# 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.

### 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)

## 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

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```

(Compiled by ??)

omega (last edited 2016-07-24 18:06:09 by BMittan)