Source Code

These source-code files are part of a reconstructed copy of Luminary 163, the first (unflown) release of the Apollo 14 Lunar Module (LM) Apollo Guidance Computer (AGC) software.

The reconstruction began with reconstructed source code for Luminary 173. Changes between revision 163 and 173 were backed out, as described by Luminary memos 157 and 158. The reconstruction was verified by matching memory-bank checksums to those listed in drawing 2021152N. Note that page numbers in the reconstructed code match those for the baseline log section mentioned in each file's changelog; the page numbers for a real Luminary 163 listing would be different.

Comments from the original source code are prefixed with a single '#' symbol, whereas comments added later are prefixed by "##" or "###". Report any errors noted by creating an issue report at the Virtual AGC project's GitHub repository.

014695,000002:                                                                                                  ## Copyright:   Public domain.
014696,000003:                                                                                                  ## Filename:    ATTITUDE_MANEUVER_ROUTINE.agc
014697,000004:                                                                                                  ## Purpose:     A section of Luminary revision 163.
014698,000005:                                                                                                  ##              It is part of the reconstructed source code for the first
014699,000006:                                                                                                  ##              (unflown) release of the flight software for the Lunar
014700,000007:                                                                                                  ##              Module's (LM) Apollo Guidance Computer (AGC) for Apollo 14.
014701,000008:                                                                                                  ##              The code has been recreated from a reconstructed copy of
014702,000009:                                                                                                  ##              Luminary 173, as well as Luminary memos 157 amd 158.
014703,000010:                                                                                                  ##              It has been adapted such that the resulting bugger words
014704,000011:                                                                                                  ##              exactly match those specified for Luminary 163 in NASA
014705,000012:                                                                                                  ##              drawing 2021152N, which gives relatively high confidence
014706,000013:                                                                                                  ##              that the reconstruction is correct.
014707,000014:                                                                                                  ## Reference:   pp. 347-368
014708,000015:                                                                                                  ## Assembler:   yaYUL
014709,000016:                                                                                                  ## Contact:     Ron Burkey <info@sandroid.org>.
014710,000017:                                                                                                  ## Website:     www.ibiblio.org/apollo/index.html
014711,000018:                                                                                                  ## Mod history: 2019-08-21 MAS  Created from Luminary 173.
014712,000019: 

Page 347

014714,000021:                                                                                                  #  BLOCK 2 LGC ATTITUDE MANEUVER ROUTINE-KALCMANU
014715,000022: 
014716,000023: 
014717,000024:                                                                                                  #  MOD 2           DATE 5/1/67     BY DON KEENE
014718,000025: 
014719,000026:                                                                                                  #  PROGRAM DESCRIPTION
014720,000027: 
014721,000028:                                                                                                  #       KALCMANU IS A ROUTINE WHICH GENERATES COMMANDS FOR THE LM DAP TO CHANGE THE ATTITUDE OF THE SPACECRAFT
014722,000029:                                                                                                  #  DURING FREE FALL.  IT IS DESIGNED TO MANEUVER THE SPACECRAFT FROM ITS INITIAL ORIENTATION TO SOME DESIRED
014723,000030:                                                                                                  #  ORIENTATION SPECIFIED BY THE PROGRAM WHICH CALLS KALCMANU, AVOIDING GIMBAL LOCK IN THE PROCESS.  IN THE
014724,000031:                                                                                                  #  MOD 2 VERSION, THIS DESIRED ATTITUDE IS SPECIFIED BY A SET OF THREE COMMANDED CDU ANGLES STORED AS 2S COMPLEMENT
014725,000032:                                                                                                  #  SINGLE PRECISION ANGLES IN THE THREE CONSECUTIVE LOCATIONS, CPHI, CTHETA, CPSI, WHERE
014726,000033: 
014727,000034:                                                                                                  #       CPHI = COMMANDED OUTER GIMBAL ANGLE
014728,000035:                                                                                                  #       CTHETA = COMMANDED INNER GIMBAL ANGLE
014729,000036:                                                                                                  #       CPSI = COMMANDED MIDDLE GIMBAL ANGLE
014730,000037: 
014731,000038:                                                                                                  #      WHEN POINTING A SPACECRAFT AXIS (E.I. X, Y, Z, THE AOT, THRUST AXIS, ETC) THE SUBROUTINE VECPOINT MAY BE
014732,000039:                                                                                                  #  USED TO GENERATE THIS SET OF DESIRED CDU ANGLES (SEE DESCRIPTION IN R60)   -
014733,000040:                                                                                                  #   WITH THIS INFORMATION KALCMANU DETERMINES THE DIRECTION OF THE SINGLE EQUIVALENT ROTATION (COF ALSO U) AND THE
014734,000041:                                                                                                  #  MAGNITUDE OF THE ROTATION (AM) TO BRING THE S/C FROM ITS INITIAL ORIENTATION TO ITS FINAL ORIENTATION.
014735,000042:                                                                                                  #  THIS DIRECTION REMAINS FIXED BOTH IN INERTIAL COORDINATES AND IN COMMANDED S/C AXES THROUGHOUT THE
014736,000043:                                                                                                  #                   -
014737,000044:                                                                                                  #  MANEUVER.  ONCE COF AND AM HAVE BEEN DETERMINED, KALCMANU THEN EXAMINES THE MANEUVER TO SEE IF IT WILL BRING
014738,000045:                                                                                                  #                                        -
014739,000046:                                                                                                  #  THE S/C THROUGH GIMBAL LOCK.  IF SO, COF AND AM ARE READJUSTED SO THAT THE S/C WILL JUST SKIM THE GIMBAL
014740,000047:                                                                                                  #  LOCK ZONE AND ALIGN THE X-AXIS.  IN GENERAL A FINAL YAW  ABOUT X WILL BE NECESSARY TO COMPLETE THE MANEUVER.
014741,000048:                                                                                                  #  NEEDLESS TO SAY, NEITHER THE INITIAL NOR THE FINAL ORIENTATION CAN BE IN GIMBAL LOCK.
014742,000049: 
014743,000050:                                                                                                  #       FOR PROPER ATTITUDE CONTROL THE DIGITAL AUTOPILOT MUST BE GIVEN AN ATTITUDE REFERENCE WHICH IT CAN TRACK.
014744,000051:                                                                                                  #  KALCMANU DOES THIS BY GENERATING A REFERENCE OF DESIRED GIMBAL ANGLES (CDUXD, CDUYD, CDUZD) WHICH ARE UPDATED
014745,000052:                                                                                                  #  EVERY ONE SECOND DURING THE MANEUVER.  TO ACHIEVE A SMOOTHER SEQUENCE OF COMMANDS BETWEEN SUCCESSIVE UPDATES,
014746,000053:                                                                                                  #  THE PROGRAM ALSO GENERATES A SET OF INCREMENTAL CDU ANGLES (DELDCDU) TO BE ADDED TO CDU DESIRED BY THE DIGITAL
014747,000054:                                                                                                  #  AUTOPILOT.  KALCMANU ALSO CALCULATES THE COMPONENT MANEUVER RATES (OMEGAPD, OMEGAQD, OMEGARD), WHICH CAN
014748,000055:                                                                                                  #                                       -
014749,000056:                                                                                                  #  BE DETERMINED SIMPLY BY MULTIPLYING COF BY SOME SCALAR (ARATE) CORRESPONDING TO THE DESIRED ROTATIONAL RATE.
014750,000057: 
014751,000058:                                                                                                  #       AUTOMATIC MANEUVERS ARE TIMED WITH THE HELP OF WAITLIST SO THAT AFTER A SPECIFIED INTERVAL THE Y AND Z
014752,000059:                                                                                                  #  DESIRED RATES ARE SET TO ZERO AND THE DESIRED CDU ANGLES (CDUYD, CDUZD) ARE SET EQUAL TO THE FINAL DESIRED CDU
014753,000060:                                                                                                  #  ANGLES (CTHETA, CPSI).  IF ANY YAW  REMAINS DUE TO GIMBAL LOCK AVOIDANCE, THE FINAL YAW  MANEUVER IS
014754,000061:                                                                                                  #  CALCULATED AND THE DESIRED YAW  RATE SET TO SOME FIXED VALUE (ROLLRATE = + OR - 2 DEGREES PER SEC).
014755,000062:                                                                                                  #  IN THIS CASE ONLY AN INCREMENTAL CDUX ANGLE (DELFROLL) IS SUPPLIED TO THE DAP.  AT THE END OF THE YAW
014756,000063:                                                                                                  #  MANEUVER OR IN THE EVENT THAT THERE WAS NO FINAL YAW,  CDUXD IS SET EQUAL TO CPHI AND THE X-AXIS DESIRED
014757,000064:                                                                                                  #  RATE SET TO ZERO.  THUS, UPON COMPLETION OF THE MANEUVER THE S/C WILL FINISH UP IN A LIMIT CYCLE ABOUT THE
014758,000065:                                                                                                  #  DESIRED FINAL GIMBAL ANGLES.
014759,000066: 
014760,000067: 
014761,000068:                                                                                                  #  PROGRAM LOGIC FLOW
014762,000069: 
014763,000070:                                                                                                  #       KALCMANU IS CALLED AS A HIGH PRIORITY JOB WITH ENTRY POINTS AT KALCMAN3 AND VECPOINT.  IT FIRST PICKS
014764,000071:                                                                                                  #  UP THE CURRENT CDU ANGLES TO BE USED AS THE BASIS FOR ALL COMPUTATIONS INVOLVING THE INITIAL S/C ORIENTATION.
014765,000072: 

