Infinitesimal angular displacement ?

AI Thread Summary
The discussion focuses on proving that infinitesimal angular displacement is a vector while questioning the vector nature of non-infinitesimal angular displacements. Key properties of vectors, such as commutativity, are examined in relation to these displacements. Participants express dissatisfaction with existing proofs and seek a more satisfactory mathematical demonstration. The conversation emphasizes the need for a clear and logical proof that aligns with vector properties. Ultimately, the quest for a robust mathematical foundation for these concepts remains central to the discussion.
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How can we proved that the infinitesimal angular displacement is a vector mathematically ?

Or~how can we prove that a non-infinitesimal angular displacement is not a vector ?
 
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This sounds suspiciously like a homework question. If it is, it should really go in the "Homework and Coursework" section.

I'll get you started on this problem: what are the properties of vectors? Do non-infinitesimal angular displacements obey these properties? How about infinitesimal displacements?
 
It's NOT a homework first ~

And I am not satisfied with the proof I saw before ~

The proof I saw is based on the commutative of a vector ~

I'm now seeking for a new proof which make sense!
 
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