Thread: help with polar co-ordinates.

x = rsinAcosB
y = rsinAsinB
z = rcosA

show that, using partial derivatives that

d(x,y,z) = r^2 sinA
d(r,A,B)

Originally Posted by heroic

x = rsinAcosB
y = rsinAsinB
z = rcosA

show that, using partial derivatives that

d(x,y,z) = r^2 sinA
d(r,A,B)

Try googling

spherical polar coordinates jacobian

or even

derivation spherical polar coordinates jacobian

One hit that might be useful is here

cheers, i got upto here.

d(x,y,z) = I sinAcosB rsinAcosB -rsinAsinB I
d(r,A,B) I sinAsinB rcosAsinB rsinAcosB I
I cosA -rsinA 0 I

= [(sinAcosB)(rcosAsinB)] - [(sinAsinB)(rcosAcosB)]

but i dont know what to do next in order to show that

d(x,y,z) = r^2sinA
d(r,A,B)