Source Code

This is an attempt to recreate Luminary 99 Rev 2, otherwise known as LUM99R2, from Luminary 99 Rev 1 and ephemeris data from Luminary 116. The differences are confined to the last 10-12 lines of the CONTROLLED CONSTANTS. Luminary 99 Rev 1 source-code was transcribed from a printout in the MIT Museum, while Luminary 116 source code was transcribed from a printout belonging to Don Eyles. AGC developer James Kernan, the "rope mother" for the Apollo 11 Lunar Module's AGC, explains as follows: "At the last minute, Dan Lickly, our chief engineer, appeared with ephemerides updates and it took two tries to get it right. The result was that we created Lum99 Revision 1 and Lum99 Revision 2." It is suspected that the former is what's in the MIT Museum, and the latter is what we are trying to recreate here. As for which revision actually flew in Apollo 11, all of the other available surviving evidence points to Rev 1 rather than to Rev 2, so we're just not sure!

013906,000002:                                                                                                  ## Copyright:   Public domain.
013907,000003:                                                                                                  ## Filename:    ATTITUDE_MANEUVER_ROUTINE.agc
013908,000004:                                                                                                  ## Purpose:     Part of the source code for Luminary 1A build 099.
013909,000005:                                                                                                  ##              It is part of the source code for the Lunar Module's (LM)
013910,000006:                                                                                                  ##              Apollo Guidance Computer (AGC), for Apollo 11.
013911,000007:                                                                                                  ## Assembler:   yaYUL
013912,000008:                                                                                                  ## Contact:     Ron Burkey <info@sandroid.org>.
013913,000009:                                                                                                  ## Website:     www.ibiblio.org/apollo.
013914,000010:                                                                                                  ## Pages:       342-363
013915,000011:                                                                                                  ## Mod history: 2009-05-16 RSB  Adapted from the corresponding 
013916,000012:                                                                                                  ##                              Luminary131 file, using page 
013917,000013:                                                                                                  ##                              images from Luminary 1A.
013918,000014:                                                                                                  ##              2016-12-14 RSB  Proofed text comments with octopus/ProoferComments
013919,000015:                                                                                                  ##                              and corrected the errors found.
013920,000016:                                                                                                  ##              2017-01-19 MAS  Corrected some USER'S to USER:S
013921,000017:                                                                                                  ##              2017-03-03 RSB  Snapshot of Luminary 99 Rev 1. 
013922,000018:                                                                                                  ##              2017-03-07 RSB  Comment-text fixes noted in proofing Luminary 116.
013923,000019:                                                                                                  ##              2017-03-15 RSB  Comment-text fixes identified in 5-way
013924,000020:                                                                                                  ##                              side-by-side diff of Luminary 69/99/116/131/210.
013925,000021: 
013926,000022:                                                                                                  ## Notations on the hardcopy document read, in part:
013927,000023:                                                                                                  ##
013928,000024:                                                                                                  ##      Assemble revision 001 of AGC program LMY99 by NASA 2021112-61
013929,000025:                                                                                                  ##      16:27 JULY 14, 1969 
013930,000026: 

Page 342

013932,000028:                                                                                                  #  BLOCK 2 LGC ATTITUDE MANEUVER ROUTINE - KALCMANU
013933,000029: 
013934,000030:                                                                                                  #  MOD 2         DATE 5/1/67     BY DON KEENE
013935,000031: 
013936,000032:                                                                                                  #  PROGRAM DESCRIPTION
013937,000033: 
013938,000034:                                                                                                  #       KALCMANU IS A ROUTINE WHICH GENERATES COMMANDS FOR THE LM DAP TO CHANGE THE ATTITUDE OF THE SPACECRAFT
013939,000035:                                                                                                  #  DURING FREE FALL.  IT IS DESIGNED TO MANEUVER THE SPACECRAFT FROM ITS INITIAL ORIENTATION TO SOME DESIRED
013940,000036:                                                                                                  #  ORIENTATION SPECIFIED BY THE PROGRAM WHICH CALLS KALCMANU, AVOIDING GIMBAL LOCK IN THE PROCESS.  IN THE 
013941,000037:                                                                                                  #  MOD 2 VERSION, THIS DESIRED ATTITUDE IS SPECIFIED BY A SET OF THREE COMMANDED CDU ANGLES STORED AS 2S COMPLEMENT
013942,000038:                                                                                                  #  SINGLE PRECISION ANGLES IN THE THREE CONSECUTIVE LOCATIONS, CPHI, CTHETA, CPSI, WHERE
013943,000039: 
013944,000040:                                                                                                  #        CPHI = COMMANDED OUTER GIMBAL ANGLE
013945,000041:                                                                                                  #        CTHETA = COMMANDED INNER GIMBAL ANGLE
013946,000042:                                                                                                  #        CPSI = COMMANDED MIDDLE GIMBAL ANGLE
013947,000043: 
013948,000044:                                                                                                  #      WHEN POINTING A SPACECRAFT AXIS (E.I. X, Y, Z, THE AOT, THRUST AXIS, ETC) THE SUBROUTINE VECPOINT MAY BE
013949,000045:                                                                                                  #  USED TO GENERATE THIS SET OF DESIRED CDU ANGLES (SEE DESCRIPTION IN R60)   -
013950,000046:                                                                                                  #   WITH THIS INFORMATION KALCMANU DETERMINES THE DIRECTION OF THE SINGLE EQUIVALENT ROTATION (COF ALSO U) AND THE
013951,000047:                                                                                                  #  MAGNITUDE OF THE ROTATION (AM) TO BRING THE S/C FROM ITS INITIAL ORIENTATION TO ITS FINAL ORIENTATION.
013952,000048:                                                                                                  #  THIS DIRECTION REMAINS FIXED BOTH IN INERTIAL COORDINATES AND IN COMMANDED S/C AXES THROUGHOUT THE 
013953,000049:                                                                                                  #                   -
013954,000050:                                                                                                  #  MANEUVER.  ONCE COF AND AM HAVE BEEN DETERMINED, KALCMANU THEN EXAMINES THE MANEUVER TO SEE IF IT WILL BRING
013955,000051:                                                                                                  #                                       -
013956,000052:                                                                                                  #  THE S/C THROUGH GIMBAL LOCK.  IF SO, COF AND AM ARE READJUSTED SO THAT THE S/C WILL JUST SKIM THE GIMBAL
013957,000053:                                                                                                  #  LOCK ZONE AND ALIGN THE X-AXIS.  IN GENERAL A FINAL YAW ABOUT X WILL BE NECESSARY TO COMPLETE THE MANEUVER.
013958,000054:                                                                                                  #  NEEDLESS TO SAY, NEITHER THE INITIAL NOR THE FINAL ORIENTATION CAN BE IN GIMBAL LOCK.
013959,000055: 
013960,000056:                                                                                                  #       FOR PROPER ATTITUDE CONTROL THE DIGITAL AUTOPILOT MUST BE GIVEN AN ATTITUDE REFERENCE WHICH IT CAN TRACK.
013961,000057:                                                                                                  #  KALCMANU DOES THIS BY GENERATING A REFERENCE OF DESIRED GIMBAL ANGLES (CDUXD, CDUYD, CDUZD) WHICH ARE UPDATED
013962,000058:                                                                                                  #  EVERY ONE SECOND DURING THE MANEUVER.  TO ACHIEVE A SMOOTHER SEQUENCE OF COMMANDS BETWEEN SUCCESSIVE UPDATES,
013963,000059:                                                                                                  #  THE PROGRAM ALSO GENERATES A SET OF INCREMENTAL CDU ANGLES (DELDCDU) TO BE ADDED TO CDU DESIRED BY THE DIGITAL
013964,000060:                                                                                                  #  AUTOPILOT.  KALCMANU ALSO CALCULATES THE COMPONENT MANEUVER RATES (OMEGAPD, OMEGAQD, OMEGARD), WHICH CAN
013965,000061:                                                                                                  #                                      -
013966,000062:                                                                                                  #  BE DETERMINED SIMPLY BY MULTIPLYING COF BY SOME SCALAR (ARATE) CORRESPONDING TO THE DESIRED ROTATIONAL RATE.
013967,000063: 
013968,000064:                                                                                                  #       AUTOMATIC MANEUVERS ARE TIMED WITH THE HELP OF WAITLIST SO THAT AFTER A SPECIFIED INTERVAL THE Y AND Z
013969,000065:                                                                                                  #  DESIRED RATES ARE SET TO ZERO AND THE DESIRED CDU ANGLES (CDUYD, CDUZD) ARE SET EQUAL TO THE FINAL DESIRED CDU
013970,000066:                                                                                                  #  ANGLES (CTHETA, CPSI).  IF ANY YAW REMAINS DUE TO GIMBAL LOCK AVOIDANCE, THE FINAL YAW MANEUVER IS
013971,000067:                                                                                                  #  CALCULATED AND THE DESIRED YAW RATE SET TO SOME FIXED VALUE (ROLLRATE = + OR - 2 DEGREES PER SEC).
013972,000068:                                                                                                  #  IN THIS CASE ONLY AN INCREMENTAL CDUX ANGLE (DELFROLL) IS SUPPLIED TO THE DAP.  AT THE END OF THE YAW
013973,000069:                                                                                                  #  MANEUVER OR IN THE EVENT THAT THERE WAS NO FINAL YAW, CDUXD IS SET EQUAL TO CPHI AND THE X-AXIS DESIRED
013974,000070:                                                                                                  #  RATE SET TO ZERO.  THUS, UPON COMPLETION OF THE MANEUVER THE S/C WILL FINISH UP IN A LIMIT CYCLE ABOUT THE
013975,000071:                                                                                                  #  DESIRED FINAL GIMBAL ANGLES.
013976,000072: 
013977,000073:                                                                                                  #  PROGRAM LOGIC FLOW
013978,000074: 
013979,000075:                                                                                                  #       KALCMANU IS CALLED AS A HIGH PRIORITY JOB WITH ENTRY POINTS AT KALCMAN3 AND VECPOINT.  IT FIRST PICKS
013980,000076:                                                                                                  #  UP THE CURRENT CDU ANGLES TO BE USED AS THE BASIS FOR ALL COMPUTATIONS INVOLVING THE INITIAL S/C ORIENTATION.

