- #1

dishwasher95

- 10

- 0

Say there's a gyroscope with moments of inertia I

_{x}, I

_{y}and I

_{z}spinning around a vertical z-axis (see attached illustration) with a given angular velocity ω

_{z}. Notice that the gyroscope is floating in space as in that there's no gravity acting on the gyroscope.

Now I apply a torque τ

_{x}around the x-axis.

The torque will introduce angular momentum L

_{x}around the x-axis.

What I want to know is, how can I determine the resisting torque τ

_{res,x}that resists the motion of the applied torque τ

_{x}?

And what is the size of the torque τ

_{y}that will occur due to the applied torque τ

_{x}?

I'm look for an analytical approach to relate the applied torque τ

_{x}to τ

_{y}and τ

_{res,x}.

I feel like I've searched the whole internet for a clear explanation but failed to find one.

If anyone would be willing to go through the theory step-by-step or just show me some literature that does I'd appreciate it immensely!

Attached is also some formulas I found online but I would love a derivation.

Thanks in advance!