- #1
tub08918
- 8
- 0
Hi everyone
My professor just asked us a question that I can't get my head around. So we have the original vector in Cartesian format, <y^2,z^2,x^2>
Then I am asked to convert to cylindrical coordinates:
z= z;
θ==arctan(z^2/y^2);
r = \sqrt(y^4+z^4)
However , I am then asked to take the divergence and curl of these items, I have the formula for both but I don't know how to fit them in!
∇⋅v=1r∂∂r(rvr)+1r∂vθ∂θ+∂vz∂z
∇×v=(1r∂vz∂θ−∂vθ∂z)r^+(∂vr∂z−∂vz∂r)θ^+(1r∂∂r(rvθ)−1r∂vr∂θ)z^
For example, for div in tems of r, 1r∂∂r(r(sqrt(z^4+y^4))) which doesn't seem to work
My professor just asked us a question that I can't get my head around. So we have the original vector in Cartesian format, <y^2,z^2,x^2>
Then I am asked to convert to cylindrical coordinates:
z= z;
θ==arctan(z^2/y^2);
r = \sqrt(y^4+z^4)
However , I am then asked to take the divergence and curl of these items, I have the formula for both but I don't know how to fit them in!
∇⋅v=1r∂∂r(rvr)+1r∂vθ∂θ+∂vz∂z
∇×v=(1r∂vz∂θ−∂vθ∂z)r^+(∂vr∂z−∂vz∂r)θ^+(1r∂∂r(rvθ)−1r∂vr∂θ)z^
For example, for div in tems of r, 1r∂∂r(r(sqrt(z^4+y^4))) which doesn't seem to work