Source Code

These source-code files were transcribed from scans made from Don Eyles's personal copy of Luminary 069. They were scanned at archive.org's Boston facility, and the scanning was sponsored by Onno Hommes. The code was transcribed from these scans by a team of volunteers who are referenced in the program comments. Comments from the original source code are prefixed with a single '#' symbol, whereas comments added later are prefixed by "##" or "###". In some cases, where similar code blocks exist in previously-transcribed AGC programs (primarily Luminary 99, from Apollo 11) those code blocks were used as a starting point and then corrected to agree with the Luminary 69 scans. The full scans are available at the Virtual AGC project's collection at archive.org, while more-convenient reduced-size (but reduced-quality) images are available at the main Virtual AGC website. Report any errors noted by creating an issue report at the Virtual AGC project's GitHub repository. Notations on the program listing read, in part:

	GAP:  ASSEMBLE REVISION 069 OF AGC PROGRAM LUMINARY BY NASA 2021112-011
	19:02 NOV. 25,1968
Note that the date is the date of the printout, not the date of the program revision.

015267,000002:                                                                                                  ## Copyright:   Public domain.
015268,000003:                                                                                                  ## Filename:    ATTITUDE_MANEUVER_ROUTINE.agc
015269,000004:                                                                                                  ## Purpose:     The main source file for Luminary revision 069.
015270,000005:                                                                                                  ##              It is part of the source code for the original release
015271,000006:                                                                                                  ##              of the flight software for the Lunar Module's (LM) Apollo
015272,000007:                                                                                                  ##              Guidance Computer (AGC) for Apollo 10. The actual flown
015273,000008:                                                                                                  ##              version was Luminary 69 revision 2, which included a
015274,000009:                                                                                                  ##              newer lunar gravity model and only affected module 2.
015275,000010:                                                                                                  ##              This file is intended to be a faithful transcription, except
015276,000011:                                                                                                  ##              that the code format has been changed to conform to the
015277,000012:                                                                                                  ##              requirements of the yaYUL assembler rather than the
015278,000013:                                                                                                  ##              original YUL assembler.
015279,000014:                                                                                                  ## Reference:   pp. 355-376
015280,000015:                                                                                                  ## Assembler:   yaYUL
015281,000016:                                                                                                  ## Contact:     Ron Burkey <info@sandroid.org>.
015282,000017:                                                                                                  ## Website:     www.ibiblio.org/apollo/index.html
015283,000018:                                                                                                  ## Mod history: 2016-12-13 MAS  Created from Luminary 99.
015284,000019:                                                                                                  ##              2016-12-14 MAS  Updated from comment-proofed Luminary 99 version.
015285,000020:                                                                                                  ##              2017-01-19 MAS  Updated for Luminary 69 -- just whitespace.
015286,000021:                                                                                                  ##              2017-01-27 RSB  Proofed comment text using octopus/prooferComments
015287,000022:                                                                                                  ##                              and fixed errors found.
015288,000023:                                                                                                  ##              2017-03-07 RSB  Comment-text fixes noted in proofing Luminary 116.
015289,000024: 

