Robert Dibley wrote:
>> In the rotation group SO(3), how can one characterize a maximal
>> neighborhood of the identity that has a unique analytic Euler
>> angle parametrization?
>
>My days of really understanding mathematical phraseology are long past I'm
>afraid, but surely there is no case which has a unique Euler representation,
>given that even the identity matrix has two representations in any given
>axis sequence.
>
I did choose the wrong word with "unique". Rather, I meant
"analytic", or free of singularities, which would also imply
one-to-one. That is, I seek maximal neighborhoods of the identity
that can be covered analtyically with an Euler-angle coordinate patch.
Surely, any sufficiently small neighborhood of the identity can be so
covered (not uniquely, but in multiple ways). How do I characterize a
largest such neighborhood.
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