Page 343

013982,000078:                                                                                                  #  IT THEN DETERMINES THE DIRECTION COSINE MATRICES RELATING BOTH THE INITIAL AND FINAL S/C ORIENTATION TO STABLE
013983,000079:                                                                                                  #                *   *                                                                               *
013984,000080:                                                                                                  #  MEMBER AXES (MIS,MFS).  IT ALSO COMPUTES THE MATRIX RELATING FINAL S/C AXES TO INITIAL S/C AXES (MFI).  THE
013985,000081:                                                                                                  #  ANGLE OF ROTATION (AM) IS THEN EXTRACTED FROM THIS MATRIX, AND TESTS ARE MADE TO DETERMINE IF
013986,000082: 
013987,000083:                                                                                                  #        A)      AM LESS THAN .25 DEGREES (MINANG)
013988,000084:                                                                                                  #        B)      AM GREATER THAN 170 DEGREES (MAXANG)
013989,000085: 
013990,000086:                                                                                                  #  IF AM LESS THAN .25 DEGREES, NO COMPLICATED AUTOMATIC MANEUVERING IS NECESSARY.  THEREFORE WE CAN SIMPLY
013991,000087:                                                                                                  #  SET CDU DESIRED EQUAL TO THE FINAL CDU DESIRED ANGLES AND TERMINATE THE JOB.
013992,000088: 
013993,000089:                                                                                                  #  IF AM IS GREATER THAN .25 DEGREES BUT LESS THAN 170 DEGREES, THE AXES OF THE SINGLE EQUIVALENT ROTATION
013994,000090:                                                                                                  #    -                                                       *
013995,000091:                                                                                                  #  (COF) IS EXTRACTED FROM THE SKEW SYMMETRIC COMPONENTS OF MFI.                       *     *
013996,000092:                                                                                                  #  IF AM GREATER THAN 170 DEGREES AN ALTERNATE METHOD EMPLOYING THE SYMMETRIC PART OF MFI (MFISYM) IS USED
013997,000093:                                                                                                  #                -
013998,000094:                                                                                                  #  TO DETERMINE COF.
013999,000095: 
014000,000096:                                                                                                  #  THE PROGRAM THEN CHECKS TO SEE IF THE MANEUVER AS COMPUTED WILL BRING THE S/C THROUGH GIMBAL LOCK.  IF
014001,000097:                                                                                                  #  SO, A NEW MANEUVER IS CALCULATED WHICH WILL JUST SKIM THE GIMBAL LOCK ZONE AND ALIGN THE S/C X-AXIS.  THIS
014002,000098:                                                                                                  #  METHOD ASSURES THAT THE ADDITIONAL MANEUVERING TO AVOID GIMBAL LOCK WILL BE KEPT TO A MINIMUM.  SINCE A FINAL
014003,000099:                                                                                                  #  P AXIS YAW WILL BE NECESSARY, A SWITCH IS RESET (STATE SWITCH 31) TO ALLOW FOR THE COMPUTATION OF THIS FINAL
014004,000100:                                                                                                  #  YAW.
014005,000101: 
014006,000102:                                                                                                  #  AS STATED PREVIOUSLY KALCMANU GENERATES A SEQUENCE OF DESIRED GIMBAL ANGLES WHICH ARE UPDATED EVERY 
014007,000103:                                                                                                  #                                                                                               -
014008,000104:                                                                                                  #  SECOND.  THIS IS ACCOMPLISHED BY A SMALL ROTATION OF THE DESIRED S/C FRAME ABOUT THE VECTOR COF.  THE NEW
014009,000105:                                                                                                  #  DESIRED REFERENCE MATRIX IS THEN,
014010,000106:                                                                                                  #         *               *       *
014011,000107:                                                                                                  #        MIS     =       MIS     DEL
014012,000108:                                                                                                  #           N+1             N
014013,000109:                                                                                                  #         *
014014,000110:                                                                                                  #  WHERE DEL IS THE MATRIX CORRESPONDING TO THIS SMALL ROTATION.  THE NEW CDU ANGLES CAN THEN BE EXTRACTED
014015,000111:                                                                                                  #        *
014016,000112:                                                                                                  #  FROM MIS.
014017,000113: 
014018,000114:                                                                                                  #  AT THE BEGINNING OF THE MANEUVER THE AUTOPILOT DESIRED RATES (OMEGAPD, OMEGAQD, OMEGARD) AND THE 
014019,000115:                                                                                                  #  MANEUVER TIMINGS ARE ESTABLISHED.  ON THE FIRST PASS AND ON ALL SUBSEQUENT UPDATES THE CDU DESIRED
014020,000116:                                                                                                  #  ANGLES ARE LOADED WITH THE APPROPRIATE VALUES AND THE INCREMENTAL CDU ANGLES ARE COMPUTED.  THE AGC CLOCKS
014021,000117:                                                                                                  #  (TIME1 AND TIME2) ARE THAN CHECKED TO SEE IF THE MANEUVER WILL TERMINATE BEFORE THE NEXT UPDATE.  IF
014022,000118:                                                                                                  #  NOT, KALCMANU CALLS FOR ANOTHER UPDATE (RUN AS A JOB WITH PRIORITY TBD) IN ONE SECOND.  ANY DELAYS IN THIS
014023,000119:                                                                                                  #  CALLING SEQUENCE ARE AUTOMATICALLY COMPENSATED IN CALLING FOR THE NEXT UPDATE.
014024,000120: 
014025,000121:                                                                                                  #  IF IT IS FOUND THAT THE MANEUVER IS TO TERMINATE BEFORE THE NEXT UPDATE A ROUTINE IS CALLED (AS A WAIT-
014026,000122:                                                                                                  #  LIST TASK) TO STOP THE MANEUVER AT THE APPROPRIATE TIME AS EXPLAINED ABOVE.
014027,000123: 

Page 344

014029,000125:                                                                                                  #  CALLING SEQUENCE
014030,000126: 
014031,000127:                                                                                                  #  IN ORDER TO PERFORM A KALCMANU SUPERVISED MANEUVER, THE COMMANDED GIMBAL ANGLES MUST BE PRECOMPUTED AND
014032,000128:                                                                                                  #  STORED IN LOCATIONS CPHI, CTHETA, CPSI.  THE USER:S PROGRAM MUST THEN CLEAR STATE SWITCH NO 33 TO ALLOW THE 
014033,000129:                                                                                                  #  ATTITUDE MANEUVER ROUTINE TO PERFORM ANY FINAL P-AXIS YAW INCURRED BY AVOIDING GIMBAL LOCK.  THE MANEUVER IS
014034,000130:                                                                                                  #  THEN INITIATED BY ESTABLISHING THE FOLLOWING EXECUTIVE JOB
014035,000131:                                                                                                  #                       *
014036,000132:                                                                                                  #        CAF     PRIO XX
014037,000133:                                                                                                  #                     --
014038,000134:                                                                                                  #        INHINT
014039,000135:                                                                                                  #        TC      FINDVAC
014040,000136:                                                                                                  #        2CADR   KALCMAN3
014041,000137:                                                                                                  #        RELINT
014042,000138: 
014043,000139:                                                                                                  #  THE USER:S PROGRAM MAY EITHER CONTINUE OR WAIT FOR THE TERMINATION OF THE MANEUVER.  IF THE USER WISHES TO
014044,000140:                                                                                                  #  WAIT, HE MAY PUT HIS JOB TO SLEEP WITH THE FOLLOWING INSTRUCTIONS
014045,000141: 
014046,000142:                                                                                                  #        L       TC      BANKCALL
014047,000143:                                                                                                  #        L+1     CADR    ATTSTALL
014048,000144:                                                                                                  #        L+2     (BAD RETURN)
014049,000145:                                                                                                  #        L+3     (GOOD RETURN)
014050,000146: 
014051,000147:                                                                                                  #  UPON COMPLETION OF THE MANEUVER, THE PROGRAM WILL BE AWAKENED AT L+3 IF THE MANEUVER WAS COMPLETED
014052,000148:                                                                                                  #  SUCCESSFULLY, OR AT L+2 IF THE MANEUVER WAS ABORTED.  THIS ABORT WOULD OCCUR IF THE INITIAL OR FINAL ATTITUDE
014053,000149:                                                                                                  #  WAS IN GIMBAL LOCK.
014054,000150: 
014055,000151:                                                                                                  #  *** NOTA BENE ***  IT IS ASSUMED THAT THE DESIRED MANEUVERING RATE (0.5, 2, 5, 10, DEG/SEC) HAS BEEN SELECTED BY
014056,000152:                                                                                                  #  KEYBOARD ENTRY PRIOR TO THE EXECUTION OF KALCMANU.
014057,000153:                                                                                                  #  IT IS ALSO ASSUMED THAT THE AUTOPILOT IS IN THE AUTO MODE.  IF THE MODE SWITCH IS CHANGED DURING THE
014058,000154:                                                                                                  #  MANEUVER, KALCMANU WILL TERMINATE VIA GOODEND WITHIN 1 SECOND SO THAT R60 MAY REQUEST A TRIM OF THE S/C ATTITUDE
014059,000155:                                                                                                  #  THIS IS THE ONLY MEANS FOR MANUALLY TERMINATING A KALCMANU SUPERVISED MANEUVER.
014060,000156:                                                                                                  #  SUBROUTINES
014061,000157: 
014062,000158:                                                                                                  #  KALCMANU USES A NUMBER OF INTERPRETIVE SUBROUTINES WHICH MAY BE OF GENERAL INTEREST.  SINCE THESE ROUTINES
014063,000159:                                                                                                  #  WERE PROGRAMMED EXCLUSIVELY FOR KALCMANU, THEY ARE NOT, AS YET, GENERALLY AVAILABLE FOR USE BY OTHER PROGRAMS.
014064,000160: 
014065,000161:                                                                                                  #  MXM3
014066,000162:                                                                                                  #  ----
014067,000163: 
014068,000164:                                                                                                  #  THIS SUBROUTINE MULTIPLIES TWO 3X3 MATRICES AND LEAVES THE RESULT IN THE FIRST 18 LOCATIONS OF THE PUSH
014069,000165:                                                                                                  #  DOWN LIST, I.E.,
014070,000166:                                                                                                  #                        ( M     M     M  )
014071,000167:                                                                                                  #                        (  0     1     2 )
014072,000168:                                                                                                  #        *               (                )              *               *
014073,000169:                                                                                                  #        M       =       ( M     M     M  )      =       M1      X       M2
014074,000170:                                                                                                  #                        (  3     4     5 )
014075,000171:                                                                                                  #                        (                )
014076,000172:                                                                                                  #                        ( M     M     M  )

