Conversions Between Cartesian, Cylindrical and Spherical Coordinates

Posted by Luke on Sep 20, 2009 in Basic Electrical Engineering Concepts, Dynamics, Electromagnetic Theory, Math, Physics, Statics |
Subscribe

The 3 common methods of describing a point in a three dimensional coordinate system are Cartesian, Cylindrical and Spherical. The most simple is Cartesian but certain teachers find it necessary to use the others. There are a few simple conversions between them but first it is necessary to know their notation.

Cartesian: (x,y,z)

Cylindrical: (\rho,\phi,z)

Spherical: (r,\theta,\phi)

In most cases you will only need to work from Cartesian to Cylindrical or Spherical OR back, so I will only supply those equations. If you need to work between Cylindrical and Spherical, it would be one more simple step working from one of those, to Cartesian, then on to the other.

Cartesian \rightarrow Cylindrical:

x = \rho \cdot cos (\phi)
y = \rho \cdot sin (\phi)
z = z

Cartesian \leftarrow Cylindrical:

\rho = \sqrt{x^2 + y^2}
\phi = tan^{-1} (\frac{y}{x})
z = z

Cartesian \rightarrow Spherical:

x = r \cdot sin(\theta) \cdot cos(\phi)
y = r \cdot sin(\theta) \cdot sin(\phi)
z = r \cdot cos(\theta)

Cartesian \leftarrow Spherical:

r = \sqrt{x^2 + y^2 + z^2}
\theta = tan^{-1}(\frac{\sqrt{x^2 + y^2}}{z})
\phi = tan^{-1}(\frac{y}{x})

Plug the values from any given points into the correct equation to convert to a different type of coordinate system.

Tags: , , , ,

If you found this page useful, consider linking to it.
Simply copy and paste the code below into your web site (Ctrl+C to copy)
It will look like this: Conversions Between Cartesian, Cylindrical and Spherical Coordinates

1 Comment

Coupon Codes Peapod
Dec 12, 2011 at 11:30 pm

Some genuinely nice and useful info on this site, as well I think the style and design has got great features.


 

Engineersphere Logo

Copyright © 2012 EngineerSphere.com All rights reserved .
Sitemap      Electrical Engineer