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I have a controller with a MEMS gyroscope on it. Is there any difference if I put gyroscope not in center of the mass? Will be gyroscope drift increase?

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No, because the rotational motion is shared with the entire body and it not location dependent. You measured rates would be identical regardless of location.

As a side note, a body will not necessarily rotate about the center of mass, even if it is in free motion. See https://physics.stackexchange.com/a/201139/392 for more detals.

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