Page 345

014078,000174:                                                                                                  #                        (  6     7     8 )
014079,000175:                                                                                                  #                                                                                   *
014080,000176:                                                                                                  #  INDEX REGISTER X1 MUST BE LOADED WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M1, AND X2 MUST BE
014081,000177:                                                                                                  #                                                         *
014082,000178:                                                                                                  #  LOADED WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M2.  THE ROUTINE USES THE FIRST 20 LOCATIONS OF THE PUSH
014083,000179:                                                                                                  #  DOWN LIST.  THE FIRST ELEMENT OF THE MATRIX APPEARS IN PDO.  PUSH UP FOR M .
014084,000180:                                                                                                  #                                                                            8
014085,000181:                                                                                                  #  TRANSPOS
014086,000182:                                                                                                  #  --------
014087,000183: 
014088,000184:                                                                                                  #  THIS ROUTINE TRANSPOSES A 3X3 MATRIX AND LEAVES THE RESULT IN THE PUSH DOWN LIST, I.E.,
014089,000185:                                                                                                  #  
014090,000186:                                                                                                  #        *               * T
014091,000187:                                                                                                  #        M       =       M1
014092,000188: 
014093,000189:                                                                                                  #  INDEX REGISTER X1 MUST CONTAIN THE COMPLEMENT OF THE STARTING ADDRESS FOR M1.  PUSH UP FOR THE FIRST AND SUB-
014094,000190:                                                                                                  #                         *
014095,000191:                                                                                                  #  SEQUENT COMPONENTS OF M.  THIS SUBROUTINE ALSO USES THE FIRST 20 LOCATIONS OF THE PUSH DOWN LIST.
014096,000192: 
014097,000193:                                                                                                  #  CDU TO DCM
014098,000194:                                                                                                  #  ----------
014099,000195: 
014100,000196:                                                                                                  #  THIS SUBROUTINE CONVERTS THREE CDU ANGLES IN T(MPAC) TO A DIRECTION COSINE MATRIX (SCALED BY 2) RELATING
014101,000197:                                                                                                  #  THE CORRESPONDING S/C ORIENTATIONS TO THE STABLE MEMBER FRAME.  THE FORMULAS FOR THIS CONVERSION ARE
014102,000198: 
014103,000199:                                                                                                  #        M       =       COSY COSZ
014104,000200:                                                                                                  #         0
014105,000201: 
014106,000202:                                                                                                  #        M       =       -COSY SINZ COSX + SINY SINX
014107,000203:                                                                                                  #         1
014108,000204: 
014109,000205:                                                                                                  #        M       =       COSY SINZ SINX + SINY COSX
014110,000206:                                                                                                  #         2
014111,000207: 
014112,000208:                                                                                                  #        M       =       SINZ
014113,000209:                                                                                                  #         3
014114,000210: 
014115,000211:                                                                                                  #        M       =       COSZ COSX
014116,000212:                                                                                                  #         4
014117,000213: 
014118,000214:                                                                                                  #        M       =       -COSZ SINX
014119,000215:                                                                                                  #         5
014120,000216: 
014121,000217:                                                                                                  #        M       =       -SINY COSZ
014122,000218:                                                                                                  #         6
014123,000219:                                                                                                  #        
014124,000220:                                                                                                  #        M       =       SINY SINZ COSX + COSY SINX
014125,000221:                                                                                                  #         7

Page 346

014127,000223:                                                                                                  #        M       =       -SINY SINZ SINX + COSY COSX
014128,000224:                                                                                                  #         8
014129,000225: 
014130,000226:                                                                                                  #  WHERE         X       =       OUTER GIMBAL ANGLE
014131,000227:                                                                                                  #                Y       =       INNER GIMBAL ANGLE
014132,000228:                                                                                                  #                Z       =       MIDDLE GIMBAL ANGLE
014133,000229: 
014134,000230:                                                                                                  #  THE INTERPRETATION OF THIS MATRIX IS AS FOLLOWS
014135,000231: 
014136,000232:                                                                                                  #  IF A , A , A  REPRESENT THE COMPONENTS OF A VECTOR IN S/C AXES THEN THE COMPONENTS OF THE SAME VECTOR IN
014137,000233:                                                                                                  #      X   Y   Z
014138,000234:                                                                                                  #  STABLE MEMBER AXES (B , B , B ) ARE
014139,000235:                                                                                                  #                       X   Y   Z
014140,000236: 
014141,000237:                                                                                                  #        ( B  )                  ( A  )
014142,000238:                                                                                                  #        (  X )                  (  X )
014143,000239:                                                                                                  #        (    )                  (    )
014144,000240:                                                                                                  #        (    )            *     (    )
014145,000241:                                                                                                  #        ( B  )     =      M     ( A  )
014146,000242:                                                                                                  #        (  Y )                  (  Y )
014147,000243:                                                                                                  #        (    )                  (    )
014148,000244:                                                                                                  #        ( B  )                  ( A  )
014149,000245:                                                                                                  #        (  Z )                  (  Z )
014150,000246: 
014151,000247:                                                                                                  #  THE SUBROUTINE WILL STORE THIS MATRIX IN SEQUENTIAL LOCATIONS OF ERASABLE MEMORY AS SPECIFIED BY THE CALLING
014152,000248:                                                                                                  #                                                                                                              *
014153,000249:                                                                                                  #  PROGRAM.  TO DO THIS THE CALLING PROGRAM MUST FIRST LOAD X2 WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M.
014154,000250: 
014155,000251:                                                                                                  #  INTERNALLY, THE ROUTINE USES THE FIRST 16 LOCATIONS OF THE PUSH DOWN LIST, ALSO STEP REGISTER S1 AND INDEX
014156,000252:                                                                                                  #  REGISTER X2.
014157,000253: 
014158,000254:                                                                                                  #  DCM TO CDU
014159,000255:                                                                                                  #  ----------
014160,000256:                                                                                                  #                                                                       *
014161,000257:                                                                                                  #  THIS ROUTINE EXTRACTS THE CDU ANGLES FROM A DIRECTION COSINE MATRIX (M SCALED BY 2) RELATING S/C AXIS TO
014162,000258:                                                                                                  #                                                                                  *
014163,000259:                                                                                                  #  STABLE MEMBER AXES.  X1 MUST CONTAIN THE COMPLEMENT OF THE STARTING ADDRESS FOR M.  THE SUBROUTINE LEAVES THE
014164,000260:                                                                                                  #  CORRESPONDING GIMBAL ANGLES IN V(MPAC) AS DOUBLE PRECISION 1:S COMPLEMENT ANGLES SCALED BY 2PI.  THE FORMULAS
014165,000261:                                                                                                  #  FOR THIS CONVERSION ARE
014166,000262: 
014167,000263:                                                                                                  #        Z       =       ARCSIN (M  )
014168,000264:                                                                                                  #                                 3
014169,000265: 
014170,000266:                                                                                                  #        Y       =       ARCSIN (-M /COSZ)
014171,000267:                                                                                                  #                                  6
014172,000268: 
014173,000269:                                                                                                  #  IF M  IS NEGATIVE, Y IS REPLACED BY PI SGN Y - Y
014174,000270:                                                                                                  #      0

Page 347

014176,000272:                                                                                                  #        X       =       ARCSIN (-M /COSZ)
014177,000273:                                                                                                  #                                  5
014178,000274: 
014179,000275:                                                                                                  #  IF M  IS NEGATIVE X IS REPLACED BY PI SGN X - X
014180,000276:                                                                                                  #      4
014181,000277: 
014182,000278:                                                                                                  #  THIS ROUTINE DOES NOT SET THE PUSH DOWN POINTER, BUT USES THE NEXT 8 LOCATIONS OF THE PUSH DOWN LIST AND
014183,000279:                                                                                                  #  RETURNS THE POINTER TO ITS ORIGINAL SETTING.  THIS PROCEDURE ALLOWS THE CALLER TO STORE THE MATRIX AT THE TOP OF
014184,000280:                                                                                                  #  THE PUSH DOWN LIST.
014185,000281: 
014186,000282:                                                                                                  #  DELCOMP
014187,000283:                                                                                                  #  -------
014188,000284:                                                                                                  #                                                      *
014189,000285:                                                                                                  #  THIS ROUTINE COMPUTES THE DIRECTION COSINE MATRIX (DEL) RELATING ON
014190,000286:                                                                                                  #                                                                            -
014191,000287:                                                                                                  #  IS ROTATED WITH RESPECT TO THE FIRST BY AN ANGLE, A, ABOUT A UNIT VECTOR, U.  THE FORMULA FOR THIS MATRIX IS
014192,000288: 
014193,000289:                                                                                                  #         *              *        - -T              *
014194,000290:                                                                                                  #        DEL     =       I COSA + U U  (1 - COSA) + V  SINA
014195,000291:                                                                                                  #                                                    X
014196,000292: 
014197,000293:                                                                                                  #  WHERE         *               ( 1    0    0 )
014198,000294:                                                                                                  #                I       =       ( 0    1    0 )
014199,000295:                                                                                                  #                                ( 0    0    1 )
014200,000296: 
014201,000297:                                                                                                  #                                     2                             
014202,000298:                                                                                                  #                                (  U           U  U          U  U  )
014203,000299:                                                                                                  #                                (   X           X  Y          X  Z )
014204,000300:                                                                                                  #                                (                                  )
014205,000301:                                                                                                  #                - -T            (                 2                )
014206,000302:                                                                                                  #                U U     =       ( U  U          U            U  U  )
014207,000303:                                                                                                  #                                (  Y  X          Y            Y  Z )
014208,000304:                                                                                                  #                                (                                  )
014209,000305:                                                                                                  #                                (                               2  )
014210,000306:                                                                                                  #                                ( U  U         U  U           U    )
014211,000307:                                                                                                  #                                (  Z  X         Z  Y           Z   )
014212,000308: 
014213,000309: 
014214,000310:                                                                                                  #                                (   0           -U               U  )
014215,000311:                                                                                                  #                                (                 Z               Y )
014216,000312:                                                                                                  #                *               (                                   )
014217,000313:                                                                                                  #                V       =       (  U             0              -U  )
014218,000314:                                                                                                  #                 X              (   Z                             X )
014219,000315:                                                                                                  #                                (                                   )
014220,000316:                                                                                                  #                                ( -U             U               0  )
014221,000317:                                                                                                  #                                (   Y             X                 )
014222,000318: 

