Looking for a good webpage with different coordinate systesms

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In summary, the conversation is about finding a website with a list of different transformations, specifically for polar and ellipsoidal coordinates. The question then focuses on the best approach for integrating the volume of an ellipsoid, with one suggestion being to use spherical coordinates and the jacobian determinant. However, it is noted that the resulting integral may not be aesthetically pleasing and the possibility of using other ellipsoidal coordinates is brought up.
  • #1
foges
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Anyone have a good link to a site explaining the different coordinate systems and the jacobian determinant for each of them. Thanks

EDIT: I actually just need a website wiht a list of the different transformations ie.
polar:
x = u*cos(v)
y = u*sin(v)
[tex] v \in [0,2\pi], u \in [0,radius] [/tex]
J = r
 
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  • #2
Seems like no one has a link. Could someone maybe explain to me how i would best go about integrating the volume of a elipsoid then...
Elipsoid: [tex](\frac{x^2}{a^2}) + (\frac{y^2}{b^2}) + (\frac{z^2}{c^2}) = 1[/tex]

I'd go about it with spherical coordinates and the jacobian determinant [tex]r^2\sin(\theta)[/tex], but the integral you end up with isn't exactly prety. Are there any elipsoidal coordinates that are better suited?
 

Related to Looking for a good webpage with different coordinate systesms

1. What is a coordinate system?

A coordinate system is a method of representing and identifying locations on a planar or curved surface. It is typically composed of a set of axes, a reference point, and units of measurement.

2. How many types of coordinate systems are there?

There are many different types of coordinate systems, but they can generally be grouped into two categories: Cartesian (or rectangular) coordinate systems and polar coordinate systems. Within these categories, there are multiple variations and subtypes.

3. What is the difference between Cartesian and polar coordinate systems?

In a Cartesian coordinate system, positions are represented by a set of numeric coordinates that correspond to points on orthogonal axes (usually x and y). In a polar coordinate system, positions are represented by a distance from a central point and an angle from a reference direction.

4. How do I convert between different coordinate systems?

The process of converting between different coordinate systems depends on the specific systems involved. Generally, it involves using mathematical equations or formulas to translate the coordinates from one system to another.

5. Can you recommend a good webpage for learning about different coordinate systems?

Yes, there are many good webpages that provide information and resources for learning about different coordinate systems. Some examples include Math is Fun, Math Open Reference, and Math 10.

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