Page 348

014767,000074:                                                                                                  #  IT THEN DETERMINES THE DIRECTION COSINE MATRICES RELATING BOTH THE INITIAL AND FINAL S/C ORIENTATION TO STABLE
014768,000075:                                                                                                  #                *    *                                                                               *
014769,000076:                                                                                                  #  MEMBER AXES (MIS, MFS).  IT ALSO COMPUTES THE MATRIX RELATING FINAL S/C AXES TO INITIAL S/C AXES (MFI).  THE
014770,000077:                                                                                                  #  ANGLE OF ROTATION (AM) IS THEN EXTRACTED FROM THIS MATRIX, AND TESTS ARE MADE TO DETERMINE IF
014771,000078: 
014772,000079:                                                                                                  #       A)  AM LESS THAN .25 DEGREES (MINANG)
014773,000080:                                                                                                  #       B)  AM GREATER THAN 170 DEGREES (MAXANG)
014774,000081: 
014775,000082:                                                                                                  #       IF AM LESS THAN .25 DEGREES, NO COMPLICATED AUTOMATIC MANEUVERING IS NECESSARY.  THEREFORE WE CAN SIMPLY
014776,000083:                                                                                                  #  SET CDU DESIRED EQUAL TO THE FINAL CDU DESIRED ANGLES AND TERMINATE THE JOB.
014777,000084: 
014778,000085:                                                                                                  #       IF AM IS GREATER THAN .25 DEGREES BUT LESS THAN 170 DEGREES, THE AXES OF THE SINGLE EQUIVALENT ROTATION
014779,000086:                                                                                                  #    -                                                       *
014780,000087:                                                                                                  #  (COF) IS EXTRACTED FROM THE SKEW SYMMETRIC COMPONENTS OF MFI.                            *     *
014781,000088:                                                                                                  #       IF AM GREATER THAN 170 DEGREES AN ALTERNATE METHOD EMPLOYING THE SYMMETRIC PART OF MFI (MFISYM) IS USED
014782,000089:                                                                                                  #                -
014783,000090:                                                                                                  #  TO DETERMINE COF.
014784,000091: 
014785,000092:                                                                                                  #       THE PROGRAM THEN CHECKS TO SEE IF THE MANEUVER AS COMPUTED WILL BRING THE S/C THROUGH GIMBAL LOCK.  IF
014786,000093:                                                                                                  #  SO, A NEW MANEUVER IS CALCULATED WHICH WILL JUST SKIM THE GIMBAL LOCK ZONE AND ALIGN THE S/C X-AXIS.  THIS
014787,000094:                                                                                                  #  METHOD ASSURES THAT THE ADDITIONAL MANEUVERING TO AVOID GIMBAL LOCK WILL BE KEPT TO A MINIMUM.  SINCE A FINAL
014788,000095:                                                                                                  #  P AXIS YAW WILL BE NECESSARY, A SWITCH IS RESET (STATE SWITCH 31) TO ALLOW FOR THE COMPUTATION OF THIS FINAL
014789,000096:                                                                                                  #  YAW.
014790,000097: 
014791,000098:                                                                                                  #       AS STATED PREVIOUSLY KALCMANU GENERATES A SEQUENCE OF DESIRED GIMBAL ANGLES WHICH ARE UPDATED EVERY
014792,000099:                                                                                                  #                                                                                               -
014793,000100:                                                                                                  #  SECOND.  THIS IS ACCOMPLISHED BY A SMALL ROTATION OF THE DESIRED S/C FRAME ABOUT THE VECTOR COF.  THE NEW
014794,000101:                                                                                                  #  DESIRED REFERENCE MATRIX IS THEN,
014795,000102: 
014796,000103:                                                                                                  #                   *              *         *
014797,000104:                                                                                                  #                  MIS       =    MIS       DEL
014798,000105:                                                                                                  #                     N+1             N
014799,000106:                                                                                                  #         *
014800,000107:                                                                                                  #  WHERE DEL IS THE MATRIX CORRESPONDING TO THIS SMALL ROTATION.  THE NEW CDU ANGLES CAN THEN BE EXTRACTED
014801,000108:                                                                                                  #        *
014802,000109:                                                                                                  #  FROM MIS.
014803,000110: 
014804,000111:                                                                                                  #       AT THE BEGINNING OF THE MANEUVER THE AUTOPILOT DESIRED RATES (OMEGAPD, OMEGAQD, OMEGARD) AND THE
014805,000112:                                                                                                  #  MANEUVER TIMINGS ARE ESTABLISHED.  ON THE FIRST PASS AND ON ALL SUBSEQUENT UPDATES THE CDU DESIRED
014806,000113:                                                                                                  #  ANGLES ARE LOADED WITH THE APPROPRIATE VALUES AND THE INCREMENTAL CDU ANGLES ARE COMPUTED.  THE AGC CLOCKS
014807,000114:                                                                                                  #  (TIME1 AND TIME2) ARE THAN CHECKED TO SEE IF THE MANEUVER WILL TERMINATE BEFORE THE NEXT UPDATE.  IF
014808,000115:                                                                                                  #  NOT, KALCMANU CALLS FOR ANOTHER UPDATE (RUN AS A JOB WITH PRIORITY TBD) IN ONE SECOND.  ANY DELAYS IN THIS
014809,000116:                                                                                                  #  CALLING SEQUENCE ARE AUTOMATICALLY COMPENSATED IN CALLING FOR THE NEXT UPDATE.
014810,000117: 
014811,000118:                                                                                                  #       IF IT IS FOUND THAT THE MANEUVER IS TO TERMINATE BEFORE THE NEXT UPDATE A ROUTINE IS CALLED (AS A WAIT-
014812,000119:                                                                                                  #  LIST TASK) TO STOP THE MANEUVER AT THE APPROPRIATE TIME AS EXPLAINED ABOVE.
014813,000120: 

Page 349

014815,000122:                                                                                                  #  CALLING SEQUENCE
014816,000123: 
014817,000124:                                                                                                  #       IN ORDER TO PERFORM A KALCMANU SUPERVISED MANEUVER, THE COMMANDED GIMBAL ANGLES MUST BE PRECOMPUTED AND
014818,000125:                                                                                                  #  STORED IN LOCATIONS CPHI, CTHETA, CPSI.  THE USER:S PROGRAM MUST THEN CLEAR STATE SWITCH NO 33 TO ALLOW THE
014819,000126:                                                                                                  #  ATTITUDE MANEUVER ROUTINE TO PERFORM ANY FINAL P-AXIS YAW INCURRED BY AVOIDING GIMBAL LOCK.  THE MANEUVER IS
014820,000127:                                                                                                  #  THEN INITIATED BY ESTABLISHING THE FOLLOWING EXECUTIVE JOB
014821,000128: 
014822,000129:                                                                                                  #                         *
014823,000130:                                                                                                  #       CAF     PRIO    XX
014824,000131:                                                                                                  #                       --
014825,000132:                                                                                                  #       INHINT
014826,000133:                                                                                                  #       TC         FINDVAC
014827,000134:                                                                                                  #       2CADR      KALCMAN3
014828,000135:                                                                                                  #       RELINT
014829,000136: 
014830,000137:                                                                                                  #  THE USER:S PROGRAM MAY EITHER CONTINUE OR WAIT FOR THE TERMINATION OF THE MANEUVER.  IF THE USER WISHES TO
014831,000138:                                                                                                  #  WAIT, HE MAY PUT HIS JOB TO SLEEP WITH THE FOLLOWING INSTRUCTIONS
014832,000139: 
014833,000140:                                                                                                  #       L          TC        BANKCALL
014834,000141:                                                                                                  #       L+1        CADR      ATTSTALL
014835,000142:                                                                                                  #       L+2        (BAD      RETURN)
014836,000143:                                                                                                  #       L+3        (GOOD     RETURN)
014837,000144: 
014838,000145:                                                                                                  #       UPON COMPLETION OF THE MANEUVER, THE PROGRAM WILL BE AWAKENED AT L+3 IF THE MANEUVER WAS COMPLETED
014839,000146:                                                                                                  #  SUCCESSFULLY, OR AT L+2 IF THE MANEUVER WAS ABORTED.  THIS ABORT WOULD OCCUR IF THE INITIAL OR FINAL ATTITUDE
014840,000147:                                                                                                  #  WAS IN GIMBAL LOCK.
014841,000148: 
014842,000149:                                                                                                  #  ***NOTA BENE***  IT IS ASSUMED THAT THE DESIRED MANEUVERING RATE (0.5, 2, 5, 10, DEG/SEC) HAS BEEN SELECTED BY
014843,000150:                                                                                                  #  KEYBOARD ENTRY PRIOR TO THE EXECUTION OF KALCMANU.
014844,000151:                                                                                                  #      IT IS ALSO ASSUMED THAT THE AUTOPILOT IS IN THE AUTO MODE.  IF THE MODE SWITCH IS CHANGED DURING THE
014845,000152:                                                                                                  #  MANEUVER, KALCMANU WILL TERMINATE VIA GOODEND WITHIN 1 SECOND SO THAT R60 MAY REQUEST A TRIM OF THE S/C ATTITUDE
014846,000153:                                                                                                  #  THIS IS THE ONLY MEANS FOR MANUALLY TERMINATING A KALCMANU SUPERVISED MANEUVER.
014847,000154:                                                                                                  #  SUBROUTINES
014848,000155: 
014849,000156:                                                                                                  #       KALCMANU USES A NUMBER OF INTERPRETIVE SUBROUTINES WHICH MAY BE OF GENERAL INTEREST.  SINCE THESE ROUTINES
014850,000157:                                                                                                  #  WERE PROGRAMMED EXCLUSIVELY FOR KALCMANU, THEY ARE NOT, AS YET, GENERALLY AVAILABLE FOR USE BY OTHER PROGRAMS.
014851,000158: 
014852,000159:                                                                                                  #       MXM3
014853,000160:                                                                                                  #       ----
014854,000161: 
014855,000162:                                                                                                  #       THIS SUBROUTINE MULTIPLIES TWO 3X3 MATRICES AND LEAVES THE RESULT IN THE FIRST 18 LOCATIONS OF THE PUSH
014856,000163:                                                                                                  #  DOWN LIST, I.E.,
014857,000164: 
014858,000165:                                                                                                  #                 (M    M    M )
014859,000166:                                                                                                  #                 (  0   1    2)
014860,000167:                                                                                                  #        *        (            )       *         *
014861,000168:                                                                                                  #        M    =   (M    M    M )  =    M1   X    M2
014862,000169:                                                                                                  #                 ( 3    4    5)
014863,000170:                                                                                                  #                 (            )
014864,000171:                                                                                                  #                 (M    M    M )
014865,000172: 