Page 348

014224,000320:                                                                                                  #        -
014225,000321:                                                                                                  #        U       =       UNIT ROTATION VECTOR RESOLVED INTO S/C AXES
014226,000322:                                                                                                  #        A       =       ROTATION ANGLE
014227,000323: 
014228,000324:                                                                                                  #                         *
014229,000325:                                                                                                  #  THE INTERPRETATION OF DEL IS AS FOLLOWS
014230,000326: 
014231,000327:                                                                                                  #  IF A , A , A  REPRESENT THE COMPONENT OF A VECTOR IN THE ROTATED FRAME, THEN THE COMPONENTS OF THE SAME
014232,000328:                                                                                                  #      X   Y   Z
014233,000329:                                                                                                  #  VECTOR IN THE ORIGINAL S/C AXES (B , B , B ) ARE
014234,000330:                                                                                                  #                                    X   Y   Z
014235,000331: 
014236,000332:                                                                                                  #        ( B  )                  ( A  )
014237,000333:                                                                                                  #        (  X )                  (  X )
014238,000334:                                                                                                  #        (    )            *     (    )
014239,000335:                                                                                                  #        ( B  )     =     DEL    ( A  )
014240,000336:                                                                                                  #        (  Y )                  (  Y )
014241,000337:                                                                                                  #        (    )                  (    )
014242,000338:                                                                                                  #        ( B  )                  ( A  )
014243,000339:                                                                                                  #        (  Z )                  (  Z )
014244,000340: 
014245,000341:                                                                                                  #  THE ROUTINE WILL STORE THIS MATRIX (SCALED UNITY) IN SEQUENTIAL LOCATIONS OF ERASABLE MEMORY BEGINNING WITH
014246,000342:                                                                                                  #                                                                                              -
014247,000343:                                                                                                  #  THE LOCATION CALLED DEL.  IN ORDER TO USE THE ROUTINE, THE CALLING PROGRAM MUST FIRST STORE U (A HALF UNIT
014248,000344:                                                                                                  #  DOUBLE PRECISION VECTOR) IN THE SET OF ERASABLE LOCATIONS BEGINNING WITH THE ADDRESS CALLED COF.  THE ANGLE, A,
014249,000345:                                                                                                  #  MUST THEN BE LOADED INTO D(MPAC).
014250,000346:                                                                                                  #  
014251,000347:                                                                                                  #  INTERNALLY, THE PROGRAM ALSO USES THE FIRST 10 LOCATIONS OF THE PUSH DOWN LIST.
014252,000348: 
014253,000349:                                                                                                  #  READCDUK
014254,000350:                                                                                                  #  --------
014255,000351: 
014256,000352:                                                                                                  #  THIS BASIC LANGUAGE SUBROUTINE LOADS T(MPAC) WITH THE THREE CDU ANGLES.
014257,000353: 
014258,000354:                                                                                                  #  SIGNMPAC
014259,000355:                                                                                                  #  --------
014260,000356: 
014261,000357:                                                                                                  #  THIS IS A BASIC LANGUAGE SUBROUTINE WHICH LIMITS THE MAGNITUDE OF D(MPAC) TO + OR - DPOSMAX ON OVERFLOW.
014262,000358: 
014263,000359:                                                                                                  #  PROGRAM STORAGE ALLOCATION
014264,000360: 
014265,000361:                                                                                                  #        1)      FIXED MEMORY            1059 WORDS
014266,000362:                                                                                                  #        2)      ERASABLE MEMORY           98
014267,000363:                                                                                                  #        3)      STATE SWITCHES             3

Page 349

014269,000365:                                                                                                  #        4)      FLAGS                      1
014270,000366: 
014271,000367:                                                                                                  #  JOB PRIORITIES
014272,000368: 
014273,000369:                                                                                                  #        1)      KALCMANU                TBD
014274,000370:                                                                                                  #        2)      ONE SECOND UPDATE       TBD
014275,000371: 
014276,000372:                                                                                                  #  SUMMARY OF STATE SWITCHES AND FLAGWORDS USED BY KALCMANU.
014277,000373: 
014278,000374:                                                                                                  #        STATE           FLAGWRD 2       SETTING         MEANING
014279,000375:                                                                                                  #        SWITCH NO.      BIT NO.
014280,000376: 
014281,000377:                                                                                                  #          *
014282,000378:                                                                                                  #        31              14              0               MANEUVER WENT THROUGH GIMBAL LOCK
014283,000379:                                                                                                  #                                        1               MANEUVER DID NOT GO THROUGH GIMBAL LOCK
014284,000380:                                                                                                  #          *
014285,000381:                                                                                                  #        32              13              0               CONTINUE UPDATE PROCESS
014286,000382:                                                                                                  #                                        1               START UPDATE PROCESS
014287,000383: 
014288,000384:                                                                                                  #        33              12              0               PERFORM FINAL P-AXIS YAW IF REQUIRED
014289,000385:                                                                                                  #                                        1               IGNORE ANY FINAL P-AXIS YAW
014290,000386: 
014291,000387:                                                                                                  #        34              11              0               SIGNAL END OF KALCMANU
014292,000388:                                                                                                  #                                        1               KALCMANU IN PROCESS     USER MUST SET SWITCH BEFORE INITIATING
014293,000389: 
014294,000390:                                                                                                  #        * INTERNAL TO KALCMANU
014295,000391: 
014296,000392:                                                                                                  #  SUGGESTIONS FOR PROGRAM INTEGRATION
014297,000393: 
014298,000394:                                                                                                  #  THE FOLLOWING VARIABLES SHOULD BE ASSIGNED TO UNSWITCH ERASABLE
014299,000395: 
014300,000396:                                                                                                  #        CPHI
014301,000397:                                                                                                  #        CTHETA
014302,000398:                                                                                                  #        CPSI
014303,000399:                                                                                                  #        POINTVSM +5
014304,000400:                                                                                                  #        SCAXIS   +5
014305,000401:                                                                                                  #        DELDCDU
014306,000402:                                                                                                  #        DELDCDU1
014307,000403:                                                                                                  #        DELDCDU2
014308,000404:                                                                                                  #        RATEINDX
014309,000405: 
014310,000406:                                                                                                  #  THE FOLLOWING SUBROUTINES MAY BE PUT IN A DIFFERENT BANK
014311,000407: 
014312,000408:                                                                                                  #        MXM3

Page 350

014314,000410:                                                                                                  #        TRANSPOS
014315,000411:                                                                                                  #        SIGNMPAC
014316,000412:                                                                                                  #        READCDUK
014317,000413:                                                                                                  #        CDUTODCM
014318,000414: 

Page 351

014320,000416: 15,2050                                           BANK     15                                    
014321,000417: 22,2000                                           SETLOC   KALCMON1                              
014322,000418: 22,2000                                           BANK                                           
014323,000419: 
014324,000420: 22,2004  E6,1676                                  EBANK=   BCDU                                  
014325,000421: 
014326,000422:                                                                                                  #  THE THREE DESIRED CDU ANGLES MUST BE STORED AS SINGLE PRECISION TWOS COMPLEMENT ANGLES IN THE THREE SUCCESSIVE
014327,000423:                                                                                                  #  LOCATIONS, CPHI, CTHETA, CPSI.
014328,000424: 
014329,000425: 22,2004                                           COUNT*   $$/KALC                               
014330,000426: 22,2004           06037        KALCMAN3           TC       INTPRET                               #  PICK UP THE CURRENT CDU ANGLES AND
014331,000427: 22,2005           77634                           RTB                                            #        COMPUTE THE MATRIX FROM INITIAL S/C
014332,000428: 22,2006           44403                                    READCDUK                              #        AXES TO FINAL S/C AXES
014333,000429: 22,2007           03277                           STORE    BCDU                                  #  STORE INITIAL S/C ANGLES
014334,000430: 22,2010           51535                           SLOAD    ABS                                   #  CHECK THE MAGNITUDE OF THE DESIRED
014335,000431: 22,2011           00324                                    CPSI                                  #  MIDDLE GIMBAL ANGLE
014336,000432: 22,2012           51025                           DSU      BPL                                   
014337,000433: 22,2013           04403                                    LOCKANGL                              #  IF GREATER THAN 70 DEG ABORT MANEUVER
014338,000434: 22,2014           44724                                    TOOBADF                               
014339,000435: 22,2015           72364                           AXC,2    TLOAD                                 
014340,000436: 22,2016           03246                                    MIS                                   
014341,000437: 22,2017           03277                                    BCDU                                  
014342,000438: 22,2020           77624                           CALL                                           #  COMPUTE THE TRANSFORMATION FROM INITIAL
014343,000439: 22,2021           44410                                    CDUTODCM                              #  S/C AXES TO STABLE MEMBER AXES
014344,000440: 22,2022           72364                           AXC,2    TLOAD                                 
014345,000441: 22,2023           02230                                    MFS                                   #  PREPARE TO CALCULATE ARRAY MFS
014346,000442: 22,2024           00322                                    CPHI                                  
014347,000443: 22,2025           77624                           CALL                                           
014348,000444: 22,2026           44410                                    CDUTODCM                              
014349,000445: 22,2027           45160        SECAD              AXC,1    CALL                                  #  MIS AND MFS ARRAYS CALCULATED         $2
014350,000446: 22,2030           03246                                    MIS                                   
014351,000447: 22,2031           44326                                    TRANSPOS                              
014352,000448: 22,2032           45575                           VLOAD    STADR                                 
014353,000449: 22,2033           50457                           STOVL    TMIS       +12D                       
014354,000450: 22,2034           77626                           STADR                                          
014355,000451: 22,2035           50465                           STOVL    TMIS       +6                         
014356,000452: 22,2036           77626                           STADR                                          
014357,000453: 22,2037           74473                           STORE    TMIS                                  #  TMIS = TRANSPOSE(MIS) SCALED BY 2
014358,000454: 22,2040           75160                           AXC,1    AXC,2                                 
014359,000455: 22,2041           03303                                    TMIS                                  
014360,000456: 22,2042           02230                                    MFS                                   
014361,000457: 22,2043           77624                           CALL                                           
014362,000458: 22,2044           44312                                    MXM3                                  
014363,000459: 22,2045           45575                           VLOAD    STADR                                 
014364,000460: 22,2046           51532                           STOVL    MFI        +12D                       
014365,000461: 22,2047           77626                           STADR                                          
014366,000462: 22,2050           51540                           STOVL    MFI        +6                         
014367,000463: 22,2051           77626                           STADR                                          
014368,000464: 22,2052           75546                           STORE    MFI                                   #  MFI = TMIS MFS (SCALED BY 4)
014369,000465: 22,2053           45001                           SETPD    CALL                                  #  TRANSPOSE MFI IN PD LIST