Page 355

015291,000026:                                                                                                  #  BLOCK 2 LGC ATTITUDE MANEUVER ROUTINE-KALCMANU
015292,000027: 
015293,000028: 
015294,000029:                                                                                                  #  MOD 2           DATE  5/1/67    BY DON KEENE
015295,000030:                                                                                                  #  PROGRAM DESCRIPTION
015296,000031: 
015297,000032:                                                                                                  #       KALCMANU IS A ROUTINE WHICH GENERATES COMMANDS FOR THE LM DAP TO CHANGE THE ATTITUDE OF THE SPACECRAFT
015298,000033:                                                                                                  #  DURING FREE FALL.  IT IS DESIGNED TO MANEUVER THE SPACECRAFT FROM ITS INITIAL ORIENTATION TO SOME DESIRED
015299,000034:                                                                                                  #  ORIENTATION SPECIFIED BY THE PROGRAM WHICH CALLS KALCMANU, AVOIDING GIMBAL LOCK IN THE PROCESS.  IN THE 
015300,000035:                                                                                                  #  MOD 2 VERSION, THIS DESIRED ATTITUDE IS SPECIFIED BY A SET OF THREE COMMANDED CDU ANGLES STORED AS 2S COMPLEMENT
015301,000036:                                                                                                  #  SINGLE PRECISION ANGLES IN THE THREE CONSECUTIVE LOCATIONS, CPHI, CTHETA, CPSI, WHERE
015302,000037: 
015303,000038:                                                                                                  #       CPHI = COMMANDED OUTER GIMBAL ANGLE
015304,000039:                                                                                                  #       CTHETA = COMMANDED INNER GIMBAL ANGLE
015305,000040:                                                                                                  #       CPSI = COMMANDED MIDDLE GIMBAL ANGLE
015306,000041: 
015307,000042:                                                                                                  #      WHEN POINTING A SPACECRAFT AXIS (E.I. X, Y, Z, THE AOT, THRUST AXIS, ETC) THE SUBROUTINE VECPOINT MAY BE
015308,000043:                                                                                                  #  USED TO GENERATE THIS SET OF DESIRED CDU ANGLES (SEE DESCRIPTION IN R60)   -
015309,000044:                                                                                                  #   WITH THIS INFORMATION KALCMANU DETERMINES THE DIRECTION OF THE SINGLE EQUIVALENT ROTATION (COF ALSO U) AND THE
015310,000045:                                                                                                  #  MAGNITUDE OF THE ROTATION (AM) TO BRING THE S/C FROM ITS INITIAL ORIENTATION TO ITS FINAL ORIENTATION.
015311,000046:                                                                                                  #  THIS DIRECTION REMAINS FIXED BOTH IN INERTIAL COORDINATES AND IN COMMANDED S/C AXES THROUGHOUT THE
015312,000047:                                                                                                  #                   -
015313,000048:                                                                                                  #  MANEUVER.  ONCE COF AND AM HAVE BEEN DETERMINED, KALCMANU THEN EXAMINES THE MANEUVER TO SEE IF IT WILL BRING
015314,000049:                                                                                                  #                                        -
015315,000050:                                                                                                  #  THE S/C THROUGH GIMBAL LOCK.  IF SO, COF AND AM ARE READJUSTED SO THAT THE S/C WILL JUST SKIM THE GIMBAL
015316,000051:                                                                                                  #  LOCK ZONE AND ALIGN THE X-AXIS.  IN GENERAL A FINAL YAW  ABOUT X WILL BE NECESSARY TO COMPLETE THE MANEUVER.