Page 350

014867,000174:                                                                                                  #                 ( 6    7    8)
014868,000175: 
014869,000176:                                                                                                  #                                                                                        *
014870,000177:                                                                                                  #       INDEX REGISTER X1 MUST BE LOADED WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M1, AND X2 MUST BE
014871,000178:                                                                                                  #                                                         *
014872,000179:                                                                                                  #  LOADED WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M2.   THE ROUTINE USES THE FIRST 20 LOCATIONS OF THE PUSH
014873,000180:                                                                                                  #  DOWN LIST.  THE FIRST ELEMENT OF THE MATRIX APPEARS IN PDO.  PUSH UP FOR M .
014874,000181:                                                                                                  #                                                                            8
014875,000182: 
014876,000183:                                                                                                  #       TRANSPOS
014877,000184:                                                                                                  #       --------
014878,000185: 
014879,000186:                                                                                                  #       THIS ROUTINE TRANSPOSES A 3X3 MATRIX AND LEAVES THE RESULT IN THE PUSH DOWN LIST, I.E.,
014880,000187: 
014881,000188:                                                                                                  #        *         * T
014882,000189:                                                                                                  #        M    =    M1
014883,000190: 
014884,000191:                                                                                                  #  INDEX REGISTER X1 MUST CONTAIN THE COMPLEMENT OF THE STARTING ADDRESS FOR M1.  PUSH UP FOR THE FIRST AND SUB-
014885,000192:                                                                                                  #                        *
014886,000193:                                                                                                  #  SEQUENT COMPONENTS OF M.   THIS SUBROUTINE ALSO USES THE FIRST 20 LOCATIONS OF THE PUSH DOWN LIST.
014887,000194: 
014888,000195:                                                                                                  #       CDU TO DCM
014889,000196:                                                                                                  #       ----------
014890,000197: 
014891,000198:                                                                                                  #       THIS SUBROUTINE CONVERTS THREE CDU ANGLES IN T(MPAC) TO A DIRECTION COSINE MATRIX (SCALED BY 2) RELATING
014892,000199:                                                                                                  #  THE CORRESPONDING S/C ORIENTATIONS TO THE STABLE MEMBER FRAME.  THE FORMULAS FOR THIS CONVERSION ARE
014893,000200: 
014894,000201:                                                                                                  #        M    =    COSY  COSZ
014895,000202:                                                                                                  #         0
014896,000203: 
014897,000204:                                                                                                  #        M    =    -COSY  SINZ  COSX  +  SINY  SINX
014898,000205:                                                                                                  #         1
014899,000206: 
014900,000207:                                                                                                  #        M    =    COSY  SINZ  SINX  +  SINY  COSX
014901,000208:                                                                                                  #         2
014902,000209: 
014903,000210:                                                                                                  #        M    =    SINZ
014904,000211:                                                                                                  #         3
014905,000212: 
014906,000213:                                                                                                  #        M    =    COSZ  COSX
014907,000214:                                                                                                  #         4
014908,000215: 
014909,000216:                                                                                                  #        M    =    -COSZ  SINX
014910,000217:                                                                                                  #         5
014911,000218: 
014912,000219:                                                                                                  #        M    =    -SINY  COSZ
014913,000220:                                                                                                  #         6
014914,000221: 
014915,000222:                                                                                                  #        M    =    SINY  SINZ  COSX  +  COSY  SINX
014916,000223:                                                                                                  #         7
014917,000224: 

Page 351

014919,000226:                                                                                                  #        M    =    -SINY  SINZ  SINX  +  COSY  COSX
014920,000227:                                                                                                  #         8
014921,000228: 
014922,000229:                                                                                                  #  WHERE      X    =    OUTER GIMBAL ANGLE
014923,000230:                                                                                                  #             Y    =    INNER GIMBAL ANGLE
014924,000231:                                                                                                  #             Z    =    MIDDLE GIMBAL ANGLE
014925,000232: 
014926,000233:                                                                                                  #       THE INTERPRETATION OF THIS MATRIX IS AS FOLLOWS
014927,000234: 
014928,000235:                                                                                                  #       IF A , A , A  REPRESENT THE COMPONENTS OF A VECTOR IN S/C AXES THEN THE COMPONENTS OF THE SAME VECTOR IN
014929,000236:                                                                                                  #           X   Y   Z
014930,000237:                                                                                                  #  STABLE MEMBER AXES (B , B , B ) ARE
014931,000238:                                                                                                  #                       X   Y   Z
014932,000239: 
014933,000240:                                                                                                  #             (B )                (A )
014934,000241:                                                                                                  #             ( X)                ( X)
014935,000242:                                                                                                  #             (  )                (  )
014936,000243:                                                                                                  #             (  )           *    (  )
014937,000244:                                                                                                  #             (B )      =    M    (A )
014938,000245:                                                                                                  #             ( Y)                ( Y)
014939,000246:                                                                                                  #             (  )                (  )
014940,000247:                                                                                                  #             (B )                (A )
014941,000248:                                                                                                  #             ( Z)                ( Z)
014942,000249: 
014943,000250:                                                                                                  #      THE SUBROUTINE WILL STORE THIS MATRIX IN SEQUENTIAL LOCATIONS OF ERASABLE MEMORY AS SPECIFIED BY THE CALLING
014944,000251:                                                                                                  #                                                                                                              *
014945,000252:                                                                                                  #  PROGRAM.  TO DO THIS THE CALLING PROGRAM MUST FIRST LOAD X2 WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M.
014946,000253: 
014947,000254:                                                                                                  #       INTERNALLY, THE ROUTINE USES THE FIRST 16 LOCATIONS OF THE PUSH DOWN LIST, ALSO STEP REGISTER S1 AND INDEX
014948,000255:                                                                                                  #  REGISTER X2.
014949,000256: 
014950,000257: 
014951,000258:                                                                                                  #       DCM TO CDU
014952,000259:                                                                                                  #       ----------
014953,000260:                                                                                                  #                                                                            *
014954,000261:                                                                                                  #       THIS ROUTINE EXTRACTS THE CDU ANGLES FROM A DIRECTION COSINE MATRIX (M SCALED BY 2) RELATING S/C AXIS TO
014955,000262:                                                                                                  #                                                                                  *
014956,000263:                                                                                                  #  STABLE MEMBER AXES.  X1 MUST CONTAIN THE COMPLEMENT OF THE STARTING ADDRESS FOR M.  THE SUBROUTINE LEAVES THE
014957,000264:                                                                                                  #  CORRESPONDING GIMBAL ANGLES IN V(MPAC) AS DOUBLE PRECISION 1:S COMPLEMENT ANGLES SCALED BY 2PI.  THE FORMULAS
014958,000265:                                                                                                  #  FOR THIS CONVERSION ARE
014959,000266: 
014960,000267:                                                                                                  #        Z    =    ARCSIN (M  )
014961,000268:                                                                                                  #                           3
014962,000269: 
014963,000270:                                                                                                  #        Y    =    ARCSIN (-M /COSZ)
014964,000271:                                                                                                  #                            6
014965,000272: 
014966,000273:                                                                                                  #  IF M  IS NEGATIVE, Y IS REPLACED BY PI SGN Y - Y
014967,000274:                                                                                                  #      0
014968,000275: 

Page 352

014970,000277:                                                                                                  #        X    =    ARCSIN (-M /COSZ)
014971,000278:                                                                                                  #                            5
014972,000279: 
014973,000280:                                                                                                  #  IF M  IS NEGATIVE X IS REPLACED BY PI SGN X - X
014974,000281:                                                                                                  #      4
014975,000282: 
014976,000283:                                                                                                  #       THIS ROUTINE DOES NOT SET THE PUSH DOWN POINTER, BUT USES THE NEXT 8 LOCATIONS OF THE PUSH DOWN LIST AND
014977,000284:                                                                                                  #  RETURNS THE POINTER TO ITS ORIGINAL SETTING.  THIS PROCEDURE ALLOWS THE CALLER TO STORE THE MATRIX AT THE TOP OF
014978,000285:                                                                                                  #  THE PUSH DOWN LIST.
014979,000286: 
014980,000287: 
014981,000288:                                                                                                  #       DELCOMP
014982,000289:                                                                                                  #       -------
014983,000290: 
014984,000291:                                                                                                  #                                                           *
014985,000292:                                                                                                  #       THIS ROUTINE COMPUTES THE DIRECTION COSINE MATRIX (DEL) RELATING ON
014986,000293:                                                                                                  #                                                                           -
014987,000294:                                                                                                  #  IS ROTATED WITH RESPECT TO THE FIRST BY AN ANGLE, A, ABOUT A UNIT VECTOR, U.  THE FORMULA FOR THIS MATRIX IS
014988,000295: 
014989,000296:                                                                                                  #        *         *           --T           *
014990,000297:                                                                                                  #        DEL  =    I  COSA  +  UU (1-COSA) + V SINA
014991,000298:                                                                                                  #                                             X
014992,000299: 
014993,000300:                                                                                                  #  WHERE      *         (1    0    0)
014994,000301:                                                                                                  #             I    =    (0    1    0)
014995,000302:                                                                                                  #                       (0    0    1)
014996,000303: 
014997,000304: 
014998,000305:                                                                                                  #                          2
014999,000306:                                                                                                  #                       (U         U U       U  U )
015000,000307:                                                                                                  #                       ( X         X Y       X  Z)
015001,000308:                                                                                                  #                       (                         )
015002,000309:                                                                                                  #             --T       (            2            )
015003,000310:                                                                                                  #             UU   =    (U U       U         U U  )
015004,000311:                                                                                                  #                       ( Y X       Y         Y Z )
015005,000312:                                                                                                  #                       (                         )
015006,000313:                                                                                                  #                       (                      2  )
015007,000314:                                                                                                  #                       (U U       U U       U   )
015008,000315:                                                                                                  #                       ( Z X       Z Y       Z   )
015009,000316: 
015010,000317: 
015011,000318:                                                                                                  #                       (0         -U        U  )
015012,000319:                                                                                                  #                       (            Z        Y )
015013,000320:                                                                                                  #             *         (                       )
015014,000321:                                                                                                  #             V    =    (U         0         -U )
015015,000322:                                                                                                  #              X        ( Z                    X)
015016,000323:                                                                                                  #                       (                       )
015017,000324:                                                                                                  #                       (-U        U         0  )
015018,000325:                                                                                                  #                       (  Y        X           )
015019,000326: 

