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- What is the approach to determining the resisting and precessing torque of a spinning gyroscope?

Hi,

Say there's a gyroscope with moments of inertia I

Now I apply a torque τ

The torque will introduce angular momentum L

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

And what is the size of the torque τ

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

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!

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!