015317,000052:                                                                                                  #  NEEDLESS TO SAY, NEITHER THE INITIAL NOR THE FINAL ORIENTATION CAN BE IN GIMBAL LOCK.
015318,000053: 
015319,000054:                                                                                                  #       FOR PROPER ATTITUDE CONTROL THE DIGITAL AUTOPILOT MUST BE GIVEN AN ATTITUDE REFERENCE WHICH IT CAN TRACK.
015320,000055:                                                                                                  #  KALCMANU DOES THIS BY GENERATING A REFERENCE OF DESIRED GIMBAL ANGLES (CDUXD, CDUYD, CDUZD) WHICH ARE UPDATED
015321,000056:                                                                                                  #  EVERY ONE SECOND DURING THE MANEUVER.  TO ACHIEVE A SMOOTHER SEQUENCE OF COMMANDS BETWEEN SUCCESSIVE UPDATES,
015322,000057:                                                                                                  #  THE PROGRAM ALSO GENERATES A SET OF INCREMENTAL CDU ANGLES (DELDCDU) TO BE ADDED TO CDU DESIRED BY THE DIGITAL
015323,000058:                                                                                                  #  AUTOPILOT.  KALCMANU ALSO CALCULATES THE COMPONENT MANEUVER RATES (OMEGAPD, OMEGAQD, OMEGARD), WHICH CAN
015324,000059:                                                                                                  #                                       -
015325,000060:                                                                                                  #  BE DETERMINED SIMPLY BY MULTIPLYING COF BY SOME SCALAR (ARATE) CORRESPONDING TO THE DESIRED ROTATIONAL RATE.
015326,000061: 
015327,000062:                                                                                                  #       AUTOMATIC MANEUVERS ARE TIMED WITH THE HELP OF WAITLIST SO THAT AFTER A SPECIFIED INTERVAL THE Y AND Z
015328,000063:                                                                                                  #  DESIRED RATES ARE SET TO ZERO AND THE DESIRED CDU ANGLES (CDUYD, CDUZD) ARE SET EQUAL TO THE FINAL DESIRED CDU
015329,000064:                                                                                                  #  ANGLES (CTHETA, CPSI).  IF ANY YAW  REMAINS DUE TO GIMBAL LOCK AVOIDANCE, THE FINAL YAW  MANEUVER IS
015330,000065:                                                                                                  #  CALCULATED AND THE DESIRED YAW  RATE SET TO SOME FIXED VALUE (ROLLRATE = + OR - 2 DEGREES PER SEC).
015331,000066:                                                                                                  #  IN THIS CASE ONLY AN INCREMENTAL CDUX ANGLE (DELFROLL) IS SUPPLIED TO THE DAP.  AT THE END OF THE YAW
015332,000067:                                                                                                  #  MANEUVER OR IN THE EVENT THAT THERE WAS NO FINAL YAW,  CDUXD IS SET EQUAL TO CPHI AND THE X-AXIS DESIRED
015333,000068:                                                                                                  #  RATE SET TO ZERO.  THUS, UPON COMPLETION OF THE MANEUVER THE S/C WILL FINISH UP IN A LIMIT CYCLE ABOUT THE
015334,000069:                                                                                                  #  DESIRED FINAL GIMBAL ANGLES.
015335,000070: 
015336,000071: 
015337,000072:                                                                                                  #  PROGRAM LOGIC FLOW
015338,000073: 
015339,000074:                                                                                                  #       KALCMANU IS CALLED AS A HIGH PRIORITY JOB WITH ENTRY POINTS AT KALCMAN3 AND VECPOINT.  IT FIRST PICKS
015340,000075:                                                                                                  #  UP THE CURRENT CDU ANGLES TO BE USED AS THE BASIS FOR ALL COMPUTATIONS INVOLVING THE INITIAL S/C ORIENTATION.

