Thanks for writing back.
Hmmm… been thinking hard about this. I understand what you did there, but am failing to see any relationship outside the explicit one. You took a partial derivate of the radial->cartesian coordinate conversion formula.
Working “dumbly”, I have the following at my disposal:
The partial derivatives of each spherical function with regard to the spherical coords
dFr/dr dFr/dt dFr/dp
dFt/dr dFt/dt dFt/dp
dFp/dr dFp/dt dFp/dp
The formula to convert a point from spherical to cartesian
Partial derivatives of these formulas, worked out after your hint
[b]dx/dr = sin(t)cos§
dx/dt = rcos§cos(t)
dx/dp = rsin(t)-sin§
dy/dr = sin(t)sin§
dy/dt = rsin§cos(t)
dy/dp = rsin(t)*cos§
dz/dr = cos(t)
dz/dt = -r*sin(t)
dz/dp = 0[/b]
But I’m not sure how that helps me… I need partial derivatives of functions of cartesian coords:
dFx/dx dFx/dy dFx/dz
dFy/dx dFy/dy dFy/dz
dFz/dx dFz/dy dFz/dz
But there are no such functions Fx, Fy, Fz…
I really want to learn this… I feel like I’m close to understanding. Thanks for your input!