Page 352

014371,000467: 22,2054           00023                                    18D                                   
014372,000468: 22,2055           44335                                    TRNSPSPD                              
014373,000469: 22,2056           45575                           VLOAD    STADR                                 
014374,000470: 22,2057           50457                           STOVL    TMFI       +12D                       
014375,000471: 22,2060           77626                           STADR                                          
014376,000472: 22,2061           50465                           STOVL    TMFI       +6                         
014377,000473: 22,2062           77626                           STADR                                          
014378,000474: 22,2063           74473                           STORE    TMFI                                  #  TMFI = TRANSPOSE (MFI) SCALED BY 4
014379,000475: 
014380,000476:                                                                                                  #  CALCULATE COFSKEW AND MFISYM
014381,000477: 
014382,000478: 22,2064           45345                           DLOAD    DSU                                   
014383,000479: 22,2065           03306                                    TMFI       +2                         
014384,000480: 22,2066           02233                                    MFI        +2                         
014385,000481: 22,2067           45325                           PDDL     DSU                                   #  CALCULATE COF SCALED BY 2/SIN(AM)
014386,000482: 22,2070           02235                                    MFI        +4                         
014387,000483: 22,2071           03310                                    TMFI       +4                         
014388,000484: 22,2072           45325                           PDDL     DSU                                   
014389,000485: 22,2073           03316                                    TMFI       +10D                       
014390,000486: 22,2074           02243                                    MFI        +10D                       
014391,000487: 22,2075           77666                           VDEF                                           
014392,000488: 22,2076           03326                           STORE    COFSKEW                               #  EQUALS MFISKEW
014393,000489: 
014394,000490:                                                                                                  #  CALCULATE AM AND PROCEED ACCORDING TO ITS MAGNITUDE
014395,000491: 
014396,000492: 22,2077           43345                           DLOAD    DAD                                   
014397,000493: 22,2100           02231                                    MFI                                   
014398,000494: 22,2101           02251                                    MFI        +16D                       
014399,000495: 22,2102           43225                           DSU      DAD                                   
014400,000496: 22,2103           06512                                    DP1/4TH                               
014401,000497: 22,2104           02241                                    MFI        +8D                        
014402,000498: 22,2105           03334                           STORE    CAM                                   #  CAM = (MFI0+MFI4+MFI8-1)/2 HALF SCALE
014403,000499: 22,2106           77726                           ARCCOS                                         
014404,000500: 22,2107           03336                           STORE    AM                                    #  AM=ARCCOS(CAM)        (AM SCALED BY 2)
014405,000501: 22,2110           51025                           DSU      BPL                                   
014406,000502: 22,2111           04363                                    MINANG                                
014407,000503: 22,2112           44117                                    CHECKMAX                              
014408,000504: 22,2113           77751                           TLOAD                                          #  MANEUVER LESS THAN .25 DEGREES
014409,000505: 22,2114           00322                                    CPHI                                  #  GO DIRECTLY INTO ATTITUDE HOLD
014410,000506: 22,2115           37236                           STCALL   CDUXD                                 #  ABOUT COMMANDED ANGLES
014411,000507: 22,2116           44742                                    TOOBADI                               #  STOP RATE AND EXIT
014412,000508: 
014413,000509: 22,2117           45345        CHECKMAX           DLOAD    DSU                                   
014414,000510: 22,2120           03336                                    AM                                    
014415,000511: 22,2121           04365                                    MAXANG                                
014416,000512: 22,2122           77244                           BPL      VLOAD                                 
014417,000513: 22,2123           44131                                    ALTCALC                               #  UNIT
014418,000514: 22,2124           03326                                    COFSKEW                               #  COFSKEW
014419,000515: 22,2125           77656                           UNIT                                           
014420,000516: 22,2126           03271                           STORE    COF                                   #  COF IS THE MANEUVER AXIS

Page 353

014422,000518: 22,2127           77650                           GOTO                                           #  SEE IF MANEUVER GOES THRU GIMBAL LOCK
014423,000519: 22,2130           44744                                    LOCSKIRT                              
014424,000520: 22,2131           53375        ALTCALC            VLOAD    VAD                                   #  IF AM GREATER THAN 170 DEGREES
014425,000521: 22,2132           02231                                    MFI                                   
014426,000522: 22,2133           03304                                    TMFI                                  
014427,000523: 22,2134           77762                           VSR1                                           
014428,000524: 22,2135           27304                           STOVL    MFISYM                                
014429,000525: 22,2136           02237                                    MFI        +6                         
014430,000526: 22,2137           74455                           VAD      VSR1                                  
014431,000527: 22,2140           03312                                    TMFI       +6                         
014432,000528: 22,2141           27312                           STOVL    MFISYM     +6                         
014433,000529: 22,2142           02245                                    MFI        +12D                       
014434,000530: 22,2143           74455                           VAD      VSR1                                  
014435,000531: 22,2144           03320                                    TMFI       +12D                       
014436,000532: 22,2145           03320                           STORE    MFISYM     +12D                       #  MFISYM=(MFI+TMFI)/2   SCALED BY 4
014437,000533: 
014438,000534:                                                                                                  #  CALCULATE COF
014439,000535: 
014440,000536: 22,2146           70545                           DLOAD    SR1                                   
014441,000537: 22,2147           03334                                    CAM                                   
014442,000538: 22,2150           45325                           PDDL     DSU                                   #  PDO CAM                               $4
014443,000539: 22,2151           06520                                    DPHALF                                
014444,000540: 22,2152           03334                                    CAM                                   
014445,000541: 22,2153           65204                           BOVB     PDDL                                  #  PD2 1 - CAM                           $2
014446,000542: 22,2154           21712                                    SIGNMPAC                              
014447,000543: 22,2155           03324                                    MFISYM     +16D                       
014448,000544: 22,2156           56225                           DSU      DDV                                   
014449,000545: 22,2157           00001                                    0                                     
014450,000546: 22,2160           00003                                    2                                     
014451,000547: 22,2161           65366                           SQRT     PDDL                                  #  COFZ = SQRT(MFISYM8-CAM)/1-CAM)
014452,000548: 22,2162           03314                                    MFISYM     +8D                        #                                $ ROOT 2
014453,000549: 22,2163           56225                           DSU      DDV                                   
014454,000550: 22,2164           00001                                    0                                     
014455,000551: 22,2165           00003                                    2                                     
014456,000552: 22,2166           65366                           SQRT     PDDL                                  #  COFY = SQRT(MFISYM4-CAM)/(1-CAM)  $ROOT2
014457,000553: 22,2167           03304                                    MFISYM                                
014458,000554: 22,2170           56225                           DSU      DDV                                   
014459,000555: 22,2171           00001                                    0                                     
014460,000556: 22,2172           00003                                    2                                     
014461,000557: 22,2173           55566                           SQRT     VDEF                                  #  COFX = SQRT(MFISYM-CAM)/(1-CAM)  $ROOT 2
014462,000558: 22,2174           77656                           UNIT                                           
014463,000559: 22,2175           03271                           STORE    COF                                   
014464,000560: 
014465,000561:                                                                                                  #  DETERMINE LARGEST COF AND ADJUST ACCORDINGLY
014466,000562: 
014467,000563: 22,2176           45345        COFMAXGO           DLOAD    DSU                                   
014468,000564: 22,2177           03271                                    COF                                   
014469,000565: 22,2200           03273                                    COF        +2                         
014470,000566: 22,2201           71240                           BMN      DLOAD                                 #  COFY G COFX

Page 354

014472,000568: 22,2202           44211                                    COMP12                                
014473,000569: 22,2203           03271                                    COF                                   
014474,000570: 22,2204           50025                           DSU      BMN                                   
014475,000571: 22,2205           03275                                    COF        +4                         
014476,000572: 22,2206           44266                                    METHOD3                               #  COFZ G COFX OR COFY
014477,000573: 22,2207           77650                           GOTO                                           
014478,000574: 22,2210           44242                                    METHOD1                               #  COFX G COFY OR COFZ
014479,000575: 22,2211           45345        COMP12             DLOAD    DSU                                   
014480,000576: 22,2212           03273                                    COF        +2                         
014481,000577: 22,2213           03275                                    COF        +4                         
014482,000578: 22,2214           77640                           BMN                                            
014483,000579: 22,2215           44266                                    METHOD3                               #  COFZ G COFY OR COFX
014484,000580: 
014485,000581: 22,2216           51145        METHOD2            DLOAD    BPL                                   #  COFY MAX
014486,000582: 22,2217           03330                                    COFSKEW    +2                         #  UY
014487,000583: 22,2220           44224                                    U2POS                                 
014488,000584: 22,2221           57575                           VLOAD    VCOMP                                 
014489,000585: 22,2222           03271                                    COF                                   
014490,000586: 22,2223           03271                           STORE    COF                                   
014491,000587: 22,2224           51145        U2POS              DLOAD    BPL                                   
014492,000588: 22,2225           03306                                    MFISYM     +2                         #  UX UY
014493,000589: 22,2226           44232                                    OKU21                                 
014494,000590: 22,2227           57545                           DLOAD    DCOMP                                 #  SIGN OF UX OPPOSITE TO UY
014495,000591: 22,2230           03271                                    COF                                   
014496,000592: 22,2231           03271                           STORE    COF                                   
014497,000593: 22,2232           51145        OKU21              DLOAD    BPL                                   
014498,000594: 22,2233           03316                                    MFISYM     +10D                       #  UY UZ
014499,000595: 22,2234           44744                                    LOCSKIRT                              
014500,000596: 22,2235           57545                           DLOAD    DCOMP                                 #  SIGN OF UZ OPPOSITE TO UY
014501,000597: 22,2236           03275                                    COF        +4                         
014502,000598: 22,2237           03275                           STORE    COF        +4                         
014503,000599: 22,2240           77650                           GOTO                                           
014504,000600: 22,2241           44744                                    LOCSKIRT                              
014505,000601: 22,2242           51145        METHOD1            DLOAD    BPL                                   #  COFX MAX
014506,000602: 22,2243           03326                                    COFSKEW                               #  UX
014507,000603: 22,2244           44250                                    U1POS                                 
014508,000604: 22,2245           57575                           VLOAD    VCOMP                                 
014509,000605: 22,2246           03271                                    COF                                   
014510,000606: 22,2247           03271                           STORE    COF                                   
014511,000607: 22,2250           51145        U1POS              DLOAD    BPL                                   
014512,000608: 22,2251           03306                                    MFISYM     +2                         #  UX UY
014513,000609: 22,2252           44256                                    OKU12                                 
014514,000610: 22,2253           57545                           DLOAD    DCOMP                                 
014515,000611: 22,2254           03273                                    COF        +2                         #  SIGN OF UY OPPOSITE TO UX
014516,000612: 22,2255           03273                           STORE    COF        +2                         
014517,000613: 22,2256           51145        OKU12              DLOAD    BPL                                   
014518,000614: 22,2257           03310                                    MFISYM     +4                         #  UX UZ
014519,000615: 22,2260           44744                                    LOCSKIRT                              
014520,000616: 22,2261           57545                           DLOAD    DCOMP                                 #  SIGN OF UZ OPPOSITE TO UY
014521,000617: 22,2262           03275                                    COF        +4                         

