Can anyone help with cylindrical polar coords?

[kala]

1. Homework Statement
This is a question in my classical mechanics book, and i am not very good with polar coordinates. I am suppose to fine r, phi, z in terms of x,y,z.
Basically I need to derive the cylindrical polar coordinates from the Cartesian coordinates.
The question specifically asks Find expressions for the unit vectors r,phi,z of cylindrical polar coordinates in terms of the Cartesian coordinates.





3. The Attempt at a Solution
So far I have drawn a picture of cylinder and labeled everything i could. Now I know z=z, that is no problem. I know that x=r*cos[theta] and y=r*sin[theta], I also know that r=sqrt[x^2+y^2] and i know that phi=arctan[y/x]. The only way that i know how to derive these is drawing a triangle and showing it, is there any other way, like actually deriving them?

 

[Dick]

I think drawing a triangle is exactly what you are expected to do. Well done. But why do you have both a phi and a theta floating around? There's only one angle in cylindrical coordinates.

 

[Jumblebee]

Oops, i didn't catch that before thank you, another quick question, I am suppose to differentiate these expressions with respect to time to get dr/dt, dphi/dt and dz/dt.
But i got confused on this part because i don't really understand partial differentiation, would i have like something with a dot. I don't know sorry i am confused.

 

[Dick]

If you are the original poster, you aren't supposed to be running around with two user names. If you are stop using one, ok? Those aren't partial derivatives. I'm going to take a wild guess that the original problem is given x(t), y(t) and z(t), find those derivatives? If so then just take your equations and use the product and chain rules.

 

[Jumblebee]

the question really says differentiate these expressions with respect to time to find dr/dt, dphi/dt, and dz/dt.
i guess i just don't see how to differentiate these, because aren't I differentiating with respect to t, but there isn't a t in any of the polar terms.

 

[Dick]

The only way I can interpret that is to find e.g. r'(t) as a function of x(t),x'(t),y(t),y'(t),z(t) and z'(t). Same for z(t) (easy one) and theta'(t).