= OMEGA =

||Category ?||Version 3.0||

== Description ==

This program calculates the angular velocity of a body's rotation by using the position of landmarks in subsequent images.

The images should be at least roughly registered ([[REGISTER]]) before starting.

The pointing and spacecraft position is originally determined in body-fixed space from a nominal .pck file.  Then they are transformed back to inertial space.  

If V is the vector of a landmark at time = 0 (PICNM0) then the inertial space vector V' at time = t (PICNM1) is  given by
 V' = Vcos(a) +(AxV)sin(a)/a +A(A.V)(1-cos(a))/a^2
  where A is the inertial space vector OMEGA x t and a is its magnitude with OMEGA = angular velocity.  

The program solves for A, for an offset of image PICNM1 due to relative pointing errors and for the inertial space landmark positions at t=0.  Many iterations (~100) are required for convergence (but it is very fast) and OMEGA is printed both as an inertial space vector and in RA, DEC,|OMEGA| in deg and deg/da.


=== Required Files ===
 * [[POLE.TXT]] which has an initial guess for the RA/DEC of omega and its magnitude in deg/da.
 * [[PICTLIST.TXT]]
 * [[LMRKLIST.TXT]]

=== Inputs ===
 * The image name of two images that have some common landmarks in them
 * Option to do additional iterations
 * Option to update the SCOBJ and C vectors in the [[SUMFILES]]


=== Outputs ===
 * <imagename>_ROT.TXT - Log of the translation of each common landmark from inertial to body-fixed frame.
 * Standard out - showing 
  * Omega value
  * RA/DEC calculated for the angular momentum vector, as well as the rotate rate in degrees per day
  * the difference in time between the two image (in ET)

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== Using OMEGA ==

Here is a sample of the standard input:

{{{
$ omega
 Input PICNM0
P601293196F2
 Input PICNM1
P601293203F2

OMEGA:                  0.10196E-04    0.17130E-03   -0.36799E-03


                       ALPHA                          DP1            DL1
       -0.00020        0.00138       -0.00247       -0.05370        0.03372

  -1.3347563804838266E-004

 Iterate? (y/n)
n
        0.02842        0.01714

OMEGA:                 -0.28363E-04    0.19784E-03   -0.35343E-03
ET1 - ET0:                  7.00000
RA DEC DEG/DA:        98.15845      -60.51164     2009.99984

 Return to iteration? (y/n)
n
 Update SUMFILE? (y/n)
n
}}}


Here is a sample output file P601293196F2_ROT.TXT:
{{{
 PICNM0 = P601293196F2  PICNM1 = P601293203F2

                              INERTIAL                                    BODY FIXED

EE0001        0.79740E-01   -0.24443E+00   -0.76561E-01   -0.24352E-01    0.26146E+00   -0.28265E-01
EE0002        0.76654E-01   -0.24740E+00   -0.76961E-01   -0.28215E-01    0.26180E+00   -0.28335E-01
EE0003        0.72600E-01   -0.24614E+00   -0.78760E-01   -0.31991E-01    0.26251E+00   -0.28429E-01
EE0004        0.69034E-01   -0.24720E+00   -0.79739E-01   -0.35877E-01    0.26275E+00   -0.28361E-01
EE0006        0.79252E-01   -0.24506E+00   -0.73033E-01   -0.24417E-01    0.26092E+00   -0.32141E-01
EE0007        0.75892E-01   -0.24655E+00   -0.73990E-01   -0.28216E-01    0.26158E+00   -0.32223E-01
...

OMEGA:                 -0.47507E-04    0.15800E-03   -0.37100E-03
RA DEC DEG/DA:         106.73459      -66.02445     2009.99984
ET1 - ET0:               7.00000
Rotation:                0.16285
IMAX:                        76
dP, dL, dS:            -0.91703E+00    0.51699E+00   -0.25762E-03

Body fixed frame:        87.19928      -64.78164     -115.42772

    0.2404600643D+00   -0.3024911368D+01    0.2313284431D+01   SCOBJ
    0.6384185077D+00   -0.4531136654D+00   -0.6280592064D+00   CX
    0.7669571811D+00    0.4425514816D+00    0.4690669420D+00   CY
    0.6479576942D-01   -0.7738450699D+00    0.6360038956D+00   CZ
   -0.5260644620D+00    0.8478532108D+00    0.6696761722D-01   SZ
}}}

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''(Compiled by ??)''

CategoryPrograms