Page 355

014523,000619: 22,2263           03275                           STORE    COF        +4                         
014524,000620: 22,2264           77650                           GOTO                                           
014525,000621: 22,2265           44744                                    LOCSKIRT                              
014526,000622: 22,2266           51145        METHOD3            DLOAD    BPL                                   #  COFZ MAX
014527,000623: 22,2267           03332                                    COFSKEW    +4                         #  UZ
014528,000624: 22,2270           44274                                    U3POS                                 
014529,000625: 22,2271           57575                           VLOAD    VCOMP                                 
014530,000626: 22,2272           03271                                    COF                                   
014531,000627: 22,2273           03271                           STORE    COF                                   
014532,000628: 22,2274           51145        U3POS              DLOAD    BPL                                   
014533,000629: 22,2275           03310                                    MFISYM     +4                         #  UX UZ
014534,000630: 22,2276           44302                                    OKU31                                 
014535,000631: 22,2277           57545                           DLOAD    DCOMP                                 
014536,000632: 22,2300           03271                                    COF                                   #  SIGN OF UX OPPOSITE TO UZ
014537,000633: 22,2301           03271                           STORE    COF                                   
014538,000634: 22,2302           51145        OKU31              DLOAD    BPL                                   
014539,000635: 22,2303           03316                                    MFISYM     +10D                       #  UY UZ
014540,000636: 22,2304           44744                                    LOCSKIRT                              
014541,000637: 22,2305           57545                           DLOAD    DCOMP                                 
014542,000638: 22,2306           03273                                    COF        +2                         #  SIGN OF UY OPPOSITE TO UZ
014543,000639: 22,2307           03273                           STORE    COF        +2                         
014544,000640: 22,2310           77650                           GOTO                                           
014545,000641: 22,2311           44744                                    LOCSKIRT                              

Page 356

014547,000643:                                                                                                  #  MATRIX OPERATIONS
014548,000644: 
014549,000645: 13,2207                                           BANK     13                                    
014550,000646: 22,2000                                           SETLOC   KALCMON2                              
014551,000647: 22,2000                                           BANK                                           
014552,000648: 
014553,000649: 22,2312  E6,1676                                  EBANK=   BCDU                                  
014554,000650: 
014555,000651: 22,2312           76601        MXM3               SETPD    VLOAD*                                #  MXM3 MULTIPLIES 2 3X3 MATRICES
014556,000652: 22,2313           00001                                    0                                     #  AND LEAVES RESULT IN PD LIST
014557,000653: 22,2314           00001                                    0,1                                   #  AND MPAC
014558,000654: 22,2315           62703                           VXM*     PDVL*                                 
014559,000655: 22,2316           77776                                    0,2                                   
014560,000656: 22,2317           00007                                    6,1                                   
014561,000657: 22,2320           62703                           VXM*     PDVL*                                 
014562,000658: 22,2321           77776                                    0,2                                   
014563,000659: 22,2322           00015                                    12D,1                                 
014564,000660: 22,2323           41503                           VXM*     PUSH                                  
014565,000661: 22,2324           77776                                    0,2                                   
014566,000662: 22,2325           77616                           RVQ                                            
014567,000663: 
014568,000664:                                                                                                  #  RETURN WITH M1XM2 IN PD LIST
014569,000665: 
014570,000666: 22,2326           76601        TRANSPOS           SETPD    VLOAD*                                #  TRANSPOS TRANSPOSES A 3X3 MATRIX
014571,000667: 22,2327           00001                                    0                                     #        AND LEAVES RESULT IN PD LIST
014572,000668: 22,2330           00001                                    0,1                                   #  MATRIX ADDRESS IN XR1
014573,000669: 22,2331           62713                           PDVL*    PDVL*                                 
014574,000670: 22,2332           00007                                    6,1                                   
014575,000671: 22,2333           00015                                    12D,1                                 
014576,000672: 22,2334           77606                           PUSH                                           #  MATRIX IN PD
014577,000673: 22,2335           77776        TRNSPSPD           EXIT                                           #  ENTER WITH MATRIX AT 0 IN PD LIST
014578,000674: 22,2336           50120                           INDEX    FIXLOC                                
014579,000675: 22,2337           52013                           DXCH     12                                    
014580,000676: 22,2340           50120                           INDEX    FIXLOC                                
014581,000677: 22,2341           52017                           DXCH     16                                    
014582,000678: 22,2342           50120                           INDEX    FIXLOC                                
014583,000679: 22,2343           52013                           DXCH     12                                    
014584,000680: 22,2344           50120                           INDEX    FIXLOC                                
014585,000681: 22,2345           52015                           DXCH     14                                    
014586,000682: 22,2346           50120                           INDEX    FIXLOC                                
014587,000683: 22,2347           52005                           DXCH     4                                     
014588,000684: 22,2350           50120                           INDEX    FIXLOC                                
014589,000685: 22,2351           52015                           DXCH     14                                    
014590,000686: 22,2352           50120                           INDEX    FIXLOC                                
014591,000687: 22,2353           52003                           DXCH     2                                     
014592,000688: 22,2354           50120                           INDEX    FIXLOC                                
014593,000689: 22,2355           52007                           DXCH     6                                     
014594,000690: 22,2356           50120                           INDEX    FIXLOC                                
014595,000691: 22,2357           52003                           DXCH     2                                     

Page 357

014597,000693: 22,2360           06037                           TC       INTPRET                               
014598,000694: 22,2361           77616                           RVQ                                            
014599,000695: 
014600,000696: 15,2050                                           BANK     15                                    
014601,000697: 22,2000                                           SETLOC   KALCMON1                              
014602,000698: 22,2000                                           BANK                                           
014603,000699: 
014604,000700: 22,2362  E6,1676                                  EBANK=   BCDU                                  
014605,000701: 
014606,000702: 22,2362           00013 13563  MINANG             2DEC     0.00069375                            
014607,000703: 
014608,000704: 22,2364           17070 34343  MAXANG             2DEC     0.472222222                            
014609,000705: 
014610,000706:                                                                                                  #  GIMBAL LOCK CONSTANTS
014611,000707: 
014612,000708:                                                                                                  #  D = MGA CORRESPONDING TO GIMBAL LOCK = 60 DEGREES
014613,000709:                                                                                                  #        NGL = BUFFER ANGLE (TO AVOID DIVISIONS BY ZERO) = 2 DEGREES
014614,000710: 
014615,000711: 22,2366           15666 20443  SD                 2DEC     .433015                               #  = SIN(D)                      $2
014616,000712: 
014617,000713: 22,2370           33555 01106  K3S1               2DEC     .86603                                #  = SIN(D)                      $1
014618,000714: 
014619,000715: 22,2372           67777 77777  K4                 2DEC     -.25                                  #  = -COS(D)                     $2
014620,000716: 
014621,000717: 22,2374           04000 00000  K4SQ               2DEC     .125                                  #  = COS(D)COS(D)                $2
014622,000718: 
014623,000719: 22,2376           00216 36323  SNGLCD             2DEC     .008725                               #  = SIN(NGL)COS(D)              $2
014624,000720: 
014625,000721: 22,2400           17773 00057  CNGL               2DEC     .499695                               #  COS(NGL)                      $2
014626,000722: 
014627,000723: 22,2402           14344        LOCKANGL           DEC      .388889                               #  = 70 DEGREES
014628,000724: 
014629,000725:                                                                                                  #  INTERPRETIVE SUBROUTINE TO READ THE CDU ANGLES
014630,000726: 
014631,000727: 22,2403           30034        READCDUK           CA       CDUZ                                  #  LOAD T(MPAC) WITH CDU ANGLES
014632,000728: 22,2404           54156                           TS       MPAC       +2                         
014633,000729: 22,2405           00006                           EXTEND                                         
014634,000730: 22,2406           30033                           DCA      CDUX                                  #  AND CHANGE MODE TO TRIPLE PRECISION
014635,000731: 22,2407           16476                           TCF      TLOAD      +6                         
014636,000732: 
014637,000733: 22,2410           66370        CDUTODCM           AXT,1    SSP                                   
014638,000734: 22,2411           00003                           OCT      3                                     
014639,000735: 22,2412           00051                                    S1                                    
014640,000736: 22,2413           00001                           OCT      1                                     #  SET XR1, S1, AND PD FOR LOOP
014641,000737: 22,2414           00010                           STORE    7                                     
014642,000738: 22,2415           77601                           SETPD                                          
014643,000739: 22,2416           00001                                    0                                     
014644,000740: 22,2417           47133        LOOPSIN            SLOAD*   RTB                                   
014645,000741: 22,2420           00013                                    10D,1                                 
014646,000742: 22,2421           21576                                    CDULOGIC                              