Page 353

015021,000328:                                                                                                  #             -
015022,000329:                                                                                                  #             U    =    UNIT ROTATION VECTOR RESOLVED INTO S/C AXES
015023,000330:                                                                                                  #             A    =    ROTATION ANGLE
015024,000331: 
015025,000332:                                                                                                  #                              *
015026,000333:                                                                                                  #       THE INTERPRETATION OF DEL IS AS FOLLOWS
015027,000334: 
015028,000335:                                                                                                  #       IF A , A , A  REPRESENT THE COMPONENT OF A VECTOR INTHE ROTATED FRAME, THEN THE COMPONENTS OF THE SAME
015029,000336:                                                                                                  #           X   Y   Z
015030,000337:                                                                                                  #  VECTOR IN THE ORIGINAL S/C AXES (B , B , B ) ARE
015031,000338:                                                                                                  #                                    X   Y   Z
015032,000339: 
015033,000340:                                                                                                  #              (B )                    (A )
015034,000341:                                                                                                  #              ( X)                    ( X)
015035,000342:                                                                                                  #              (  )           *        (  )
015036,000343:                                                                                                  #              (B )     =    DEL       (A )
015037,000344:                                                                                                  #              ( Y)                    ( Y)
015038,000345:                                                                                                  #              (  )                    (  )
015039,000346:                                                                                                  #              (B )                    (A )
015040,000347:                                                                                                  #              ( Z)                    ( Z)
015041,000348: 
015042,000349:                                                                                                  #       THE ROUTINE WILL STORE THIS MATRIX (SCALED UNITY) IN SEQUENTIAL LOCATIONS OF ERASABLE MEMORY BEGINNING WITH
015043,000350:                                                                                                  #                                                                                              -
015044,000351:                                                                                                  #  THE LOCATION CALLED DEL.  IN ORDER TO USE THE ROUTINE, THE CALLING PROGRAM MUST FIRST STORE U (A HALF UNIT
015045,000352:                                                                                                  #  DOUBLE PRECISION VECTOR) IN THE SET OF ERASABLE LOCATIONS BEGINNING WITH THE ADDRESS CALLED COF.  THE ANGLE, A,
015046,000353:                                                                                                  #  MUST THEN BE LOADED INTO D(MPAC).
015047,000354: 
015048,000355:                                                                                                  #       INTERNALLY, THE PROGRAM ALSO USES THE FIRST 10 LOCATIONS OF THE PUSH DOWN LIST.
015049,000356: 
015050,000357: 
015051,000358:                                                                                                  #       READCDUK
015052,000359:                                                                                                  #       --------
015053,000360: 
015054,000361:                                                                                                  #       THIS BASIC LANGUAGE SUBROUTINE LOADS T(MPAC) WITH THE THREE CDU ANGLES.
015055,000362: 
015056,000363: 
015057,000364:                                                                                                  #      SIGNMPAC
015058,000365:                                                                                                  #       --------
015059,000366: 
015060,000367:                                                                                                  #       THIS IS A BASIC LANGUAGE SUBROUTINE WHICH LIMITS THE MAGNITUDE OF D(MPAC) TO + OR - DPOSMAX ON OVERFLOW.
015061,000368: 
015062,000369: 
015063,000370:                                                                                                  #       PROGRAM STORAGE ALLOCATION
015064,000371: 
015065,000372:                                                                                                  #             1)   FIXED MEMORY                       1059 WORDS
015066,000373:                                                                                                  #             2)   ERASABLE MEMORY                      98
015067,000374:                                                                                                  #             3)   STATE SWITCHES                        3
015068,000375: 

Page 354

015070,000377:                                                                                                  #             4)   FLAGS                                 1
015071,000378: 
015072,000379:                                                                                                  #       JOB PRIORITIES
015073,000380: 
015074,000381:                                                                                                  #             1)   KALCMANU                            TBD
015075,000382:                                                                                                  #             2)   ONE SECOND UPDATE                   TBD
015076,000383: 
015077,000384: 
015078,000385:                                                                                                  #       SUMMARY OF STATE SWITCHES AND FLAGWORDS USED BY KALCMANU.
015079,000386: 
015080,000387: 
015081,000388:                                                                                                  #  STATE                FLAGWRD 2      SETTING             MEANING
015082,000389:                                                                                                  #  SWITCH NO.            BIT NO.
015083,000390: 
015084,000391:                                                                                                  #    *
015085,000392:                                                                                                  #  31                      14            0       MANEUVER WENT THROUGH GIMBAL LOCK
015086,000393:                                                                                                  #                                        1       MANEUVER DID NOT GO THROUGH GIMBAL LOCK
015087,000394: 
015088,000395:                                                                                                  #    *
015089,000396:                                                                                                  #  32                      13            0       CONTINUE UPDATE PROCESS
015090,000397:                                                                                                  #                                        1       START UPDATE PROCESS
015091,000398: 
015092,000399:                                                                                                  #  33                      12            0       PERFORM FINAL P-AXIS YAW IF REQUIRED
015093,000400:                                                                                                  #                                        1       IGNORE ANY FINAL P-AXIS YAW
015094,000401: 
015095,000402:                                                                                                  #  34                      11            0       SIGNAL END OF KALCMANU
015096,000403:                                                                                                  #                                        1       KALCMANU IN PROCESS       USER MUST SET SWITCH BEFORE INITIATING
015097,000404: 
015098,000405: 
015099,000406:                                                                                                  #          * INTERNAL TO KALCMANU
015100,000407: 
015101,000408: 
015102,000409:                                                                                                  #       SUGGESTIONS FOR PROGRAM INTEGRATION
015103,000410: 
015104,000411:                                                                                                  #       THE FOLLOWING VARIABLES SHOULD BE ASSIGNED TO UNSWITCH ERASABLE
015105,000412: 
015106,000413:                                                                                                  #                       CPHI
015107,000414:                                                                                                  #                       CTHETA
015108,000415:                                                                                                  #                       CPSI
015109,000416:                                                                                                  #                       POINTVSM  +5
015110,000417:                                                                                                  #                       SCAXIS    +5
015111,000418:                                                                                                  #                       DELDCDU
015112,000419:                                                                                                  #                       DELDCDU1
015113,000420:                                                                                                  #                       DELDCDU2
015114,000421:                                                                                                  #                       RATEINDX
015115,000422: 
015116,000423:                                                                                                  #       THE FOLLOWING SUBROUTINES MAY BE PUT IN A DIFFERENT BANK
015117,000424: 
015118,000425:                                                                                                  #                       MXM3

Page 355

015120,000427:                                                                                                  #                       TRANSPOS
015121,000428:                                                                                                  #                       SIGNMPAC
015122,000429:                                                                                                  #                       READCDUK
015123,000430:                                                                                                  #                       CDUTODCM
015124,000431: 

Page 356

015126,000433: 15,2050                                           BANK     15                                    
015127,000434: 22,2000                                           SETLOC   KALCMON1                              
015128,000435: 22,2000                                           BANK                                           
015129,000436: 
015130,000437: 22,2004  E6,1675                                  EBANK=   BCDU                                  
015131,000438: 
015132,000439:                                                                                                  #  THE THREE DESIRED CDU ANGLES MUST BE STORED AS SINGLE PRECISION TWOS COMPLEMENT ANGLES IN THE THREE SUCCESSIVE
015133,000440:                                                                                                  #  LOCATIONS, CPHI, CTHETA, CPSI.
015134,000441: 
015135,000442: 22,2004                                           COUNT*   $$/KALC                               
015136,000443: 22,2004           06042        KALCMAN3           TC       INTPRET                               #  PICK UP THE CURRENT CDU ANGLES AND
015137,000444: 22,2005           77634                           RTB                                            #    COMPUTE THE MATRIX FROM INITIAL S/C
015138,000445: 22,2006           44403                                    READCDUK                              #    AXES TO FINAL S/C AXES
015139,000446: 22,2007           03276                           STORE    BCDU                                  #  STORE INITIAL S/C ANGLES
015140,000447: 22,2010           51535                           SLOAD    ABS                                   #  CHECK THE MAGNITUDE OF THE DESIRED
015141,000448: 22,2011           00324                                    CPSI                                  #  MIDDLE GIMBAL ANGLE
015142,000449: 22,2012           51025                           DSU      BPL                                   
015143,000450: 22,2013           04403                                    LOCKANGL                              #  IF GREATER THAN 70 DEG ABORT MANEUVER
015144,000451: 22,2014           44724                                    TOOBADF                               
015145,000452: 22,2015           72364                           AXC,2    TLOAD                                 
015146,000453: 22,2016           03245                                    MIS                                   
015147,000454: 22,2017           03276                                    BCDU                                  
015148,000455: 22,2020           77624                           CALL                                           #  COMPUTE THE TRANSFORMATION FROM INITIAL
015149,000456: 22,2021           44410                                    CDUTODCM                              #  S/C AXES TO STABLE MEMBER AXES
015150,000457: 22,2022           72364                           AXC,2    TLOAD                                 
015151,000458: 22,2023           02230                                    MFS                                   #  PREPARE TO CALCULATE ARRAY MFS
015152,000459: 22,2024           00322                                    CPHI                                  
015153,000460: 22,2025           77624                           CALL                                           
015154,000461: 22,2026           44410                                    CDUTODCM                              
015155,000462: 22,2027           45160        SECAD              AXC,1    CALL                                  #  MIS AND MFS ARRAYS CALCULATED         $2
015156,000463: 22,2030           03245                                    MIS                                   
015157,000464: 22,2031           44326                                    TRANSPOS                              
015158,000465: 22,2032           45575                           VLOAD    STADR                                 
015159,000466: 22,2033           50460                           STOVL    TMIS       +12D                       
015160,000467: 22,2034           77626                           STADR                                          
015161,000468: 22,2035           50466                           STOVL    TMIS       +6                         
015162,000469: 22,2036           77626                           STADR                                          
015163,000470: 22,2037           74474                           STORE    TMIS                                  #  TMIS = TRANSPOSE(MIS) SCALED BY 2
015164,000471: 22,2040           75160                           AXC,1    AXC,2                                 
015165,000472: 22,2041           03302                                    TMIS                                  
015166,000473: 22,2042           02230                                    MFS                                   
015167,000474: 22,2043           77624                           CALL                                           
015168,000475: 22,2044           44312                                    MXM3                                  
015169,000476: 22,2045           45575                           VLOAD    STADR                                 
015170,000477: 22,2046           51532                           STOVL    MFI        +12D                       
015171,000478: 22,2047           77626                           STADR                                          
015172,000479: 22,2050           51540                           STOVL    MFI        +6                         
015173,000480: 22,2051           77626                           STADR                                          
015174,000481: 22,2052           75546                           STORE    MFI                                   #  MFI = TMIS MFS (SCALED BY 4)
015175,000482: 22,2053           45001                           SETPD    CALL                                  #  TRANSPOSE MFI IN PD LIST
015176,000483: 

