Ball coordinates to cartesian coordinates

[martine]

I am struggeling with the following problem:

give the x,y,z coordinates from the following ball points/vectors

1. (r, theta, phi) = (sqrt3, 3/4pi, 3/4pi)

2. (r, theta, phi) = (1, 1/6pi, 1 1/6pi)

the sollutions I found in my reader are as followed:

1. (x, y, z) = (-1/2 sqrt3, 1/2 sqrt3, -sqrt3/sqrt2)

2. (x, y, z) = 1/4 sqrt3, -1/4, 1/2 sqrt3)

can someone explain to me what was actually done here? I understand the conversion from carthesian coordinates to ball and cylinder coordinates but I can't seem to find the sollution for the other way around. Thanks a lot.

 

[Muzza]

These equations might be of some use...

 

[Galileo]

These equations might be of some use...

Yep. It seems the angles $$\theta$$ and $$\phi$$ are interchanged though.
It's funny. In my physics books the azimuthal angle is always $$\phi$$ and in most of my mathematics books it's $$\theta$$.
Oh well, guess it doesn`t matter as long as you're aware of it.

 

[ahrkron]

I would suggest that, instead of plugging this into a set of "conversion equations", you draw the situation (or even build a little model with a box) so that you see how the quantities are related. Once you do this with one problem, the second will be much easier.

 

[Muzza]

Yep. It seems the angles $$\theta$$ and $$\phi$$ are interchanged though.

It brings this up.

Unfortunately, the convention in which the symbols $$\theta$$ and $$\phi$$ are reversed is frequently used, especially in physics, leading to unnecessary confusion.

:P

 

[MiGUi]

That's because notation is not as important as meaning, but we must always specify.

Using astronomy language, I always used $$\theta$$ for "declination" (angle from vertical axe) and $$\phi$$ for "Right ascension" (angle from horizontal axe from left to right)