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Can we consider rotation of an object about an axis as an extremely complicated form of circular translation as radius becomes very small. If not, what is the reason?

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No, we cannot.

Translation in Euclidean space, any dimensional Euclidean space, is abelian (order doesn't matter) while rotation in Euclidean space, at least beyond two dimensional Euclidean space, is non-abelian (order does matter).

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  • $\begingroup$ But this isn't true for infinitely small angular rotations, they will commute $\endgroup$ Dec 10, 2022 at 17:30

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