When I create a vector in spherical coordinates and map it to cartesian coordinates with Physics[Vectors] package as follows,
q_:=a _r + b _theta + c _phi
I get the answer:
(a*cos(phi)*sin(theta)+b*cos(phi)*cos(theta)-c*sin(phi)) i + (a*sin(theta)*sin(phi)+b*cos(theta)*sin(phi)+c*cos(phi)) j + (-b*sin(theta)+a*cos(theta)) k
which is what I would expect.
But if I try to do that with VectorCalculus package as follows,
q := SetCoordinates(<a, b, c>, spherical)
(a*sin(b)*cos(c)) ex + (a*sin(b)*sin(c)) ey + (a*cos(b)) ez
I am confused about this!
The SetCoordinates(<a, b, c>, spherical) command outputs
q:=(a) er + (b) ephi + (c) etheta
here, a,b, and c are depicted as the components of the vector q in spherical coordinates, but when I map to cartesian coordinates, a,b, and c are treated as if they were the coordinates in spherical coordinates rather than components-- unlike ChangeBasis in Physics[Vectors] package.
Why are these two different?