| 1. | Spatial rotations alone are also Lorentz transformations they leave the spacetime interval invariant.
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| 2. | For the kinematics of rotation in three dimensions, see quaternions and spatial rotation.
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| 3. | In representation theory, this corresponds to decomposing perturbations under the group of spatial rotations.
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| 4. | Thus quaternions are a preferred method for representing spatial rotations see quaternions and spatial rotation.
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| 5. | Thus quaternions are a preferred method for representing spatial rotations see quaternions and spatial rotation.
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| 6. | It is, in fact, already the subject of the article quaternions and spatial rotation.
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| 7. | That is to say, any spatial rotation can be decomposed into a combination of principal rotations.
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| 8. | :: Quaternions are used to represent rotations in 3D and 4D space-see Quaternions and spatial rotation.
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| 9. | It is true that spatial rotations always mix two space dimensions and never mix the time with a apatial dimension.
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| 10. | The map from unit quaternions to rotations of 3D space described in quaternions and spatial rotation is also a universal cover.
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