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2 sets of coordinates in EuclideanSpace?


I would like to work with 2 vectors in EuclideanSpace each having x1,y1,z1 and x2,y2,z2 coordinates. I will be needing to switch back and forth between cartesian and spherical coordinates as well.

As an example, say, (r1,0,0) -> (x1,y1,z1) while (r2,0,0)->(x2,y2,z2) in the same EuclideanSpace.

How would one work with multiple vectors (with independent coordinates) in EuclideanSpace?

Should one define 2 chart for spherical coordinates and 2 for cartesian coordinates?

Or should one create 2 different EuclideanSpace and combine them (if possible)?