Page 356

015342,000077:                                                                                                  #  IT THEN DETERMINES THE DIRECTION COSINE MATRICES RELATING BOTH THE INITIAL AND FINAL S/C ORIENTATION TO STABLE
015343,000078:                                                                                                  #                *    *                                                                               *
015344,000079:                                                                                                  #  MEMBER AXES (MIS, MFS).  IT ALSO COMPUTES THE MATRIX RELATING FINAL S/C AXES TO INITIAL S/C AXES (MFI).  THE
015345,000080:                                                                                                  #  ANGLE OF ROTATION (AM) IS THEN EXTRACTED FROM THIS MATRIX, AND TESTS ARE MADE TO DETERMINE IF
015346,000081: 
015347,000082:                                                                                                  #       A)  AM LESS THAN .25 DEGREES (MINANG)
015348,000083:                                                                                                  #       B)  AM GREATER THAN 170 DEGREES (MAXANG)
015349,000084: 
015350,000085:                                                                                                  #       IF AM LESS THAN .25 DEGREES, NO COMPLICATED AUTOMATIC MANEUVERING IS NECESSARY.  THEREFORE WE CAN SIMPLY
015351,000086:                                                                                                  #  SET CDU DESIRED EQUAL TO THE FINAL CDU DESIRED ANGLES AND TERMINATE THE JOB.
015352,000087: 
015353,000088:                                                                                                  #       IF AM IS GREATER THAN .25 DEGREES BUT LESS THAN 170 DEGREES, THE AXES OF THE SINGLE EQUIVALENT ROTATION
015354,000089:                                                                                                  #    -                                                       *
015355,000090:                                                                                                  #  (COF) IS EXTRACTED FROM THE SKEW SYMMETRIC COMPONENTS OF MFI.                            *     *
015356,000091:                                                                                                  #       IF AM GREATER THAN 170 DEGREES AN ALTERNATE METHOD EMPLOYING THE SYMMETRIC PART OF MFI (MFISYM) IS USED
015357,000092:                                                                                                  #                -
015358,000093:                                                                                                  #  TO DETERMINE COF.
015359,000094: 
015360,000095:                                                                                                  #       THE PROGRAM THEN CHECKS TO SEE IF THE MANEUVER AS COMPUTED WILL BRING THE S/C THROUGH GIMBAL LOCK.  IF
015361,000096:                                                                                                  #  SO, A NEW MANEUVER IS CALCULATED WHICH WILL JUST SKIM THE GIMBAL LOCK ZONE AND ALIGN THE S/C X-AXIS.  THIS
015362,000097:                                                                                                  #  METHOD ASSURES THAT THE ADDITIONAL MANEUVERING TO AVOID GIMBAL LOCK WILL BE KEPT TO A MINIMUM.  SINCE A FINAL
015363,000098:                                                                                                  #  P AXIS YAW WILL BE NECESSARY, A SWITCH IS RESET (STATE SWITCH 31) TO ALLOW FOR THE COMPUTATION OF THIS FINAL
015364,000099:                                                                                                  #  YAW.
015365,000100: 
015366,000101:                                                                                                  #       AS STATED PREVIOUSLY KALCMANU GENERATES A SEQUENCE OF DESIRED GIMBAL ANGLES WHICH ARE UPDATED EVERY 
015367,000102:                                                                                                  #                                                                                               -
015368,000103:                                                                                                  #  SECOND.  THIS IS ACCOMPLISHED BY A SMALL ROTATION OF THE DESIRED S/C FRAME ABOUT THE VECTOR COF.  THE NEW
015369,000104:                                                                                                  #  DESIRED REFERENCE MATRIX IS THEN,
015370,000105: 
015371,000106:                                                                                                  #                   *              *         *
015372,000107:                                                                                                  #                  MIS       =    MIS       DEL
015373,000108:                                                                                                  #                     N+1            N
015374,000109: 
015375,000110:                                                                                                  #         *
015376,000111:                                                                                                  #  WHERE DEL IS THE MATRIX CORRESPONDING TO THIS SMALL ROTATION.  THE NEW CDU ANGLES CAN THEN BE EXTRACTED
015377,000112:                                                                                                  #        *
015378,000113:                                                                                                  #  FROM MIS.
015379,000114: 
015380,000115:                                                                                                  #       AT THE BEGINNING OF THE MANEUVER THE AUTOPILOT DESIRED RATES (OMEGAPD, OMEGAQD, OMEGARD) AND THE 
015381,000116:                                                                                                  #  MANEUVER TIMINGS ARE ESTABLISHED.  ON THE FIRST PASS AND ON ALL SUBSEQUENT UPDATES THE CDU DESIRED
015382,000117:                                                                                                  #  ANGLES ARE LOADED WITH THE APPROPRIATE VALUES AND THE INCREMENTAL CDU ANGLES ARE COMPUTED.  THE AGC CLOCKS
015383,000118:                                                                                                  #  (TIME1 AND TIME2) ARE THAN CHECKED TO SEE IF THE MANEUVER WILL TERMINATE BEFORE THE NEXT UPDATE.  IF
015384,000119:                                                                                                  #  NOT, KALCMANU CALLS FOR ANOTHER UPDATE (RUN AS A JOB WITH PRIORITY TBD) IN ONE SECOND.  ANY DELAYS IN THIS
015385,000120:                                                                                                  #  CALLING SEQUENCE ARE AUTOMATICALLY COMPENSATED IN CALLING FOR THE NEXT UPDATE.
015386,000121: 
015387,000122:                                                                                                  #       IF IT IS FOUND THAT THE MANEUVER IS TO TERMINATE BEFORE THE NEXT UPDATE A ROUTINE IS CALLED (AS A WAIT-
015388,000123:                                                                                                  #  LIST TASK) TO STOP THE MANEUVER AT THE APPROPRIATE TIME AS EXPLAINED ABOVE.
015389,000124: 

