Hi, I have a vector field in Cartesian coordinates where all field components depends on all three (x,y,z) coordinates. I need t express it in a specific cylindrical coordinate system where the origo of the new system is on the cartesian z-axis, -R distance from the cartesian origo, the new z-axis is the negative of the cartesian y-axis, the r-axis is the cartesian z-axis and the new theta is measured n the cartesian xz-plane. If I call the new cylindrical coordinates (rp,thetap,zp) then:

rp = Sqrt[(z+R)^2 +x^2];
thetap = ArcTan[x/(z+r)];
zp =-y

one way I can do it is by discretizing the field and do the above transformation for every point, but I would like to do it a more elegant way. Thanks ahead, János