Page 357

015178,000485: 22,2054           00023                                    18D                                   
015179,000486: 22,2055           44335                                    TRNSPSPD                              
015180,000487: 22,2056           45575                           VLOAD    STADR                                 
015181,000488: 22,2057           50460                           STOVL    TMFI       +12D                       
015182,000489: 22,2060           77626                           STADR                                          
015183,000490: 22,2061           50466                           STOVL    TMFI       +6                         
015184,000491: 22,2062           77626                           STADR                                          
015185,000492: 22,2063           74474                           STORE    TMFI                                  #  TMFI = TRANSPOSE (MFI) SCALED BY 4
015186,000493: 
015187,000494:                                                                                                  #  CALCULATE COFSKEW AND MFISYM
015188,000495: 
015189,000496: 22,2064           45345                           DLOAD    DSU                                   
015190,000497: 22,2065           03305                                    TMFI       +2                         
015191,000498: 22,2066           02233                                    MFI        +2                         
015192,000499: 22,2067           45325                           PDDL     DSU                                   #  CALCULATE COF SCALED BY 2/SIN(AM)
015193,000500: 22,2070           02235                                    MFI        +4                         
015194,000501: 22,2071           03307                                    TMFI       +4                         
015195,000502: 22,2072           45325                           PDDL     DSU                                   
015196,000503: 22,2073           03315                                    TMFI       +10D                       
015197,000504: 22,2074           02243                                    MFI        +10D                       
015198,000505: 22,2075           77666                           VDEF                                           
015199,000506: 22,2076           03325                           STORE    COFSKEW                               #  EQUALS MFISKEW
015200,000507: 
015201,000508:                                                                                                  #  CALCULATE AM AND PROCEED ACCORDING TO ITS MAGNITUDE
015202,000509: 
015203,000510: 22,2077           43345                           DLOAD    DAD                                   
015204,000511: 22,2100           02231                                    MFI                                   
015205,000512: 22,2101           02251                                    MFI        +16D                       
015206,000513: 22,2102           43225                           DSU      DAD                                   
015207,000514: 22,2103           06510                                    DP1/4TH                               
015208,000515: 22,2104           02241                                    MFI        +8D                        
015209,000516: 22,2105           03333                           STORE    CAM                                   #  CAM = (MFI0+MFI4+MFI8-1)/2 HALF SCALE
015210,000517: 22,2106           77726                           ARCCOS                                         
015211,000518: 22,2107           03335                           STORE    AM                                    #  AM=ARCCOS(CAM)  (AM SCALED BY 2)
015212,000519: 22,2110           51025                           DSU      BPL                                   
015213,000520: 22,2111           04363                                    MINANG                                
015214,000521: 22,2112           44117                                    CHECKMAX                              
015215,000522: 22,2113           77751                           TLOAD                                          #  MANEUVER LESS THAN .25 DEGREES
015216,000523: 22,2114           00322                                    CPHI                                  #  GO DIRECTLY INTO ATTITUDE HOLD
015217,000524: 22,2115           37235                           STCALL   CDUXD                                 #  ABOUT COMMANDED ANGLES
015218,000525: 22,2116           44742                                    TOOBADI                               #  STOP RATE AND EXIT
015219,000526: 
015220,000527: 22,2117           45345        CHECKMAX           DLOAD    DSU                                   
015221,000528: 22,2120           03335                                    AM                                    
015222,000529: 22,2121           04365                                    MAXANG                                
015223,000530: 22,2122           77244                           BPL      VLOAD                                 
015224,000531: 22,2123           44131                                    ALTCALC                               #  UNIT
015225,000532: 22,2124           03325                                    COFSKEW                               #  COFSKEW
015226,000533: 22,2125           77656                           UNIT                                           
015227,000534: 22,2126           03270                           STORE    COF                                   #  COF IS THE MANEUVER AXIS
015228,000535: 

Page 358

015230,000537: 22,2127           77650                           GOTO                                           #  SEE IF MANEUVER GOES THRU GIMBAL LOCK
015231,000538: 22,2130           44744                                    LOCSKIRT                              
015232,000539: 22,2131           53375        ALTCALC            VLOAD    VAD                                   #  IF AM GREATER THAN 170 DEGREES
015233,000540: 22,2132           02231                                    MFI                                   
015234,000541: 22,2133           03303                                    TMFI                                  
015235,000542: 22,2134           77762                           VSR1                                           
015236,000543: 22,2135           27303                           STOVL    MFISYM                                
015237,000544: 22,2136           02237                                    MFI        +6                         
015238,000545: 22,2137           74455                           VAD      VSR1                                  
015239,000546: 22,2140           03311                                    TMFI       +6                         
015240,000547: 22,2141           27311                           STOVL    MFISYM     +6                         
015241,000548: 22,2142           02245                                    MFI        +12D                       
015242,000549: 22,2143           74455                           VAD      VSR1                                  
015243,000550: 22,2144           03317                                    TMFI       +12D                       
015244,000551: 22,2145           03317                           STORE    MFISYM     +12D                       #  MFISYM=(MFI+TMFI)/2   SCALED BY 4
015245,000552: 
015246,000553: 
015247,000554:                                                                                                  #  CALCULATE COF
015248,000555: 
015249,000556: 
015250,000557: 22,2146           70545                           DLOAD    SR1                                   
015251,000558: 22,2147           03333                                    CAM                                   
015252,000559: 22,2150           45325                           PDDL     DSU                                   #  PDO CAM                                $4
015253,000560: 22,2151           06516                                    DPHALF                                
015254,000561: 22,2152           03333                                    CAM                                   
015255,000562: 22,2153           65204                           BOVB     PDDL                                  #  PD2 1 - CAM                            $2
015256,000563: 22,2154           21713                                    SIGNMPAC                              
015257,000564: 22,2155           03323                                    MFISYM     +16D                       
015258,000565: 22,2156           56225                           DSU      DDV                                   
015259,000566: 22,2157           00001                                    0                                     
015260,000567: 22,2160           00003                                    2                                     
015261,000568: 22,2161           65366                           SQRT     PDDL                                  #  COFZ = SQRT(MFISYM8-CAM)/1-CAM)
015262,000569: 22,2162           03313                                    MFISYM     +8D                        #                                 $ ROOT 2
015263,000570: 22,2163           56225                           DSU      DDV                                   
015264,000571: 22,2164           00001                                    0                                     
015265,000572: 22,2165           00003                                    2                                     
015266,000573: 22,2166           65366                           SQRT     PDDL                                  #  COFY = SQRT(MFISYM4-CAM)/(1-CAM)   $ROOT2
015267,000574: 22,2167           03303                                    MFISYM                                
015268,000575: 22,2170           56225                           DSU      DDV                                   
015269,000576: 22,2171           00001                                    0                                     
015270,000577: 22,2172           00003                                    2                                     
015271,000578: 22,2173           55566                           SQRT     VDEF                                  #  COFX = SQRT(MFISYM-CAM)/(1-CAM)   $ROOT 2
015272,000579: 22,2174           77656                           UNIT                                           
015273,000580: 22,2175           03270                           STORE    COF                                   
015274,000581: 
015275,000582:                                                                                                  #  DETERMINE LARGEST COF AND ADJUST ACCORDINGLY
015276,000583: 
015277,000584: 22,2176           45345        COFMAXGO           DLOAD    DSU                                   
015278,000585: 22,2177           03270                                    COF                                   
015279,000586: 22,2200           03272                                    COF        +2                         
015280,000587: 22,2201           71240                           BMN      DLOAD                                 #  COFY G COFX
015281,000588: 