Page 357

015391,000126:                                                                                                  #  CALLING SEQUENCE
015392,000127: 
015393,000128:                                                                                                  #       IN ORDER TO PERFORM A KALCMANU SUPERVISED MANEUVER, THE COMMANDED GIMBAL ANGLES MUST BE PRECOMPUTED AND
015394,000129:                                                                                                  #  STORED IN LOCATIONS CPHI, CTHETA, CPSI.  THE USER:S PROGRAM MUST THEN CLEAR STATE SWITCH NO 33 TO ALLOW THE 
015395,000130:                                                                                                  #  ATTITUDE MANEUVER ROUTINE TO PERFORM ANY FINAL P-AXIS YAW INCURRED BY AVOIDING GIMBAL LOCK.  THE MANEUVER IS
015396,000131:                                                                                                  #  THEN INITIATED BY ESTABLISHING THE FOLLOWING EXECUTIVE JOB
015397,000132: 
015398,000133:                                                                                                  #                         *
015399,000134:                                                                                                  #       CAF     PRIO    XX
015400,000135:                                                                                                  #                       --
015401,000136:                                                                                                  #       INHINT
015402,000137:                                                                                                  #       TC         FINDVAC
015403,000138:                                                                                                  #       2CADR      KALCMAN3
015404,000139:                                                                                                  #       RELINT
015405,000140: 
015406,000141:                                                                                                  #  THE USER:S PROGRAM MAY EITHER CONTINUE OR WAIT FOR THE TERMINATION OF THE MANEUVER.  IF THE USER WISHES TO
015407,000142:                                                                                                  #  WAIT, HE MAY PUT HIS JOB TO SLEEP WITH THE FOLLOWING INSTRUCTIONS
015408,000143: 
015409,000144:                                                                                                  #       L          TC        BANKCALL
015410,000145:                                                                                                  #       L+1        CADR      ATTSTALL
015411,000146:                                                                                                  #       L+2        (BAD      RETURN)
015412,000147:                                                                                                  #       L+3        (GOOD     RETURN)
015413,000148: 
015414,000149:                                                                                                  #       UPON COMPLETION OF THE MANEUVER, THE PROGRAM WILL BE AWAKENED AT L+3 IF THE MANEUVER WAS COMPLETED
015415,000150:                                                                                                  #  SUCCESSFULLY, OR AT L+2 IF THE MANEUVER WAS ABORTED.  THIS ABORT WOULD OCCUR IF THE INITIAL OR FINAL ATTITUDE
015416,000151:                                                                                                  #  WAS IN GIMBAL LOCK.
015417,000152: 
015418,000153:                                                                                                  #  ***NOTA BENE***  IT IS ASSUMED THAT THE DESIRED MANEUVERING RATE (0.5, 2, 5, 10, DEG/SEC) HAS BEEN SELECTED BY
015419,000154:                                                                                                  #  KEYBOARD ENTRY PRIOR TO THE EXECUTION OF KALCMANU.
015420,000155:                                                                                                  #      IT IS ALSO ASSUMED THAT THE AUTOPILOT IS IN THE AUTO MODE.  IF THE MODE SWITCH IS CHANGED DURING THE
015421,000156:                                                                                                  #  MANEUVER, KALCMANU WILL TERMINATE VIA GOODEND WITHIN 1 SECOND SO THAT R60 MAY REQUEST A TRIM OF THE S/C ATTITUDE
015422,000157:                                                                                                  #  THIS IS THE ONLY MEANS FOR MANUALLY TERMINATING A KALCMANU SUPERVISED MANEUVER.
015423,000158:                                                                                                  #  SUBROUTINES
015424,000159: 
015425,000160:                                                                                                  #       KALCMANU USES A NUMBER OF INTERPRETIVE SUBROUTINES WHICH MAY BE OF GENERAL INTEREST.  SINCE THESE ROUTINES
015426,000161:                                                                                                  #  WERE PROGRAMMED EXCLUSIVELY FOR KALCMANU, THEY ARE NOT, AS YET, GENERALLY AVAILABLE FOR USE BY OTHER PROGRAMS.
015427,000162: 
015428,000163:                                                                                                  #       MXM3
015429,000164:                                                                                                  #       ----
015430,000165: 
015431,000166:                                                                                                  #       THIS SUBROUTINE MULTIPLIES TWO 3X3 MATRICES AND LEAVES THE RESULT IN THE FIRST 18 LOCATIONS OF THE PUSH
015432,000167:                                                                                                  #  DOWN LIST, I.E.,
015433,000168: 
015434,000169:                                                                                                  #                 (M    M    M )
015435,000170:                                                                                                  #                 ( 0    1    2)
015436,000171:                                                                                                  #        *        (            )       *         *
015437,000172:                                                                                                  #        M    =   (M    M    M )  =    M1   X    M2
015438,000173:                                                                                                  #                 ( 3    4    5)
015439,000174:                                                                                                  #                 (            )
015440,000175:                                                                                                  #                 (M    M    M )

