Math question

[Darien]

How do I go about integrating dl of a sphere in spherical coordinates?

I don't remember the formula or how to do it 😱 I've been so used to integrating over a circle to get 2*pi*s that I've forgotten how to solve for any other cases.

Thanks in advance!

 

[KLin]

ummm, 42?

 

[Darien]

bump

 

[raptor13]

You have three coordinates when dealing with spherical coordinates. You've got theta and r, just like in radial coordinates, with the addition of phi which is the angle from the z-axis measured positive downward. Phi is always between (or equal to) 0 and pi radians.

So to get the volume of a sphere, you do triple integration with respect to phi between 0 and pi, theta between 0 and 2*pi, and 0 and r. Anything else you need to find such as partial volumes, surface areas, etc., can be found by varying your limits of theta, phi, and r.

 

[Darien]

Right. But I don't need the volume. I need to compute a length. So are you saying I change one of the limits of integration in the triple integral to get length? That doesn't make much sense to me, when the outcome should be a distance. I know in cartesian, infinitesimal length goes something like

dl = dx*unit vector in x + dy...etc

but spherical is a different beast.

 

[MrDudeMan]

Originally posted by: Darien
Right. But I don't need the volume. I need to compute a length. So are you saying I change one of the limits of integration in the triple integral to get length? That doesn't make much sense to me, when the outcome should be a distance. I know in cartesian, infinitesimal length goes something like

dl = dx*unit vector in x + dy...etc

but spherical is a different beast.

you can shorten that to be dx*i + dy*j

dont you have your book? example problems are your friend.

 

[Darien]

Originally posted by: MrDudeMan

Originally posted by: Darien
Right. But I don't need the volume. I need to compute a length. So are you saying I change one of the limits of integration in the triple integral to get length? That doesn't make much sense to me, when the outcome should be a distance. I know in cartesian, infinitesimal length goes something like

dl = dx*unit vector in x + dy...etc

but spherical is a different beast.

you can shorten that to be dx*i + dy*j

dont you have your book? example problems are your friend.

...holy !@%$@!$@#

it was on the front cover!


😱

Thanks for all your helps guys :beer:



For future reference:

in spherical coordinates, infinitesimal length is

dl = dr*r' + r d(theta)*theta' + r*sin(theta) d(phi) phi'

where r', theta' and phi' are unit vectors