I am reading the Wikipedia entry http://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates" [Broken]. There, in particular I see this:

So, I wonder, what is the rationale behind assuming that x,y,z are time-independent but [tex]\rho, \theta,\phi[/tex] suddenly depend on time even if the realtions between the two are time-independent? Can someone help me here?

Time derivative of a vector field

To find out how the vector field A changes in time we calculate the time derivatives. In cartesian coordinates this is simply:

However, in spherical coordinates this becomes:

To find out how the vector field A changes in time we calculate the time derivatives. In cartesian coordinates this is simply:

However, in spherical coordinates this becomes:

So, I wonder, what is the rationale behind assuming that x,y,z are time-independent but [tex]\rho, \theta,\phi[/tex] suddenly depend on time even if the realtions between the two are time-independent? Can someone help me here?

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