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If a gyroscope is rotating about any axis, other than the spin axis, then that is precession and Orthogonal to that axis is the couple.
For clarity, let the red axis be along the red flywheel axis, The yellow axis is the gyro axis and the blue axis is orthogonal to these. In the model the red axis does not move, the yellow and the blue axes move but remain orthogonal to red.
In the model we have forced precession along the red axis, with equal and opposite torque about the blue axis and spin about the yellow axis. This is the starting condition.
The spinning gyroscope rotor is forced to precess about the red axis as that is the only axis that permits rotation
This simultaneously induces a torque about the other orthogonal axis, the Blue axis.
When the frame containing the spinning gyroscopes is rotated by the red motor,
That rotation induces an orthogonal couple at the blue axis.
As the spin of the gyroscopes are equal and opposite, these torques, induced by the precession about the red axis are equal and opposite.
My conclusion.The conditions for the flywheels to act as gyroscopes are fulfilled. A spin axis of the rotor, Yellow, A torque axis, Blue and a precession axis, Red.
This is a machine. It is indisputable that by judicious manipulation of the two motors the gyroscopes can be spun up to speed about the yellow axis and set freewheeling and the frame can be rotated about the red axis.
Now take one of the gyroscopes, it is rotating about two separate axes. The yellow axis, and the red axis at the same time.
The angular velocity diagram shows these two simultaneous rotations.
If Ω is the spin speed of the gyroscope at the start, then the angular momentum is I Ω
The direction of the angular momentum is the vector sum of the two rotations.
The vector sum of the initial angular momentum of the system is null.
The vector sum of the final angular momentum of the system is positive.
Precession is not rotation.
I would say, precession is a process, that manifests itself as a rotation.
At the end one will see a rotation about an axis different than the axis of spin.
Viewed as a black box, it will behave like a rock with the same mass. Net angular momentum is zero.
. So the red wheel spins one way, and the contraption to the left spins the other way. Still zero net angular momentum.
Nope. At the end, one will see a continuous change in the axis of spin, which is mandated by the change in the angular momentum resulting from the continuous applied torque. But the gyro always has only one axis of spin, and one rate at which it is spinning on that axis. If at any point in time the torque is removed, it will remain spinning only about that one axis.
1. Run the gyroscope motor to bring the gyroscope rotors up to a modest speed. As the rotors are are touching, they counter rotate. Equal and opposite. Now let the motor freewheel.2. Run the reaction motor. This rotates the Gyroscopes about their precession axis, accompanied by equal and opposite torque orthogonal to the spin axis. There can be no torque exerted by the reaction motor along a precession axis, therefore no substantial movement of the reaction flywheel.
So let us do just that. Remove the torque. Stop the rotation of the yellow mass about the red axis.The Red flywheel continues to rotate. The contraption does not.
Scenario 2Quote from: Momentus on 23/08/2020 13:51:441. Run the gyroscope motor to bring the gyroscope rotors up to a modest speed. As the rotors are are touching, they counter rotate. Equal and opposite. Now let the motor freewheel.2. Run the reaction motor. This rotates the Gyroscopes about their precession axis, accompanied by equal and opposite torque orthogonal to the spin axis. There can be no torque exerted by the reaction motor along a precession axis, therefore no substantial movement of the reaction flywheel.Remove the Torque. Gyroscopes stop precessing.
Run the reaction motor. This rotates the Gyroscopes about their precession axis, accompanied by equal and opposite torque orthogonal to the spin axis. There can be no torque exerted by the reaction motor along a precession axis, therefore no substantial movement of the reaction flywheel.
is comment shows a complete lack of understanding of rotation and momentum.If assembly A (what you're calling the yellow mass) is spinning about the red axis, then its angular momentum vector is along said red axis, and with any external torque removed, it must continue to spin, not stop (in complete violation of conservation laws). Your assertion otherwise shows said lack of understanding. Its angular momentum cannot just vanish. It's a conserved quantity. It has to go somewhere.
Forced Precession. Or Induced torque.Tb=JΩyΩrTb is the torque at the blue axis in Nm Ωy is the angular velocity about the yellow axis in rad/sec Gyroscope spin Ωr is the angular velocity about the red axis in rad/sec Precession
Yes, there is torque exerted on each gyro, but not along the red axis
Consider one gyroscope spinning about the yellow axis. Apply a torque at the blue axis, it will rotate about the red axis in a clockwise direction.
Consider the other gyroscope spinning about the yellow axis in the opposite direction. Apply a torque at the blue axis, again in the opposite direction, it will rotate about the red axis in a clockwise direction.
Put the gyroscopes in a frame and repeat the exercise, applying torque at the blue axis etc. They will rotate about the red axis in perfect harmony, precessed by the blue opposite torques. The Red flywheel plays no part, remains unmoved.
The net angular momentum has not changed, it is still null
Next spin gyroscopes as before and rotate them about the red axis, using the Red Reaction flywheel, at exactly the same precession speed as before. The net angular momentum has not changed, it is still null.
What is the physical difference in the speed and torque between the two cases? What motion or force is there in the first case that is not identical in the second case?
There is no difference. The speeds of the gyroscopes are the same, the torques are the same and the precession speed is the same.
Shown the video, how to tell the difference?
So what did the red flywheel do? There is no difference in the net angular momentum of the system in either case, so it did the same thing in both cases, nothing.
I am pointing out the inconsistency I see in your definition of precession as being a different form of rotation.If I may try to see what you are saying. I observe the contraption rotating about the red axis, it is either spinning or precessing and these are different.
