Spherical Coordinates Conundrum

• Oct 24th 2012, 01:02 AM
MaverickUK82
Spherical Coordinates Conundrum
Hello All,

I'm working with surface integrals in spherical coordinates.

The equation of the surface of the sphere is simply r, yes? (not to be confused with the equation of the surface area of a sphere 4.pi.r^2)

When calculating the surface of a hemisphere, the equation of the curved surface of a hemisphere remains as r (not to be confused with the surface area of the hemisphere 2.pi.r^2)?

What about the closed base of the hemisphere, how do I explain, where that is, in spherical terms? Is it in the manner that we explain a circle in cartesian coordinates, ie r = x^2 + y^2 (not to be confused with the surface area of a circle pi.r^2)

I am really struggling with the understanding of the equation of the surface - I can carry out definite integrals quite happily for most shapes to find their volume/area, but I don't understand this surface equation?

Hope someone can help.

Kindest regards,
• Oct 24th 2012, 09:11 PM
chiro
Re: Spherical Coordinates Conundrum
Hey MaverickUK82.

There are a number of ways you can go about this: you can use the stuff in vector calculus or you can set up an area integral where you map the surface to what is called a chart and all this means is that you take the surface and stick it on a flat piece of paper.

Mathematically this is just a transformation or a change of variables where your two variables are the north/south line and the east-west line where you are trying to find the area as if you took your surface and put it on a flat piece of paper like the following: