Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

We get some expression in Cylindrical coordinates (r, ϕ, z ) like : expr := r*z^2*sin((1/3)*ϕ) we need to convert it into Cartesian coordinates and than back to Cylindrical coordinates. How to do such thing?

So I found something like this : eval(expr, {r = sqrt(x^2+y^2), z = z,ϕ= arctan(y, x)}) but it seems incorrect, how to correct it and how make eval to convert backwords from Cartesian to Cylindrical?

ϕ == ϕ

So I try:

R := 1; 

H := h; 

sigma[0] := sig0;

sigma := sigma[0]*z^2*sin((1/3)*`ϕ`);

toCar := eval(sigma, {r = sqrt(x^2+y^2), z = z, `ϕ` = arctan(y, x)});

toCyl := collect(eval(toCar, {x = r*cos(`ϕ`), y = r*sin(`ϕ`), z = z}), `ϕ`)

It looks close to true but look: enter image description here

why arctan(r*sin(ϕ), r*cos(ϕ)) is not shown as ϕ?

share|improve this question

1 Answer 1

up vote 1 down vote accepted

I don't speak Maple, but it looks like your eval takes you from Cartesian to cylindrical coordinates. The inverse is $x=r \cos \phi , y=r \sin \phi, z=z$. The Wikipedia link you have gives this, though using $\rho$ instead of $r$

share|improve this answer
    
Please see post update... –  Kabumbus May 18 '11 at 16:13
    
Seems to me that $\arctan\left(\frac{r\sin\phi}{r\cos\phi}\right)$ should evaluate to $\phi$, but that is Maple, not math –  Ross Millikan May 18 '11 at 16:29

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.