If it is precessing that is because I am exerting equal and opposite torques about the blue axis.
If it is spinning, that is because the equal and opposite torques are being generated by rotating it about the red axis with an external torque.
No I have got that wrong. There cannot be an external torque spinning it, that would increase the spin speed over time. Inertia?
To calculate Gyroscope torque There is a formula. The angular velocity of the Gyroscope is given as rads/sec. The precession is also given in rads/sec. Same units?
Can multiply spin by precession?
for me, rotation is a kinematic quantity, it is defined without forces and torques. Let’s say, that rotation is a transformation, or a series of transformations. It doesn’t matter, whether it is a steady or constantly changing rotation, both could be described as a series of successive rotations about some steady or instantaneous axis.
The precessional motion of a gyro can be quite steady. In this case it looks like steady rotation, and it is a rotation, it has angular velocity and a moment of inertia, therefore it has angular momentum too.
The distinction of let's say "standard" rotation and "precessional" rotation is somewhat exotic to me. Could you give me some literature references, where this is discussed in detail?
Quote from: Momentus on Yesterday at 15:25:18Forced Precession. Or Induced torque.Tb=JΩyΩrTb is the torque at the blue axis in Nm Ωy is the angular velocity about the yellow axis in rad/sec Gyroscope spinΩr is the angular velocity about the red axis in rad/sec Precession
Exactly so. This is what I was talking about here:Quote from: HalcYes, there is torque exerted on each gyro, but not along the red axisYes, Tb on one gyro (gN say) is significant, probably much larger magnitude than what either motor is putting out, especially in the steady state where neither motor is exerting any torque at all. Where is the reaction for that torque? Our assembly A doesn’t start rotating about any blue axis even though it is free to.
Clockwise isn’t a direction without specification of a PoV. Your statement lacks directions for all three vectors. Be precise.Anyway, yes, there is a torque about the blue axis and thus it precesses (or rotates, if you ask Miklos) about the red axis, exactly as we observe.
Very good. Equal and opposite torque about the couple, so no net torque on assembly A. This is why it has no more resistance to rotation with the gyros spinning or not. You’d not be able to tell from holding it if they gyros were spinning. Listening would be your best bet.
The red wheel doesn’t remain unmoved because something had to get assembly A spinning in the first place. Without that, there’s no precession of the gyros and no blue torque. But such motion is real rotation, which continues once torque is removed. Precession doesn’t do that, so assembly A spins and has angular momentum about the red axis, and the red wheel has equal and opposite angular momentum about the same axis.
The device is in two halves which consists of the assembly A and the red flywheel R, both of which spin along the red axis, with say R having positive spin and A having negative spin.
With a light frame and heavy spherical gyroscopes spinning in equal and opposite directions
You ask where is the reaction to the torque applied at the blue axis of the gyroscope which is spinning about the yellow axis. You ask because you do not know?
But pleased that you managed to solve the difficult question of POV without my help.
You also understand that there is clockwise movement around the red axis. You accept that the second gyroscope also moves in the same way, about the same axis.
Quote from: HalcYou’d not be able to tell from holding it if they gyros were spinning. Listening would be your best bet. And that because they are moving in the same direction, you would not need to listen, you would see the difference?
You’d not be able to tell from holding it if they gyros were spinning. Listening would be your best bet.
You defined assembly A.
That is component A.
The two gyroscope are both moving in the same direction,
reacting the equal and opposite torques applied at the blue axis.
You have agreed that this is the case. The light frame is attached to the gyroscopes and thus rotates with them all driven by the torque applied at the blue axis. It is an applied torque. It is reacted by orthogonal rotation.
For gyroscopes spin is defined, but precession is often defined as a change in inclination of the spin axis which probably covers most situations.
Generally, precession of a gyroscope is taken to mean the response to an input rotation or a torque/couple/moment,
but the OP is using it here to refer to the input (rather than the gyroscopic precession) without qualifying the term eg input precession. This is leading to some confusing statements and lack of clear thinking.
In this system the red axis plays the part of the rolling motion, waves broadside will rotate the (yellow) flywheel axle around the red axis (ok, input precession) and the flywheel will respond by trying to pitch - gyroscopic precession- around the blue axis in either direction depending on the direction of rotation, thus the precession axis is across the boat - side to side (perpendicular to the plane of the frame in assembly A, blue axis).
In the real world system the precession axis is provided with a brake, if the brake is fully released the flywheel will pitch (precess) freely and there is a resulting torque that directly opposes the rolling motion (red axis), however it is almost instantaneous and of such force that is can damage the bearings and gyro mountings. If the brake is locked the flywheel cannot precess and there is no roll-opposing torque. So in the real world system the brake is set to provide controlled precession by applying a negative torque to the precession axis,
Although you can use 2 flywheels, in the OP’s model the axles of both of these are locked to the frame and unable to precess,
Although you can use 2 flywheels, in the OP’s model the axles of both of these are locked to the frame and unable to precess, so no roll-opposing torque on the red axis results. Because the gyroscopic precession axis is locked it doesn't matter whether the flywheels are spinning or not, whether there is 1 or 2, or whether they are co-rotating or counterrotating.
The OP claims anomalous motion, but it is not clear what this is. He has not provided videos or even photos, so there is some doubt that the model exists other than as a drawing.
Quote from: Miklos on 15/09/2020 18:16:23The distinction of let's say "standard" rotation and "precessional" rotation is somewhat exotic to me. Could you give me some literature references, where this is discussed in detail?