Coordinate system transform for antenna measuring system

[squalho]

Hello,

I have a question related to coordinate transform. If this is not the right section please feel free to move this thread.

My problem is the following: I have a positioning system to move an antenna, that allows me to perform scans according to a great circle coordinate system. Check this link out to get an idea of what I'm talking about:

http://www.ce-mag.com/archive/02/Spring/fogelle1.html

(Check "great-circle method", figures 5 and 8(a))

As you can see, the sphere surrounding the antenna being measured is scanned by controlling two angles: one is the azimuthal angle and the other is a roll angle. Therefore this coordinate system is equivalent to an equatorial coordinate system, where the roll angle represents how much every great circle is rotated with respect to the "equator", and the azimuthal angle represents one position on a given great circle. Therefore I think that the roll angle has a meaning of "altitude" and the azimuth angle has a meaning of "hour angle". Fell free to correct me if you think I am wrong.

My problem is to convert these two angles to the classical theta and phi angles of a spherical coordinates system, to map the same points on the sphere surrounding the antenna. If theta (or 90-theta) is the latitude and phi is the longitude, I want to pass from azimuth and roll to theta and phi.

I have found online formulas to convert between the two coordinate systems, but when I plug them in MATLAB they don't work quite right. In particular I am having problem figuring out what declination, right ascension, and all these sort of things are in my case. I think that in the general astronomical problems there are more variables than the ones involved in my case.

Can anybody help? I hope I explained my problem clearly enough, let me know! Thanks!

 

[jsgruszynski]

This is simply spherical transformed to spherical. Just a matter of rotations and scalings. High school trig, at worst. You could back into it using cartesian-to-spherical transform identities combined with linear transform between the coordinate frames.