Implement the rotations manifold also for quarternions

[kellertuer]

For Rotations(3) we could also implement the main functions using quaternions., since this is used in a lot of applications.

[sethaxen]

Does this require depending on a specific quaternion implementation?

[kellertuer]

...probably, I have not yet checked which ones we could use?

[sethaxen]

There's (at least) Quaternions.jl (the most used) and Quaternionic.jl. Quaternions is working to drop its only dependency (JuliaGeometry/Quaternions.jl#79 (comment)).

Then Rotations.jl has a 3x3 matrix whose underlying storage is a unit quaternion. This type could already be used with Manifolds.jl, but I think everything would end up being promoted to a 3x3 static array instead of working with the unit quaternions directly much.

[kellertuer]

Then maybe lets wait for that dependency to drop and then look which formulae we could easily get for our functions :)