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What would present for a gyroscope within a larger gyroscope? Any interesting behaviours? Thanks

O A
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    Maybe I'm confused by the wording, but I think it must depend on the mechanical connection between the "inner" and the "outer" gyros. It's not entirely clear what exactly a gyro inside a gyro is meant to convey. – Brick Sep 23 '19 at 17:38
  • i should have been clearer. no connection between the gyroscopes. just envisioning a huge gyroscope (say, the size of the earth) with a gyroscope somewhere within this space – O A Sep 24 '19 at 02:48

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In a three-dimensional space, only one rotation is possible. One object cannot rotate independently in two planes, because two two-dimensional planes cannot be independent in less than a four dimensional space. If you rotate an object in one plane (that often is referred to as "around one axis") and then add another rotation in another plane, both rotations just add up and the result is a single rotation in some resulting plane. Therefore two rotations in a gyroscope would end up just adding up to a single resulting rotation. This also relates to conservation of angular momentum.

The situation is different in a higher number of dimensions. For example, in four dimensions, a single object can rotate in two independent planes. So conceptually you could have something like a gyroscope inside another gyroscope there. However, with two simultaneous rotations, no axes of rotation can be defined. So supporting your gyroscopes each in its own plane, but without an axis, might be an engineering challenge.

In six dimensions, you can have either three simultaneous rotations in independent planes without axes or two rotations each with its own axis. There you could have two gyroscopes, one inside the other, rotating independently each around its own axis.

safesphere
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  • thanks for the answer. i'm going to accept this. where i'm coming from is IF the earth itself is a gyroscope - and it appears that it can be regarded as such, what are we seeing when we observe gyroscopes on earth (or, 'in' the earth system)? anyhow, i'd be interested in any further thoughts or corrections along this line of inquiry – O A Sep 24 '19 at 02:45
  • @OA A gyroscope on the Earth (or on or in any other rotating body) would maintain its own angular momentum (the direction of the axis of rotation relative to an external inertial reference frame) provided its mount is flexible enough to allow this. For example, the axis of a gyroscope initially parallel to the equator (horizontal) would be observed becoming vertical in 6 hours and horizontal again in the following 6 hours and so on. In other words, if the axis points to a star, then it would keep pointing to the same star while the star is observed going over the sky – safesphere Sep 24 '19 at 03:15
  • thanks again. this is somewhat what i was expecting; the confirmation and explanation is very helpful – O A Sep 25 '19 at 03:09