[Ibex-maneuver-engineering] Pointing error, rev. 4

[Mark Tapley]

All,
	many thanks to Ken for rounding up lots of pointing vectors 
for me to play with. The attached spreadsheet (also on the SFTP site) 
compares the commanded pointing vectors as captured in the ATS files 
to the resulting pointing vector as reported in the Goat Herder for 
the same orbit. Generally the vectors should be almost parallel, but 
differ slightly because the guidance system halts a pointing maneuver 
when it gets within the deadband. This analysis is an attempt to 
figure out whether that deadband is a good offset for the commanded 
pointing vector.
	For the first lap, I normalized both vectors to make sure 
they were unit vectors, took the dot-product between the ATS 
commanded vector and the Goat-Herder resulting vector, and did an 
Arc-Cos to get the angle between them. That's plotted as "Pointing 
Error vs. Orbit Number".
	Couldn't figure out how to do a histogram neatly, so I 
kludged. The Histogram on 0.5 degree bands is shown as "Histogram of 
Pointing Errors".

	To double-check that the dot-product and arc-Cos on small 
angles wasn't causing numerical problems, I then calculated the cross 
product, and took the arc-Sin. Differences from the dot-product angle 
were tiny (<10^-12) so that was OK. Finally, I plotted the magnitudes 
of the components of the cross-product vector, expecting that they 
would be mostly in the Z axis. That appears as "Magnitudes of Cross 
Product Components", and just below it for reference are the 
components of the commanded vector, as "Magnitudes of Commanded 
Vector Components".
	The cross product vectors were not mostly Z-axis! The 
Cross-product clearly leads the commanded vector around by ~90 
degrees (ie it points along Earth velocity vector in its orbit around 
the Sun, more or less). I *think* that means the error in pointing is 
almost always mostly North of the commanded vector, which does not 
make much sense to me.
	To double-check, I plotted the difference between the ATS 
vector and the Goat vector as "Error in pointing by Component"; as 
above the difference is dominated by the Z component, which is always 
negative, meaning the achieved vector is usually mostly North of the 
commanded vector.


	Comments welcome; I'll drop this on the SFTP site and mail around.

-- 
						- Mark     210-379-4635
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