– MagmaJun 20, 2020 at 14:37