From: "Mel Bartels" 
To: 
Cc: 
Reply-To: "Mel Bartels" 


I've had a few more minutes to think about the three axis mounts.

First of all, the third axis rate of movement while tracking to keep a
constant field rotation angle does vary, but not very much and for short
periods of time is essentially unchanging.  This means that if the third
axis is restricted to helping keep field rotation constant while tracking,
that the motor only needs very little dynamic range (ie, simple
halfstepping stepper motor).

For instance, here are the 3 axis distances to move while tracking an
object starting in the east over 6 hours time, each set of numbers is per
hour:

Test of AltAltAz tracking
please enter Ax3 deg (horizon point that the primary axis is aimed towards) 0
please enter altitude deg 30
please enter azimuth deg 100
please enter the time interval between position readouts in seconds 3600
please enter the # of intervals desired 6 distances to move for 6
consecutive 3600 second intervals... holding field rotation angle=         
             47.21813711761519
delta deg ax3 (rotation about sky's zenith)=        8.957802848943809
delta deg az (primary altalt axis aimed at horiz)=  15.469727658391836
delta deg alt (right angle to primary altalt axis)= 7.847275671802163
iterations 134
...
holding field rotation angle=                       47.21813711761519
delta deg ax3 (rotation about sky's zenith)=        7.586029939519961
delta deg az (primary altalt axis aimed at horiz)=  9.402466614836491 delta
deg alt (right angle to primary altalt axis)= -1.3649568606296518
iterations 42
...
holding field rotation angle=                       47.21813711761519
delta deg ax3 (rotation about sky's zenith)=        7.3495452720632946
delta deg az (primary altalt axis aimed at horiz)=  6.586007874567257 delta
deg alt (right angle to primary altalt axis)= -6.797130538655754 iterations
49
...
holding field rotation angle=                       47.21813711761519
delta deg ax3 (rotation about sky's zenith)=        7.715979585669051
delta deg az (primary altalt axis aimed at horiz)=  5.362122327063121 delta
deg alt (right angle to primary altalt axis)= -10.235129045467168
iterations 51
...
holding field rotation angle=                       47.21813711761519
delta deg ax3 (rotation about sky's zenith)=        8.549141962652502
delta deg az (primary altalt axis aimed at horiz)=  4.970736262929184 delta
deg alt (right angle to primary altalt axis)= -11.792463518022569
iterations 53
...
holding field rotation angle=                       47.21813711761519
delta deg ax3 (rotation about sky's zenith)=        9.792195761512884
delta deg az (primary altalt axis aimed at horiz)=  5.089419544383746 delta
deg alt (right angle to primary altalt axis)= -11.369678969464278
iterations 50
...

Secondly, in thinking about how to handle 3 axis coordinate translations
between the alt-alt-az coordinates and celestial ra-dec coordinates, I am
coming to the feeling that we will need two coordinate translation matrices
and 3 stars to init.

The first two stars are done with traditional alt-az and no movement at all
in the third axis.  Next, the alt axis is frozen and only the az and third
axis are used to center a third star.  It and the second star from the
first init pair form the alignment or initialization pair for the third
axis coupled to the second axis.  So you can have the full range of Z1 Z2
Z3 errors and corrections for both alt-az and az-third axis coordinate
transforms.

If the third axis is restricted to tracking purposes only, and is reset
periodically, then the second coordinate transform can largely be ignored
and one simply goes with the Z0 Z1 Z2 Z3 errors that we were talking about.

Mel Bartels

--- BBBS/NT v4.01 Flag-4