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I guess you would have to anchor those engines pretty deep. I would assume that even anchoring them to bedrock would simply cause unscheduled continental drift, and possibly only mountainous relocations.

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Goofing a bit, but couldn't you damn the Madeira river and then use the flow control to speed up/slow down the rotation of the earth[0]?

[0] https://en.wikipedia.org/wiki/Three_Gorges_Dam#Terrestrial_i...

Just walk down a hill to accelerate the rotation of the Earth a tiny bit. But when you need to walk up the hill again you decelerate it by the same amount. -- So building a dam preserves the rotational speed of the Earth with respect to the extent of the mass (or more exactly the angular momentum) of the retained water.

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