Page 358

014648,000744: 22,2422           00013                           STORE    10D                                   #  LOAD PD WITH  0 SIN(PHI)
014649,000745: 22,2423           65356                           SIN      PDDL                                  #                2 COS(PHI)
014650,000746: 22,2424           00013                                    10D                                   #                4 SIN(THETA)
014651,000747: 22,2425           41546                           COS      PUSH                                  #                6 COS(THETA)
014652,000748: 22,2426           71300                           TIX,1    DLOAD                                 #                8 SIN(PSI)
014653,000749: 22,2427           44417                                    LOOPSIN                               #                10 COS(PSI)
014654,000750: 22,2430           00007                                    6                                     
014655,000751: 22,2431           72405                           DMP      SL1                                   
014656,000752: 22,2432           00013                                    10D                                   
014657,000753: 22,2433           10001                           STORE    0,2                                   #  C0 = COS(THETA)COS(PSI)
014658,000754: 22,2434           41345                           DLOAD    DMP                                   
014659,000755: 22,2435           00005                                    4                                     
014660,000756: 22,2436           00001                                    0                                     
014661,000757: 22,2437           41325                           PDDL     DMP                                   #  (PD6 SIN(THETA)SIN(PHI))
014662,000758: 22,2440           00007                                    6                                     
014663,000759: 22,2441           00011                                    8D                                    
014664,000760: 22,2442           72405                           DMP      SL1                                   
014665,000761: 22,2443           00003                                    2                                     
014666,000762: 22,2444           72421                           BDSU     SL1                                   
014667,000763: 22,2445           00015                                    12D                                   
014668,000764: 22,2446           10003                           STORE    2,2                                   #  C1=-COS(THETA)SIN(PSI)COS(PHI)
014669,000765: 22,2447           41345                           DLOAD    DMP                                   
014670,000766: 22,2450           00003                                    2                                     
014671,000767: 22,2451           00005                                    4                                     
014672,000768: 22,2452           41325                           PDDL     DMP                                   #  (PD7 COS(PHI)SIN(THETA)) SCALED 4
014673,000769: 22,2453           00007                                    6                                     
014674,000770: 22,2454           00011                                    8D                                    
014675,000771: 22,2455           72405                           DMP      SL1                                   
014676,000772: 22,2456           00001                                    0                                     
014677,000773: 22,2457           72415                           DAD      SL1                                   
014678,000774: 22,2460           00017                                    14D                                   
014679,000775: 22,2461           10005                           STORE    4,2                                   #  C2=COS(THETA)SIN(PSI)SIN(PHI)
014680,000776: 22,2462           77745                           DLOAD                                          
014681,000777: 22,2463           00011                                    8D                                    
014682,000778: 22,2464           10007                           STORE    6,2                                   #  C3=SIN(PSI)
014683,000779: 22,2465           77745                           DLOAD                                          
014684,000780: 22,2466           00013                                    10D                                   
014685,000781: 22,2467           72405                           DMP      SL1                                   
014686,000782: 22,2470           00003                                    2                                     
014687,000783: 22,2471           10011                           STORE    8D,2                                  #  C4=COS(PSI)COS(PHI)
014688,000784: 22,2472           41345                           DLOAD    DMP                                   
014689,000785: 22,2473           00013                                    10D                                   
014690,000786: 22,2474           00001                                    0                                     
014691,000787: 22,2475           72476                           DCOMP    SL1                                   
014692,000788: 22,2476           10013                           STORE    10D,2                                 #  C5=-COS(PSI)SIN(PHI)
014693,000789: 22,2477           41345                           DLOAD    DMP                                   
014694,000790: 22,2500           00005                                    4                                     
014695,000791: 22,2501           00013                                    10D                                   
014696,000792: 22,2502           72476                           DCOMP    SL1                                   
014697,000793: 22,2503           10015                           STORE    12D,2                                 #  C6=-SIN(THETA)COS(PSI)

Page 359

014699,000795: 22,2504           77745                           DLOAD                                          
014700,000796: 22,2505           72405                           DMP      SL1                                   #  (PUSH UP 7)
014701,000797: 22,2506           00011                                    8D                                    
014702,000798: 22,2507           41325                           PDDL     DMP                                   #  (PD7 COS(PHI)SIN(THETA)SIN(PSI)) SCALE 4
014703,000799: 22,2510           00007                                    6                                     
014704,000800: 22,2511           00001                                    0                                     
014705,000801: 22,2512           72415                           DAD      SL1                                   #  (PUSH UP 7)
014706,000802: 22,2513           77626                           STADR                                          #  C7=COS(PHI)SIN(THETA)SIN(PSI)
014707,000803: 22,2514           67760                           STORE    14D,2                                 #        +COS(THETA)SIN(PHI)
014708,000804: 22,2515           77745                           DLOAD                                          
014709,000805: 22,2516           72405                           DMP      SL1                                   #  (PUSH UP 6)
014710,000806: 22,2517           00011                                    8D                                    
014711,000807: 22,2520           41325                           PDDL     DMP                                   #  (PD6 SIN(THETA)SIN(PHI)SIN(PSI)) SCALE 4
014712,000808: 22,2521           00007                                    6                                     
014713,000809: 22,2522           00003                                    2                                     
014714,000810: 22,2523           72425                           DSU      SL1                                   #  (PUSH UP 6)
014715,000811: 22,2524           77626                           STADR                                          
014716,000812: 22,2525           67756                           STORE    16D,2                                 #  C8=-SIN(THETA)SIN(PHI)SIN(PSI)
014717,000813: 22,2526           77616                           RVQ                                            #  +COS(THETA)COS(PHI)
014718,000814: 
014719,000815:                                                                                                  #  CALCULATION OF THE MATRIX DEL......
014720,000816: 
014721,000817:                                                                                                  #         *         *           --T           *
014722,000818:                                                                                                  #        DEL = (IDMATRIX)COS(A)+UU (1-COS(A))+UX SIN(A)          SCALED 1
014723,000819:                                                                                                  #              -
014724,000820:                                                                                                  #        WHERE U IS A UNIT VECTOR (DP SCALED 2) ALONG THE AXIS OF ROTATION.
014725,000821:                                                                                                  #        A IS THE ANGLE OF ROTATION (DP SCALED 2)
014726,000822:                                                                                                  #                                            -
014727,000823:                                                                                                  #        UPON ENTRY THE STARTING ADDRESS OF U IS COF, AND A IS IN MPAC
014728,000824: 
014729,000825: 22,2527           41401        DELCOMP            SETPD    PUSH                                  #  MPAC CONTAINS THE ANGLE A
014730,000826: 22,2530           00001                                    0                                     
014731,000827: 22,2531           65356                           SIN      PDDL                                  #  PD0 = SIN(A)
014732,000828: 22,2532           41546                           COS      PUSH                                  #  PD2 = COS(A)
014733,000829: 22,2533           65302                           SR2      PDDL                                  #  PD2 = COS(A)                          $8
014734,000830: 22,2534           41021                           BDSU     BOVB                                  
014735,000831: 22,2535           06520                                    DPHALF                                
014736,000832: 22,2536           21712                                    SIGNMPAC                              
014737,000833: 22,2537           77725                           PDDL                                           #  PD4 = 1-COS(A)
014738,000834: 
014739,000835:                                                                                                  #  COMPUTE THE DIAGONAL COMPONENTS OF DEL
014740,000836: 
014741,000837: 22,2540           03271                                    COF                                   
014742,000838: 22,2541           41316                           DSQ      DMP                                   
014743,000839: 22,2542           00005                                    4                                     
014744,000840: 22,2543           52415                           DAD      SL3                                   
014745,000841: 22,2544           00003                                    2                                     
014746,000842: 22,2545           77604                           BOVB                                           
014747,000843: 22,2546           21712                                    SIGNMPAC                              

Page 360

014749,000845: 22,2547           16231                           STODL    KEL                                   #  UX UX(1-COS(A)) +COS(A)               $1
014750,000846: 22,2550           03273                                    COF        +2                         
014751,000847: 22,2551           41316                           DSQ      DMP                                   
014752,000848: 22,2552           00005                                    4                                     
014753,000849: 22,2553           52415                           DAD      SL3                                   
014754,000850: 22,2554           00003                                    2                                     
014755,000851: 22,2555           77604                           BOVB                                           
014756,000852: 22,2556           21712                                    SIGNMPAC                              
014757,000853: 22,2557           16241                           STODL    KEL        +8D                        #  UY UY(1-COS(A)) +COS(A)               $1
014758,000854: 22,2560           03275                                    COF        +4                         
014759,000855: 22,2561           41316                           DSQ      DMP                                   
014760,000856: 22,2562           00005                                    4                                     
014761,000857: 22,2563           52415                           DAD      SL3                                   
014762,000858: 22,2564           00003                                    2                                     
014763,000859: 22,2565           77604                           BOVB                                           
014764,000860: 22,2566           21712                                    SIGNMPAC                              
014765,000861: 22,2567           02251                           STORE    KEL        +16D                       #  UZ UZ(1-COS(A)) +COS(A)               $1
014766,000862: 
014767,000863:                                                                                                  #  COMPUTE THE OFF DIAGONAL TERMS OF DEL
014768,000864: 
014769,000865: 22,2570           41345                           DLOAD    DMP                                   
014770,000866: 22,2571           03271                                    COF                                   
014771,000867: 22,2572           03273                                    COF        +2                         
014772,000868: 22,2573           72405                           DMP      SL1                                   
014773,000869: 22,2574           00005                                    4                                     
014774,000870: 22,2575           41325                           PDDL     DMP                                   #  D6     UX UY (1-COS A)                $4
014775,000871: 22,2576           03275                                    COF        +4                         
014776,000872: 22,2577           00001                                    0                                     
014777,000873: 22,2600           43206                           PUSH     DAD                                   #  D8    UZ SIN A                        $4
014778,000874: 22,2601           00007                                    6                                     
014779,000875: 22,2602           41112                           SL2      BOVB                                  
014780,000876: 22,2603           21712                                    SIGNMPAC                              
014781,000877: 22,2604           16237                           STODL    KEL        +6                         
014782,000878: 22,2605           62421                           BDSU     SL2                                   
014783,000879: 22,2606           77604                           BOVB                                           
014784,000880: 22,2607           21712                                    SIGNMPAC                              
014785,000881: 22,2610           16233                           STODL    KEL        +2                         
014786,000882: 22,2611           03271                                    COF                                   
014787,000883: 22,2612           41205                           DMP      DMP                                   
014788,000884: 22,2613           03275                                    COF        +4                         
014789,000885: 22,2614           00005                                    4                                     
014790,000886: 22,2615           65352                           SL1      PDDL                                  #  D6    UX UZ (1-COS A)                 $4
014791,000887: 22,2616           03273                                    COF        +2                         
014792,000888: 22,2617           41405                           DMP      PUSH                                  #  D8    UY SIN(A)
014793,000889: 22,2620           00001                                    0                                     
014794,000890: 22,2621           62415                           DAD      SL2                                   
014795,000891: 22,2622           00007                                    6                                     
014796,000892: 22,2623           77604                           BOVB                                           
014797,000893: 22,2624           21712                                    SIGNMPAC                              
014798,000894: 22,2625           16235                           STODL    KEL        +4                         #  UX UZ (1-COS(A))+UY SIN(A)

