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I want to build a world that has its geographic poles travel like the Earth magnetic poles do. What is a plausible way to do this? (besides giving it two suns that is)

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Earth's poles already do this, so you're set. It is referred to as "nutation" (as well as "precession" and "wobble"). The effects are caused by many things, including tidal forces and, strangely enough, differences in ocean pressure. Basically, the Earth is not a perfect sphere and even if it were it has various dynamic processes going on (like the fact that the oceans are not uniformly deep, the core is molten etc) that cause it to subtly change its axis.

Now, if you want a very pronounced nutation or precession, you probably need a HUGE influence by an external body, probably to the point where tidal forces dominate anyway (see here)

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    $\begingroup$ Nutation/Precession is not the wander of the spin axis within the Earth, but rather a change in the orientation of the entire Earth that results in the spin axis pointing to a different spot in the sky. It should not be confused with true polar wander. $\endgroup$
    – Arkenstein XII
    Sep 11, 2019 at 22:32
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Geographic poles are the point where the rotational axis of the planet intersect its surface.

If you want the geographic poles to move, the rotational axis has to change.

A possible way to make it happen is to have the planet experience internal motion of large masses. This motion, altering the momentum of inertia, will move the rotational axis.

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    $\begingroup$ You can't move axis of rotation by internal mass redestribution - it is the momentum conservation law $\endgroup$
    – ksbes
    Sep 12, 2019 at 10:30

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