Defining a new function.

[steveupson]

Gratitude and credit go to Hans Milton for creating this model in Mathematica.

 

http://community.wolfram.com//c/portal/getImageAttachment?filename=NSTF.gif&userId=93385

 

The first angle that we are concerned with is the elevation angle E. It is the angle that is formed between the equatorial plane (beige) and the elevation plane (yellow).

 

The second angle is more complicated. It is formed between a plane of longitude (green) and a "tangent" plane (blue) which lies in a conical orbit. The construction of the longitude plane is not too complicated, but its orientation is very specific.

 

The orientation of the longitude plane is such that it intersects a point on a small circle which is constructed on the surface of the sphere at a 45 degree angle. This small circle can be defined as a circle at the 45 degree latitude which has been tilted 45 degrees such that it intersects both the pole and the equator.

 

The "tangent" plane lies along the surface of a cone formed by the sphere center and the 45 degree small circle. As the elevation angle E is varied, the position of this tangent plane changes such that it remains coincident with the intersecting point on the circumference of the small circle.

 

If we call the angle that is made between the longitude plane and the tangent plane the angle α, then the object is defined by the function which expresses the relationship between the two angles, E and α. This function is the one that I have a lot of trouble with, for some reason or other. How is this function expressed?

 

It should be mentioned that, although a sphere is used for construction of the animation that is shown here, there actually is no sphere involved in the function itself. In other words, there is no two-dimensional surface involving spherical excess, or anything like that. The sphere is simply used as an aid in visualizing how the object is constructed.

 

 

[ajb]

How is this function expressed?

Have you asked Hans Milton?

[steveupson]

Have you asked Hans Milton?

Unfortunately, all posts where Hans and I collaborated over at Wolfram Forums have been deleted without explanation. The original thread was there until yesterday.

 

http://community.wolfram.com/groups/-/m/t/527829?p_p_auth=xWI25qyy

 

Has anyone else run into this issue?

 

Since I no longer have any way of contacting Hans (short of starting a new thread over there without knowing why the original has been removed), I cannot ask if he has figured it out yet. As of our last communication, he had not.

 

The model was published more than two months ago.

[steveupson]

The Mathematica model, NewSphericalTrigFunction, Nr 2, v9.cdf, Filesize: 0.057 MB, can be downloaded here:

 

http://s000.tinyupload.com/index.php?file_id=81679108911074343506