Gradient of a Vector Function in Other Co-ordinate Systems

[DylanB]

Homework Statement

I am trying to figure out how to take the gradient of a vector function in polar and spherical co-ordinates.

Homework Equations

The Attempt at a Solution

I am aware of how the gradient of a vector function in cartesian co-ords looks, simply the second order tensor


$$(\boldsymol{\nabla}\mathbf F)_{ij} = \frac{\partial F_i(\boldsymbol x)}{\partial x_j}$$


I am having trouble extending this idea to polar and spherical co-ords. The del operator is easy enough to derive in different co-ordinates but finding the second order tensor I am having difficulties.

 

[jca]

Any luck figuring out how to take a gradient of a vector field in spherical coordinates? I am also stumped on this and would appreciate any insight you have. Thanks!