How to Calculate Angles on a Sphere After Multiple Rotations?

[seuren83]

Hi,

I want to calculate the angle of 6 point on a sphere. Five points are aranged in a cross, one point in the middle, and one on each side. All outer points are delta degrees distance from the center point. Define the axis going through the center point and the center of the sphere as X. The axis going through the center of the sphere parallel to on pair of opositely placed points as Y and the a third one completing a right handed axis system.

Now I rotate the sphere by gamma about the X axis. Then I rotate around the original Y axis by alpha and then around the original Z axis by beta.

What are the angles between all five points and the original center point, call them theta1 to theta5

Without the rotation gamma, I managed to find this:

cos(gamma) = cos(alpha(+_delta))*cos(beta(+_delta))

But with the rotation around I have no clue.

The physical link is a 5 hole probe, or turbulence probe, where the angle between the points (pressure ports) and the original center point (airflow stagnation point) determines the pressure that is measured at the pressure port. This device can determine flow angles with only pressure measurements. I have to investigate the misalignment along the X axis, and I could use some help.

Thanks a lot,
Sören

 

[Chronos]

Very good, you deduced that a 3 point coordinate system does not work! You must deduce motion from 3 other points relative to your basic 3 'fixed' coordinates. Does that help?

 

[seuren83]

Thanks for the response, I forgot about my post, sorry.