Question

write the vector r=(x,y,z) in cylindrical co-ordinates

Answer 1

i tend to confuse cyl and sph

Answer 2

http://mathworld.wolfram.com/CylindricalCoordinates.html

Answer 3

r = sqrt(x^2 + y^2)

Answer 4

so its really just puttiing it into polars and upping it to a z

Answer 5

<r> = <\(\sqrt{x^2+y^2},tan^{-1}(\frac{y}{x})\),z> .. maybe?

Answer 6

mostly i'm just confused as to whether you can write the r component of the vector in terms of x and y or if you have to convert those to being in terms of r and theta as well? would you have to do something along the lines of \[r=\sqrt{rcos\theta^2+rsin\theta^2}, \theta = arctan\frac{rsin\theta}{rcos\theta}\] or is that all extreneous anyway because r just =r after that and arctan theta just comes out to be r theta?

Answer 7

they used a bad name for the vector as i see it.

cylindars convert the rectangular into polar but on a 3d scale

Answer 8

if the vector V is defined as (x,y,z) in rectangular coords; the its cylindrical is simply its projection on the xy plane moved up to a new z

Answer 9

the projection of (x,y,z) onto the xy plane is simply z=0; or (x,y)

polar this into (r,theta) and up it back to z

Answer 10

I'm not sure I understand... This is frustrating, I used to know how to do this really well, too much time off over the summer.

Answer 11

lets start simpler then; how would you interpret (x,y) as polar coords?