Page 359

015283,000590: 22,2202           44211                                    COMP12                                
015284,000591: 22,2203           03270                                    COF                                   
015285,000592: 22,2204           50025                           DSU      BMN                                   
015286,000593: 22,2205           03274                                    COF        +4                         
015287,000594: 22,2206           44266                                    METHOD3                               #  COFZ G COFX OR COFY
015288,000595: 22,2207           77650                           GOTO                                           
015289,000596: 22,2210           44242                                    METHOD1                               #  COFX G COFY OR COFZ
015290,000597: 22,2211           45345        COMP12             DLOAD    DSU                                   
015291,000598: 22,2212           03272                                    COF        +2                         
015292,000599: 22,2213           03274                                    COF        +4                         
015293,000600: 22,2214           77640                           BMN                                            
015294,000601: 22,2215           44266                                    METHOD3                               #  COFZ G COFY OR COFX
015295,000602: 
015296,000603: 22,2216           51145        METHOD2            DLOAD    BPL                                   #  COFY MAX
015297,000604: 22,2217           03327                                    COFSKEW    +2                         #  UY
015298,000605: 22,2220           44224                                    U2POS                                 
015299,000606: 22,2221           57575                           VLOAD    VCOMP                                 
015300,000607: 22,2222           03270                                    COF                                   
015301,000608: 22,2223           03270                           STORE    COF                                   
015302,000609: 22,2224           51145        U2POS              DLOAD    BPL                                   
015303,000610: 22,2225           03305                                    MFISYM     +2                         #  UX UY
015304,000611: 22,2226           44232                                    OKU21                                 
015305,000612: 22,2227           57545                           DLOAD    DCOMP                                 #  SIGN OF UX OPPOSITE TO UY
015306,000613: 22,2230           03270                                    COF                                   
015307,000614: 22,2231           03270                           STORE    COF                                   
015308,000615: 22,2232           51145        OKU21              DLOAD    BPL                                   
015309,000616: 22,2233           03315                                    MFISYM     +10D                       #  UY UZ
015310,000617: 22,2234           44744                                    LOCSKIRT                              
015311,000618: 22,2235           57545                           DLOAD    DCOMP                                 #  SIGN OF UZ OPPOSITE TO UY
015312,000619: 22,2236           03274                                    COF        +4                         
015313,000620: 22,2237           03274                           STORE    COF        +4                         
015314,000621: 22,2240           77650                           GOTO                                           
015315,000622: 22,2241           44744                                    LOCSKIRT                              
015316,000623: 22,2242           51145        METHOD1            DLOAD    BPL                                   #  COFX MAX
015317,000624: 22,2243           03325                                    COFSKEW                               #  UX
015318,000625: 22,2244           44250                                    U1POS                                 
015319,000626: 22,2245           57575                           VLOAD    VCOMP                                 
015320,000627: 22,2246           03270                                    COF                                   
015321,000628: 22,2247           03270                           STORE    COF                                   
015322,000629: 22,2250           51145        U1POS              DLOAD    BPL                                   
015323,000630: 22,2251           03305                                    MFISYM     +2                         #  UX UY
015324,000631: 22,2252           44256                                    OKU12                                 
015325,000632: 22,2253           57545                           DLOAD    DCOMP                                 
015326,000633: 22,2254           03272                                    COF        +2                         #  SIGN OF UY OPPOSITE TO UX
015327,000634: 22,2255           03272                           STORE    COF        +2                         
015328,000635: 22,2256           51145        OKU12              DLOAD    BPL                                   
015329,000636: 22,2257           03307                                    MFISYM     +4                         #  UX UZ
015330,000637: 22,2260           44744                                    LOCSKIRT                              
015331,000638: 22,2261           57545                           DLOAD    DCOMP                                 #  SIGN OF UZ OPPOSITE TO UY
015332,000639: 22,2262           03274                                    COF        +4                         
015333,000640: 

Page 360

015335,000642: 22,2263           03274                           STORE    COF        +4                         
015336,000643: 22,2264           77650                           GOTO                                           
015337,000644: 22,2265           44744                                    LOCSKIRT                              
015338,000645: 22,2266           51145        METHOD3            DLOAD    BPL                                   #  COFZ MAX
015339,000646: 22,2267           03331                                    COFSKEW    +4                         #  UZ
015340,000647: 22,2270           44274                                    U3POS                                 
015341,000648: 22,2271           57575                           VLOAD    VCOMP                                 
015342,000649: 22,2272           03270                                    COF                                   
015343,000650: 22,2273           03270                           STORE    COF                                   
015344,000651: 22,2274           51145        U3POS              DLOAD    BPL                                   
015345,000652: 22,2275           03307                                    MFISYM     +4                         #  UX UZ
015346,000653: 22,2276           44302                                    OKU31                                 
015347,000654: 22,2277           57545                           DLOAD    DCOMP                                 
015348,000655: 22,2300           03270                                    COF                                   #  SIGN OF UX OPPOSITE TO UZ
015349,000656: 22,2301           03270                           STORE    COF                                   
015350,000657: 22,2302           51145        OKU31              DLOAD    BPL                                   
015351,000658: 22,2303           03315                                    MFISYM     +10D                       #  UY UZ
015352,000659: 22,2304           44744                                    LOCSKIRT                              
015353,000660: 22,2305           57545                           DLOAD    DCOMP                                 
015354,000661: 22,2306           03272                                    COF        +2                         #  SIGN OF UY OPPOSITE TO UZ
015355,000662: 22,2307           03272                           STORE    COF        +2                         
015356,000663: 22,2310           77650                           GOTO                                           
015357,000664: 22,2311           44744                                    LOCSKIRT                              

Page 361

015359,000666:                                                                                                  #  MATRIX OPERATIONS
015360,000667: 
015361,000668: 13,2207                                           BANK     13                                    
015362,000669: 22,2000                                           SETLOC   KALCMON2                              
015363,000670: 22,2000                                           BANK                                           
015364,000671: 
015365,000672: 22,2312  E6,1675                                  EBANK=   BCDU                                  
015366,000673: 
015367,000674: 22,2312           76601        MXM3               SETPD    VLOAD*                                #  MXM3 MULTIPLIES 2 3X3 MATRICES
015368,000675: 22,2313           00001                                    0                                     #  AND LEAVES RESULT IN PD LIST
015369,000676: 22,2314           00001                                    0,1                                   #  AND MPAC
015370,000677: 22,2315           62703                           VXM*     PDVL*                                 
015371,000678: 22,2316           77776                                    0,2                                   
015372,000679: 22,2317           00007                                    6,1                                   
015373,000680: 22,2320           62703                           VXM*     PDVL*                                 
015374,000681: 22,2321           77776                                    0,2                                   
015375,000682: 22,2322           00015                                    12D,1                                 
015376,000683: 22,2323           41503                           VXM*     PUSH                                  
015377,000684: 22,2324           77776                                    0,2                                   
015378,000685: 22,2325           77616                           RVQ                                            
015379,000686: 
015380,000687: 
015381,000688:                                                                                                  #  RETURN WITH M1XM2 IN PD LIST
015382,000689: 
015383,000690: 22,2326           76601        TRANSPOS           SETPD    VLOAD*                                #  TRANSPOS TRANSPOSES A 3X3 MATRIX
015384,000691: 22,2327           00001                                    0                                     #   AND LEAVES RESULT IN PD LIST
015385,000692: 22,2330           00001                                    0,1                                   #  MATRIX ADDRESS IN XR1
015386,000693: 22,2331           62713                           PDVL*    PDVL*                                 
015387,000694: 22,2332           00007                                    6,1                                   
015388,000695: 22,2333           00015                                    12D,1                                 
015389,000696: 22,2334           77606                           PUSH                                           #  MATRIX IN PD
015390,000697: 22,2335           77776        TRNSPSPD           EXIT                                           #  ENTER WITH MATRIX AT 0 IN PD LIST
015391,000698: 22,2336           50120                           INDEX    FIXLOC                                
015392,000699: 22,2337           52013                           DXCH     12                                    
015393,000700: 22,2340           50120                           INDEX    FIXLOC                                
015394,000701: 22,2341           52017                           DXCH     16                                    
015395,000702: 22,2342           50120                           INDEX    FIXLOC                                
015396,000703: 22,2343           52013                           DXCH     12                                    
015397,000704: 22,2344           50120                           INDEX    FIXLOC                                
015398,000705: 22,2345           52015                           DXCH     14                                    
015399,000706: 22,2346           50120                           INDEX    FIXLOC                                
015400,000707: 22,2347           52005                           DXCH     4                                     
015401,000708: 22,2350           50120                           INDEX    FIXLOC                                
015402,000709: 22,2351           52015                           DXCH     14                                    
015403,000710: 22,2352           50120                           INDEX    FIXLOC                                
015404,000711: 22,2353           52003                           DXCH     2                                     
015405,000712: 22,2354           50120                           INDEX    FIXLOC                                
015406,000713: 22,2355           52007                           DXCH     6                                     
015407,000714: 22,2356           50120                           INDEX    FIXLOC                                
015408,000715: 22,2357           52003                           DXCH     2                                     
015409,000716: 

Page 362

015411,000718: 22,2360           06042                           TC       INTPRET                               
015412,000719: 22,2361           77616                           RVQ                                            
015413,000720: 
015414,000721: 15,2050                                           BANK     15                                    
015415,000722: 22,2000                                           SETLOC   KALCMON1                              
015416,000723: 22,2000                                           BANK                                           
015417,000724: 
015418,000725: 22,2362  E6,1675                                  EBANK=   BCDU                                  
015419,000726: 
015420,000727: 22,2362           00013 13563  MINANG             2DEC     0.00069375                            
015421,000728: 22,2364           17070 34343  MAXANG             2DEC     0.472222222                            
015422,000729:                                                                                                  #  GIMBAL LOCK CONSTANTS
015423,000730: 
015424,000731:                                                                                                  #  D = MGA CORRESPONDING TO GIMBAL LOCK = 60 DEGREES
015425,000732:                                                                                                  #           NGL = BUFFER ANGLE (TO AVOID DIVISIONS BY ZERO) = 2 DEGREES
015426,000733: 
015427,000734: 22,2366           15666 20443  SD                 2DEC     .433015                               #  = SIN(D)                        $2
015428,000735: 22,2370           33555 01106  K3S1               2DEC     .86603                                #  = SIN(D)                        $1
015429,000736: 22,2372           67777 77777  K4                 2DEC     -.25                                  #  = -COS(D)                       $2
015430,000737: 22,2374           04000 00000  K4SQ               2DEC     .125                                  #  = COS(D)COS(D)                  $2
015431,000738: 22,2376           00216 36323  SNGLCD             2DEC     .008725                               #  = SIN(NGL)COS(D)                $2
015432,000739: 22,2400           17773 00057  CNGL               2DEC     .499695                               #  COS(NGL)                        $2
015433,000740: 22,2402           14344        LOCKANGL           DEC      .388889                               #  = 70 DEGREES
015434,000741:                                                                                                  #  INTERPRETIVE SUBROUTINE TO READ THE CDU ANGLES
015435,000742: 
015436,000743: 22,2403           30034        READCDUK           CA       CDUZ                                  #  LOAD T(MPAC) WITH CDU ANGLES
015437,000744: 22,2404           54156                           TS       MPAC       +2                         
015438,000745: 22,2405           00006                           EXTEND                                         
015439,000746: 22,2406           30033                           DCA      CDUX                                  #  AND CHANGE MODE TO TRIPLE PRECISION
015440,000747: 22,2407           16501                           TCF      TLOAD      +6                         
015441,000748: 
015442,000749: 
015443,000750: 22,2410           66370        CDUTODCM           AXT,1    SSP                                   
015444,000751: 22,2411           00003                           OCT      3                                     
015445,000752: 22,2412           00051                                    S1                                    
015446,000753: 22,2413           00001                           OCT      1                                     #  SET XR1, S1, AND PD FOR LOOP
015447,000754: 22,2414           00010                           STORE    7                                     
015448,000755: 22,2415           77601                           SETPD                                          
015449,000756: 22,2416           00001                                    0                                     
015450,000757: 22,2417           47133        LOOPSIN            SLOAD*   RTB                                   
015451,000758: 22,2420           00013                                    10D,1                                 
015452,000759: 22,2421           21577                                    CDULOGIC                              
015453,000760: 

