Question

Convert the vector A = xy ax - 2x ay to cylindrical system.

Answer 1

In cylindrical coordinate system

$$x=\rho \cos\phi \\y=\rho \sin\phi \\z=z$$

And also

$$a_x ​ =\cosϕa _ ρ ​ −\sinϕa _ ϕ ​ \\a_y=\sin\phi a_\rho +\cos\phi a_\phi \\$$

Putting all value we get

$$A=(ρ\cosϕ−2)ρ ^ 2 \sinϕ\cosϕa _ ρ ​ \\ −(ρ\sin ^ 2 ϕ+2\cosϕ)ρ\cosϕa _ ϕ ​$$