# I How do three flywheels, one in each axis, behave?

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1. Jan 10, 2019

### Eloc Wolsniw

I have been struggling to visualize how three rotating reaction wheels on bearings and affixed to each other at 90 degree angles, one at each axis (picture the kind of 3-axis reaction devices used in satalites), would behave when torque is applied to the whole assembly. If all three reaction wheels where spinning clockwise (viewed from the outside of each wheel), how would the device precess? Would it precess at all, or would it resist torque from all directions?

2. Jan 11, 2019

### jbriggs444

The three wheels each have some angular momentum. The vector sum of these is the total angular momentum and controls how the assembly as a whole will precess under an external torque. Conclusion: No, it will not resist torque from all directions. It will act as if it had a single wheel with $\sqrt{1^2+1^2+1^2}=\sqrt{3}$ times the angular momentum. The axis of this virtual wheel will be parallel to the diagonal of an imaginary cube with a corner having the three original wheel axes as edges.

The same logic that leads to the conclusion that a single wheel precesses under an external torque applies with equal force to an arbitrarily complex rigid assembly with multiple wheels and non-zero total angular momentum.

3. Jan 12, 2019

### Eloc Wolsniw

Yes. I see it now! Thank you very much. This was really bugging me.