Page 363

015455,000762: 22,2422           00013                           STORE    10D                                   #  LOAD PD WITH  0 SIN(PHI)
015456,000763: 22,2423           65356                           SIN      PDDL                                  #                2 COS(PHI)
015457,000764: 22,2424           00013                                    10D                                   #                4 SIN(THETA)
015458,000765: 22,2425           41546                           COS      PUSH                                  #                6 COS(THETA)
015459,000766: 22,2426           71300                           TIX,1    DLOAD                                 #                8 SIN(PSI)
015460,000767: 22,2427           44417                                    LOOPSIN                               #               10 COS(PSI)
015461,000768: 22,2430           00007                                    6                                     
015462,000769: 22,2431           72405                           DMP      SL1                                   
015463,000770: 22,2432           00013                                    10D                                   
015464,000771: 22,2433           10001                           STORE    0,2                                   #  C0=COS(THETA)COS(PSI)
015465,000772: 22,2434           41345                           DLOAD    DMP                                   
015466,000773: 22,2435           00005                                    4                                     
015467,000774: 22,2436           00001                                    0                                     
015468,000775: 22,2437           41325                           PDDL     DMP                                   #  (PD6 SIN(THETA)SIN(PHI))
015469,000776: 22,2440           00007                                    6                                     
015470,000777: 22,2441           00011                                    8D                                    
015471,000778: 22,2442           72405                           DMP      SL1                                   
015472,000779: 22,2443           00003                                    2                                     
015473,000780: 22,2444           72421                           BDSU     SL1                                   
015474,000781: 22,2445           00015                                    12D                                   
015475,000782: 22,2446           10003                           STORE    2,2                                   #  C1=-COS(THETA)SIN(PSI)COS(PHI)
015476,000783: 22,2447           41345                           DLOAD    DMP                                   
015477,000784: 22,2450           00003                                    2                                     
015478,000785: 22,2451           00005                                    4                                     
015479,000786: 22,2452           41325                           PDDL     DMP                                   #  (PD7 COS(PHI)SIN(THETA)) SCALED 4
015480,000787: 22,2453           00007                                    6                                     
015481,000788: 22,2454           00011                                    8D                                    
015482,000789: 22,2455           72405                           DMP      SL1                                   
015483,000790: 22,2456           00001                                    0                                     
015484,000791: 22,2457           72415                           DAD      SL1                                   
015485,000792: 22,2460           00017                                    14D                                   
015486,000793: 22,2461           10005                           STORE    4,2                                   #  C2=COS(THETA)SIN(PSI)SIN(PHI)
015487,000794: 22,2462           77745                           DLOAD                                          
015488,000795: 22,2463           00011                                    8D                                    
015489,000796: 22,2464           10007                           STORE    6,2                                   #  C3=SIN(PSI)
015490,000797: 22,2465           77745                           DLOAD                                          
015491,000798: 22,2466           00013                                    10D                                   
015492,000799: 22,2467           72405                           DMP      SL1                                   
015493,000800: 22,2470           00003                                    2                                     
015494,000801: 22,2471           10011                           STORE    8D,2                                  #  C4=COS(PSI)COS(PHI)
015495,000802: 22,2472           41345                           DLOAD    DMP                                   
015496,000803: 22,2473           00013                                    10D                                   
015497,000804: 22,2474           00001                                    0                                     
015498,000805: 22,2475           72476                           DCOMP    SL1                                   
015499,000806: 22,2476           10013                           STORE    10D,2                                 #  C5=-COS(PSI)SIN(PHI)
015500,000807: 22,2477           41345                           DLOAD    DMP                                   
015501,000808: 22,2500           00005                                    4                                     
015502,000809: 22,2501           00013                                    10D                                   
015503,000810: 22,2502           72476                           DCOMP    SL1                                   
015504,000811: 22,2503           10015                           STORE    12D,2                                 #  C6=-SIN(THETA)COS(PSI)
015505,000812: 

Page 364

015507,000814: 22,2504           77745                           DLOAD                                          
015508,000815: 22,2505           72405                           DMP      SL1                                   #   (PUSH UP 7)
015509,000816: 22,2506           00011                                    8D                                    
015510,000817: 22,2507           41325                           PDDL     DMP                                   #   (PD7 COS(PHI)SIN(THETA)SIN(PSI)) SCALE4
015511,000818: 22,2510           00007                                    6                                     
015512,000819: 22,2511           00001                                    0                                     
015513,000820: 22,2512           72415                           DAD      SL1                                   #   (PUSH UP 7)
015514,000821: 22,2513           77626                           STADR                                          #  C7=COS(PHI)SIN(THETA)SIN(PSI)
015515,000822: 22,2514           67760                           STORE    14D,2                                 #   +COS(THETA)SIN(PHI)
015516,000823: 22,2515           77745                           DLOAD                                          
015517,000824: 22,2516           72405                           DMP      SL1                                   #   (PUSH UP 6)
015518,000825: 22,2517           00011                                    8D                                    
015519,000826: 22,2520           41325                           PDDL     DMP                                   #   (PD6 SIN(THETA)SIN(PHI)SIN(PSI)) SCALE4
015520,000827: 22,2521           00007                                    6                                     
015521,000828: 22,2522           00003                                    2                                     
015522,000829: 22,2523           72425                           DSU      SL1                                   #   (PUSH UP 6)
015523,000830: 22,2524           77626                           STADR                                          
015524,000831: 22,2525           67756                           STORE    16D,2                                 #  C8=-SIN(THETA)SIN(PHI)SIN(PSI)
015525,000832: 22,2526           77616                           RVQ                                            #   +COS(THETA)COS(PHI)
015526,000833: 
015527,000834:                                                                                                  #  CALCULATION OF THE MATRIX DEL......
015528,000835: 
015529,000836:                                                                                                  #           *      *               --T           *
015530,000837:                                                                                                  #           DEL = (IDMATRIX)COS(A)+UU (1-COS(A))+UX SIN(A)         SCALED 1
015531,000838: 
015532,000839:                                                                                                  #                 -
015533,000840:                                                                                                  #           WHERE U IS A UNIT VECTOR (DP SCALED 2) ALONG THE AXIS OF ROTATION.
015534,000841:                                                                                                  #           A IS THE ANGLE OF ROTATION (DP SCALED 2)
015535,000842:                                                                                                  #                                              -
015536,000843:                                                                                                  #           UPON ENTRY THE STARTING ADDRESS OF U IS COF, AND A IS IN MPAC
015537,000844: 
015538,000845: 22,2527           41401        DELCOMP            SETPD    PUSH                                  #  MPAC CONTAINS THE ANGLE A
015539,000846: 22,2530           00001                                    0                                     
015540,000847: 22,2531           65356                           SIN      PDDL                                  #  PD0 = SIN(A)
015541,000848: 22,2532           41546                           COS      PUSH                                  #  PD2 = COS(A)
015542,000849: 22,2533           65302                           SR2      PDDL                                  #  PD2 = COS(A)                            $8
015543,000850: 22,2534           41021                           BDSU     BOVB                                  
015544,000851: 22,2535           06516                                    DPHALF                                
015545,000852: 22,2536           21713                                    SIGNMPAC                              
015546,000853: 22,2537           77725                           PDDL                                           #  PD4 = 1-COS(A)
015547,000854: 
015548,000855:                                                                                                  #  COMPUTE THE DIAGONAL COMPONENTS OF DEL
015549,000856: 
015550,000857: 22,2540           03270                                    COF                                   
015551,000858: 22,2541           41316                           DSQ      DMP                                   
015552,000859: 22,2542           00005                                    4                                     
015553,000860: 22,2543           52415                           DAD      SL3                                   
015554,000861: 22,2544           00003                                    2                                     
015555,000862: 22,2545           77604                           BOVB                                           
015556,000863: 22,2546           21713                                    SIGNMPAC                              
015557,000864: 

Page 365

015559,000866: 22,2547           16231                           STODL    KEL                                   #  UX UX(1-COS(A)) +COS(A)                $1
015560,000867: 22,2550           03272                                    COF        +2                         
015561,000868: 22,2551           41316                           DSQ      DMP                                   
015562,000869: 22,2552           00005                                    4                                     
015563,000870: 22,2553           52415                           DAD      SL3                                   
015564,000871: 22,2554           00003                                    2                                     
015565,000872: 22,2555           77604                           BOVB                                           
015566,000873: 22,2556           21713                                    SIGNMPAC                              
015567,000874: 22,2557           16241                           STODL    KEL        +8D                        #  UY UY(1-COS(A)) +COS(A)                $1
015568,000875: 22,2560           03274                                    COF        +4                         
015569,000876: 22,2561           41316                           DSQ      DMP                                   
015570,000877: 22,2562           00005                                    4                                     
015571,000878: 22,2563           52415                           DAD      SL3                                   
015572,000879: 22,2564           00003                                    2                                     
015573,000880: 22,2565           77604                           BOVB                                           
015574,000881: 22,2566           21713                                    SIGNMPAC                              
015575,000882: 22,2567           02251                           STORE    KEL        +16D                       #  UZ UZ(1-COS(A)) +COS(A)                $1
015576,000883: 
015577,000884:                                                                                                  #  COMPUTE THE OFF DIAGONAL TERMS OF DEL
015578,000885: 
015579,000886: 22,2570           41345                           DLOAD    DMP                                   
015580,000887: 22,2571           03270                                    COF                                   
015581,000888: 22,2572           03272                                    COF        +2                         
015582,000889: 22,2573           72405                           DMP      SL1                                   
015583,000890: 22,2574           00005                                    4                                     
015584,000891: 22,2575           41325                           PDDL     DMP                                   #  D6  UX UY (1-COS A)                 $ 4
015585,000892: 22,2576           03274                                    COF        +4                         
015586,000893: 22,2577           00001                                    0                                     
015587,000894: 22,2600           43206                           PUSH     DAD                                   #  D8  UZ SIN A                        $ 4
015588,000895: 22,2601           00007                                    6                                     
015589,000896: 22,2602           41112                           SL2      BOVB                                  
015590,000897: 22,2603           21713                                    SIGNMPAC                              
015591,000898: 22,2604           16237                           STODL    KEL        +6                         
015592,000899: 22,2605           62421                           BDSU     SL2                                   
015593,000900: 22,2606           77604                           BOVB                                           
015594,000901: 22,2607           21713                                    SIGNMPAC                              
015595,000902: 22,2610           16233                           STODL    KEL        +2                         
015596,000903: 22,2611           03270                                    COF                                   
015597,000904: 22,2612           41205                           DMP      DMP                                   
015598,000905: 22,2613           03274                                    COF        +4                         
015599,000906: 22,2614           00005                                    4                                     
015600,000907: 22,2615           65352                           SL1      PDDL                                  #  D6  UX UZ (1-COS A)                 $ 4
015601,000908: 22,2616           03272                                    COF        +2                         
015602,000909: 22,2617           41405                           DMP      PUSH                                  #  D8  UY SIN(A)
015603,000910: 22,2620           00001                                    0                                     
015604,000911: 22,2621           62415                           DAD      SL2                                   
015605,000912: 22,2622           00007                                    6                                     
015606,000913: 22,2623           77604                           BOVB                                           
015607,000914: 22,2624           21713                                    SIGNMPAC                              
015608,000915: 22,2625           16235                           STODL    KEL        +4                         #  UX UZ (1-COS(A))+UY SIN(A)
015609,000916: 