Page 361

014800,000896: 22,2626           62421                           BDSU     SL2                                   
014801,000897: 22,2627           77604                           BOVB                                           
014802,000898: 22,2630           21712                                    SIGNMPAC                              
014803,000899: 22,2631           16245                           STODL    KEL        +12D                       #  UX UZ (1-COS(A))-UY SIN(A)
014804,000900: 22,2632           03273                                    COF        +2                         
014805,000901: 22,2633           41205                           DMP      DMP                                   
014806,000902: 22,2634           03275                                    COF        +4                         
014807,000903: 22,2635           00005                                    4                                     
014808,000904: 22,2636           65352                           SL1      PDDL                                  #  D6    UY UZ (1-COS(A))                $ 4
014809,000905: 22,2637           03271                                    COF                                   
014810,000906: 22,2640           41405                           DMP      PUSH                                  #  D8    UX SIN(A)
014811,000907: 22,2641           00001                                    0                                     
014812,000908: 22,2642           62415                           DAD      SL2                                   
014813,000909: 22,2643           00007                                    6                                     
014814,000910: 22,2644           77604                           BOVB                                           
014815,000911: 22,2645           21712                                    SIGNMPAC                              
014816,000912: 22,2646           16247                           STODL    KEL        +14D                       #  UY UZ(1-COS(A)) +UX SIN(A)
014817,000913: 22,2647           62421                           BDSU     SL2                                   
014818,000914: 22,2650           77604                           BOVB                                           
014819,000915: 22,2651           21712                                    SIGNMPAC                              
014820,000916: 22,2652           02243                           STORE    KEL        +10D                       #  UY UZ (1-COS(A)) -UX SIN(A)
014821,000917: 22,2653           77616                           RVQ                                            
014822,000918: 
014823,000919:                                                                                                  #  DIRECTION COSINE MATRIX TO CDU ANGLE ROUTINE
014824,000920:                                                                                                  #  X1 CONTAINS THE COMPLEMENT OF THE STARTING ADDRESS FOR MATRIX (SCALED 2)
014825,000921:                                                                                                  #  LEAVES CDU ANGLES SCALED 2PI IN V(MPAC)
014826,000922:                                                                                                  #  COS(MGA) WILL BE LEFT IN S1 (SCALED 1)
014827,000923: 
014828,000924:                                                                                                  #  THE DIRECTION COSINE MATRIX RELATING S/C AXES TO STABLE MEMBER AXES CAN BE WRITTEN AS***
014829,000925: 
014830,000926:                                                                                                  #        C  = COS(THETA) COS(PSI)
014831,000927:                                                                                                  #         0
014832,000928: 
014833,000929:                                                                                                  #        C  = -COS(THETA) SIN(PSI) COS(PHI) + SI (THETA) SIN(PHI)
014834,000930:                                                                                                  #         1
014835,000931: 
014836,000932:                                                                                                  #        C  = COS(THETA) SIN(PSI) SIN(PHI) + S N(THETA) COS(PHI)
014837,000933:                                                                                                  #         2
014838,000934: 
014839,000935:                                                                                                  #        C  = SIN(PSI)
014840,000936:                                                                                                  #         3
014841,000937: 
014842,000938:                                                                                                  #        C  = COS(PSI) COS(PHI)
014843,000939:                                                                                                  #         4
014844,000940: 
014845,000941:                                                                                                  #        C  = -COS(PSI) SIN(PHI)
014846,000942:                                                                                                  #         5
014847,000943: 
014848,000944:                                                                                                  #        C  = -SIN(THETA) COS(PSI)
014849,000945:                                                                                                  #         6
014850,000946: 
014851,000947:                                                                                                  #        C  = SIN(THETA) SIN(PSI) COS(PHI) + COS THETA) SIN(PHI)
014852,000948:                                                                                                  #         7
014853,000949: 
014854,000950:                                                                                                  #        C  = -SIN(THETA) SIN(PSI) SIN(PHI) + CO (THETA)COS(PHI)
014855,000951:                                                                                                  #         8

Page 362

014857,000953: 
014858,000954:                                                                                                  #  WHERE PHI = OGA
014859,000955:                                                                                                  #        THETA = IGA
014860,000956:                                                                                                  #        PSI = MGA
014861,000957: 
014862,000958: 22,2654           67543        DCMTOCDU           DLOAD*   ARCSIN                                
014863,000959: 22,2655           00007                                    6,1                                   
014864,000960: 22,2656           71406                           PUSH     COS                                   #  PD +0         PSI
014865,000961: 22,2657           41152                           SL1      BOVB                                  
014866,000962: 22,2660           21712                                    SIGNMPAC                              
014867,000963: 22,2661           00051                           STORE    S1                                    
014868,000964: 22,2662           57543                           DLOAD*   DCOMP                                 
014869,000965: 22,2663           00015                                    12D,1                                 
014870,000966: 22,2664           67471                           DDV      ARCSIN                                
014871,000967: 22,2665           00051                                    S1                                    
014872,000968: 22,2666           51123                           PDDL*    BPL                                   #  PD +2         THETA
014873,000969: 22,2667           00001                                    0,1                                   #  MUST CHECK THE SIGN OF COS(THETA)
014874,000970: 22,2670           44702                                    OKTHETA                               #  TO DETERMINE THE PROPER QUADRANT
014875,000971: 22,2671           57545                           DLOAD    DCOMP                                 
014876,000972: 22,2672           43244                           BPL      DAD                                   
014877,000973: 22,2673           44677                                    SUHALFA                               
014878,000974: 22,2674           06520                                    DPHALF                                
014879,000975: 22,2675           77650                           GOTO                                           
014880,000976: 22,2676           44701                                    CALCPHI                               
014881,000977: 22,2677           77625        SUHALFA            DSU                                            
014882,000978: 22,2700           06520                                    DPHALF                                
014883,000979: 22,2701           77606        CALCPHI            PUSH                                           
014884,000980: 22,2702           57543        OKTHETA            DLOAD*   DCOMP                                 
014885,000981: 22,2703           00013                                    10D,1                                 
014886,000982: 22,2704           67471                           DDV      ARCSIN                                
014887,000983: 22,2705           00051                                    S1                                    
014888,000984: 22,2706           51123                           PDDL*    BPL                                   #  PUSH DOWN PHI
014889,000985: 22,2707           00011                                    8D,1                                  
014890,000986: 22,2710           44722                                    OKPHI                                 
014891,000987: 22,2711           57545                           DLOAD    DCOMP                                 #  PUSH UP PHI
014892,000988: 22,2712           43244                           BPL      DAD                                   
014893,000989: 22,2713           44717                                    SUHALFAP                              
014894,000990: 22,2714           06520                                    DPHALF                                
014895,000991: 22,2715           77650                           GOTO                                           
014896,000992: 22,2716           44723                                    VECOFANG                              
014897,000993: 22,2717           52025        SUHALFAP           DSU      GOTO                                  
014898,000994: 22,2720           06520                                    DPHALF                                
014899,000995: 22,2721           44723                                    VECOFANG                              
014900,000996: 22,2722           77745        OKPHI              DLOAD                                          #  PUSH UP PHI
014901,000997: 22,2723           43466        VECOFANG           VDEF     RVQ                                   

Page 363

014903,000999:                                                                                                  #  ROUTINES FOR TERMINATING THE AUTOMATIC MANEUVER AND RETURNING TO USER
014904,001000: 
014905,001001: 22,2724           77776        TOOBADF            EXIT                                           
014906,001002: 22,2725           05567                           TC       ALARM                                 
014907,001003: 22,2726           00401                           OCT      00401                                 
014908,001004: 
014909,001005: 22,2727           12732                           TCF      NOGO                                  #  DO NOT ZERO ATTITUDE ERRORS
014910,001006: 
014911,001007: 22,2730           04616                           TC       BANKCALL                              
014912,001008: 22,2731           40153                           CADR     ZATTEROR                              #  ZERO ATTITUDE ERRORS
014913,001009: 
014914,001010: 22,2732           04616        NOGO               TC       BANKCALL                              
014915,001011: 22,2733           40165                           CADR     STOPRATE                              #  STOP RATES
014916,001012: 
014917,001013: 22,2734           34752                           CAF      TWO                                   
014918,001014: 22,2735           00004                           INHINT                                         #  ALL RETURNS ARE NOW MADE VIA GOODEND
014919,001015: 22,2736           05203                           TC       WAITLIST                              
014920,001016: 22,2737  E6,1676                                  EBANK=   BCDU                                  
014921,001017: 22,2737           03234 44066                     2CADR    GOODMANU                              
014922,001018: 
014923,001019: 22,2741           15155                           TCF      ENDOFJOB                              
014924,001020: 
014925,001021: 22,2742           77776        TOOBADI            EXIT                                           
014926,001022: 22,2743           12732                           TCF      NOGO                                  
014927,001023: 
014928,001024: 

End of include-file ATTITUDE_MANEUVER_ROUTINE.agc.  Parent file is MAIN.agc