Sum of torque

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No gravity !

The gyroscope must have only one torque on it to precession correctly. So, the angular velocity of the arms must be constant. I add an external device that recover the energy from the arm like that w is constant. The gyroscope don't turn around itself in the laboratory reference without a torque on it. But it turns like that :

https://www.youtube.com/watch?v=Pjc4dIf1aWI&feature=youtu.be

I add a torque from springs (or something else) so the gyroscope does a precession, this is only its angular velocity. The torque from the blue arm is not constant in one turn so the device that recovers the energy must be precise. The blue disk must turn at the precession.

When I commute the torque (each 180° of the blue disk in the arm reference) on the gyroscope, the gyroscope will do a nutation. The angular velocity of the precesion is small and it's good. In the arm reference, the angular velocity of the gyroscope will be at -w.cos(a)-d or -w.cos(a)+d with 'd' the angular velocity of the precession. I can choose a gyroscope with a spinning wheel very high, so high that the nutation and the precession will be low if the inertia Is of the gyroscope is very high. Sure, I need to choose a torque on the gyroscope in relation with Is.

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For start the device I use 2 gyroscope with their wheel turning in the opposite direction. After, I use 2 separated gyroscopes.

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w is the angular velocity of the arm in the lab reference
d is the angular velocity of the precession of the gyroscope when it has a torque.

I'm sure that the gyrsocope don't turn in the lab reference when the gyroscope turns at -w.cos(a) in the arm reference and when the arm turns at w. If I give a torque on the gyroscope, the gyroscope will do a precession small but it exists. And maybe when the gyroscope is not exactly at -w.cos(a) in the arm reference and the arm is at w, the gyroscope don't turn in one direction but in two directions: I'm not sure about that ! So, I will change the angular velocity of the arm in the same time I will add 2 torques on the gyroscope so I can't.

Maybe like d << w and like I change the sign of the torque each 180° so each pi/w second, this is not a problem, the gyroscope can have a mean position good enough to work like I want. The modification on the angular velocity from d to w is small.

Example, with w=10 rd/s and d=0.01 rd/s with an angle of 45°, the angular velocity of the gyroscope in the arm is -7+0.01 and 7-0.01 the precession don't change the position of the gyroscope. In 1.4 turns of the arm, the gyroscope must return to its initial position.



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Second method: I friction the gyroscope and the orange disk. The orange disk increases its angular velocity in the lab reference. The gyroscope precession.

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The arm moves the center of gravity of the gyroscope and the torque from the friction change the orientation of the gyroscope.

There is an energy from friction, an energy from the rotation of the orange torus. The arm don't receive a torque.

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And without a gyroscope. There are vertical disks (green). All others disks are with a slope (like before). All the device turns at w around the black center C.

I drawn ellipses for disks because it's a top view. I drawn one blue disk alone, one orange disk alone and one green disk alone to show the side view.