What happens when there is wobbly motion in General Relativity

Question

I know for a fact that when an object starts spinning, it can be described as an inertial frame. For the sake of this question, let's consider a disc with a person placed on the edges of it. Now, the disc is smoothly spinning in one direction, and the person feels an outward push (centrifugal force). But he can believe he is in an inertial frame and that there is a gravitational field pulling him away from the disc.
Now, we wobble the disc a bit.

Now the disc is still rotating in the original direction, but it has a little wobble in the other direction shown in green.
My question is: what exactly does the person experience? My intuition tells me he still feels the gravitational field from before, but now since he is wobbling in two directions, does he experience a variable gravitational field? Generally, how can we treat this as an inertial frame from the person's perspective. By introducing a variable gravitational field? Or by some other mechanism?

Tim Crosby · Accepted Answer

The wobble doesn't make any difference to the gravitational field the observer experiences if it is not subject to other external forces than centripetal force. Both are different ways of looking at the disc. The position of person outside the disc doesn't affect the person inside. If you look at the sun from its north or south pole, that doesn't affect its gravitational pull on the earth!
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For observer A, the disc is not tilted,

What happens when there is wobbly motion in General Relativity

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