# 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 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

*(Compiled by ??)*