Page 366

015611,000918: 22,2626           62421                           BDSU     SL2                                   
015612,000919: 22,2627           77604                           BOVB                                           
015613,000920: 22,2630           21713                                    SIGNMPAC                              
015614,000921: 22,2631           16245                           STODL    KEL        +12D                       #  UX UZ (1-COS(A))-UY SIN(A)
015615,000922: 22,2632           03272                                    COF        +2                         
015616,000923: 22,2633           41205                           DMP      DMP                                   
015617,000924: 22,2634           03274                                    COF        +4                         
015618,000925: 22,2635           00005                                    4                                     
015619,000926: 22,2636           65352                           SL1      PDDL                                  #  D6  UY UZ (1-COS(A))                $ 4
015620,000927: 22,2637           03270                                    COF                                   
015621,000928: 22,2640           41405                           DMP      PUSH                                  #  D8  UX SIN(A)
015622,000929: 22,2641           00001                                    0                                     
015623,000930: 22,2642           62415                           DAD      SL2                                   
015624,000931: 22,2643           00007                                    6                                     
015625,000932: 22,2644           77604                           BOVB                                           
015626,000933: 22,2645           21713                                    SIGNMPAC                              
015627,000934: 22,2646           16247                           STODL    KEL        +14D                       #  UY UZ(1-COS(A)) +UX SIN(A)
015628,000935: 22,2647           62421                           BDSU     SL2                                   
015629,000936: 22,2650           77604                           BOVB                                           
015630,000937: 22,2651           21713                                    SIGNMPAC                              
015631,000938: 22,2652           02243                           STORE    KEL        +10D                       #  UY UZ (1-COS(A)) -UX SIN(A)
015632,000939: 22,2653           77616                           RVQ                                            
015633,000940: 
015634,000941: 
015635,000942:                                                                                                  #  DIRECTION COSINE MATRIX TO CDU ANGLE ROUTINE
015636,000943:                                                                                                  #  X1 CONTAINS THE COMPLEMENT OF THE STARTING ADDRESS FOR MATRIX (SCALED 2)
015637,000944:                                                                                                  #  LEAVES CDU ANGLES SCALED 2PI IN V(MPAC)
015638,000945:                                                                                                  #  COS(MGA) WILL BE LEFT IN S1 (SCALED 1)
015639,000946: 
015640,000947:                                                                                                  #  THE DIRECTION COSINE MATRIX RELATING S/C AXES TO STABLE MEMBER AXES CAN BE WRITTEN AS***
015641,000948: 
015642,000949:                                                                                                  #           C =COS(THETA)COS(PSI)
015643,000950:                                                                                                  #            0
015644,000951:                                                                                                  #           C =-COS(THETA)SIN(PSI)COS(PHI)+SI (THETA)SIN(PHI)
015645,000952:                                                                                                  #            1
015646,000953:                                                                                                  #           C =COS(THETA)SIN(PSI)SIN(PHI) + S N(THETA)COS(PHI)
015647,000954:                                                                                                  #            2
015648,000955:                                                                                                  #           C =SIN(PSI)
015649,000956:                                                                                                  #            3
015650,000957:                                                                                                  #           C =COS(PSI)COS(PHI)
015651,000958:                                                                                                  #            4
015652,000959:                                                                                                  #           C =-COS(PSI)SIN(PHI)
015653,000960:                                                                                                  #            5
015654,000961:                                                                                                  #           C =-SIN(THETA)COS(PSI)
015655,000962:                                                                                                  #            6
015656,000963:                                                                                                  #           C =SIN(THETA)SIN(PSI)COS(PHI)+COS THETA)SIN(PHI)
015657,000964:                                                                                                  #            7
015658,000965:                                                                                                  #           C =-SIN(THETA)SIN(PSI)SIN(PHI)+CO (THETA)COS(PHI)
015659,000966:                                                                                                  #            8
015660,000967: 

Page 367

015662,000969: 
015663,000970:                                                                                                  #           WHERE PHI = OGA
015664,000971:                                                                                                  #                 THETA = IGA
015665,000972:                                                                                                  #                 PSI = MGA
015666,000973: 
015667,000974: 22,2654           67543        DCMTOCDU           DLOAD*   ARCSIN                                
015668,000975: 22,2655           00007                                    6,1                                   
015669,000976: 22,2656           71406                           PUSH     COS                                   #  PD +0   PSI
015670,000977: 22,2657           41152                           SL1      BOVB                                  
015671,000978: 22,2660           21713                                    SIGNMPAC                              
015672,000979: 22,2661           00051                           STORE    S1                                    
015673,000980: 22,2662           57543                           DLOAD*   DCOMP                                 
015674,000981: 22,2663           00015                                    12D,1                                 
015675,000982: 22,2664           67471                           DDV      ARCSIN                                
015676,000983: 22,2665           00051                                    S1                                    
015677,000984: 22,2666           51123                           PDDL*    BPL                                   #  PD +2  THETA
015678,000985: 22,2667           00001                                    0,1                                   #  MUST CHECK THE SIGN OF COS(THETA)
015679,000986: 22,2670           44702                                    OKTHETA                               #  TO DETERMINE THE PROPER QUADRANT
015680,000987: 22,2671           57545                           DLOAD    DCOMP                                 
015681,000988: 22,2672           43244                           BPL      DAD                                   
015682,000989: 22,2673           44677                                    SUHALFA                               
015683,000990: 22,2674           06516                                    DPHALF                                
015684,000991: 22,2675           77650                           GOTO                                           
015685,000992: 22,2676           44701                                    CALCPHI                               
015686,000993: 22,2677           77625        SUHALFA            DSU                                            
015687,000994: 22,2700           06516                                    DPHALF                                
015688,000995: 22,2701           77606        CALCPHI            PUSH                                           
015689,000996: 22,2702           57543        OKTHETA            DLOAD*   DCOMP                                 
015690,000997: 22,2703           00013                                    10D,1                                 
015691,000998: 22,2704           67471                           DDV      ARCSIN                                
015692,000999: 22,2705           00051                                    S1                                    
015693,001000: 22,2706           51123                           PDDL*    BPL                                   #  PUSH DOWN PHI
015694,001001: 22,2707           00011                                    8D,1                                  
015695,001002: 22,2710           44722                                    OKPHI                                 
015696,001003: 22,2711           57545                           DLOAD    DCOMP                                 #  PUSH UP PHI
015697,001004: 22,2712           43244                           BPL      DAD                                   
015698,001005: 22,2713           44717                                    SUHALFAP                              
015699,001006: 22,2714           06516                                    DPHALF                                
015700,001007: 22,2715           77650                           GOTO                                           
015701,001008: 22,2716           44723                                    VECOFANG                              
015702,001009: 22,2717           52025        SUHALFAP           DSU      GOTO                                  
015703,001010: 22,2720           06516                                    DPHALF                                
015704,001011: 22,2721           44723                                    VECOFANG                              
015705,001012: 22,2722           77745        OKPHI              DLOAD                                          #  PUSH UP PHI
015706,001013: 22,2723           43466        VECOFANG           VDEF     RVQ                                   
015707,001014: 

Page 368

015709,001016:                                                                                                  #  ROUTINES FOR TERMINATING THE AUTOMATIC MANEUVER AND RETURNING TO USER
015710,001017: 
015711,001018: 22,2724           77776        TOOBADF            EXIT                                           
015712,001019: 22,2725           05600                           TC       ALARM                                 
015713,001020: 22,2726           00401                           OCT      00401                                 
015714,001021: 
015715,001022: 22,2727           12732                           TCF      NOGO                                  #  DO NOT ZERO ATTITUDE ERRORS
015716,001023: 
015717,001024: 22,2730           04616                           TC       BANKCALL                              
015718,001025: 22,2731           40154                           CADR     ZATTEROR                              #  ZERO ATTITUDE ERRORS
015719,001026: 
015720,001027: 22,2732           04616        NOGO               TC       BANKCALL                              
015721,001028: 22,2733           40166                           CADR     STOPRATE                              #  STOP RATES
015722,001029: 
015723,001030: 22,2734           34752                           CAF      TWO                                   
015724,001031: 22,2735           00004                           INHINT                                         #  ALL RETURNS ARE NOW MADE VIA GOODEND
015725,001032: 22,2736           05214                           TC       WAITLIST                              
015726,001033: 22,2737  E6,1675                                  EBANK=   BCDU                                  
015727,001034: 22,2737           03234 44066                     2CADR    GOODMANU                              
015728,001035: 
015729,001036: 22,2741           15155                           TCF      ENDOFJOB                              
015730,001037: 
015731,001038: 22,2742           77776        TOOBADI            EXIT                                           
015732,001039: 22,2743           12732                           TCF      NOGO                                  

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