Page 358

015442,000177:                                                                                                  #                 ( 6    7    8)
015443,000178: 
015444,000179:                                                                                                  #                                                                                        *
015445,000180:                                                                                                  #       INDEX REGISTER X1 MUST BE LOADED WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M1, AND X2 MUST BE
015446,000181:                                                                                                  #                                                         *
015447,000182:                                                                                                  #  LOADED WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M2.   THE ROUTINE USES THE FIRST 20 LOCATIONS OF THE PUSH
015448,000183:                                                                                                  #  DOWN LIST.  THE FIRST ELEMENT OF THE MATRIX APPEARS IN PDO.  PUSH UP FOR M .
015449,000184:                                                                                                  #                                                                            8
015450,000185: 
015451,000186:                                                                                                  #       TRANSPOS
015452,000187:                                                                                                  #       --------
015453,000188: 
015454,000189:                                                                                                  #       THIS ROUTINE TRANSPOSES A 3X3 MATRIX AND LEAVES THE RESULT IN THE PUSH DOWN LIST, I.E.,
015455,000190:                                                                                                  #  
015456,000191:                                                                                                  #        *         * T
015457,000192:                                                                                                  #        M    =    M1
015458,000193: 
015459,000194:                                                                                                  #  INDEX REGISTER X1 MUST CONTAIN THE COMPLEMENT OF THE STARTING ADDRESS FOR M1.  PUSH UP FOR THE FIRST AND SUB-
015460,000195:                                                                                                  #                         *
015461,000196:                                                                                                  #  SEQUENT COMPONENTS OF M.   THIS SUBROUTINE ALSO USES THE FIRST 20 LOCATIONS OF THE PUSH DOWN LIST.
015462,000197: 
015463,000198:                                                                                                  #       CDU TO DCM
015464,000199:                                                                                                  #       ----------
015465,000200: 
015466,000201:                                                                                                  #       THIS SUBROUTINE CONVERTS THREE CDU ANGLES IN T(MPAC) TO A DIRECTION COSINE MATRIX (SCALED BY 2) RELATING
015467,000202:                                                                                                  #  THE CORRESPONDING S/C ORIENTATIONS TO THE STABLE MEMBER FRAME.  THE FORMULAS FOR THIS CONVERSION ARE
015468,000203: 
015469,000204:                                                                                                  #        M    =    COSY  COSZ
015470,000205:                                                                                                  #         0
015471,000206: 
015472,000207:                                                                                                  #        M    =    -COSY  SINZ  COSX  +  SINY  SINX
015473,000208:                                                                                                  #         1
015474,000209: 
015475,000210:                                                                                                  #        M    =    COSY  SINZ  SINX  +  SINY  COSX
015476,000211:                                                                                                  #         2
015477,000212: 
015478,000213:                                                                                                  #        M    =    SINZ
015479,000214:                                                                                                  #         3
015480,000215: 
015481,000216:                                                                                                  #        M    =    COSZ  COSX
015482,000217:                                                                                                  #         4
015483,000218: 
015484,000219:                                                                                                  #        M    =    -COSZ  SINX
015485,000220:                                                                                                  #         5
015486,000221: 
015487,000222:                                                                                                  #        M    =    -SINY  COSZ
015488,000223:                                                                                                  #         6
015489,000224:                                                                                                  #        
015490,000225:                                                                                                  #        M    =    SINY  SINZ  COSX  +  COSY  SINX
015491,000226:                                                                                                  #         7

Page 359

015493,000228:                                                                                                  #        M    =    -SINY  SINZ  SINX  +  COSY  COSX
015494,000229:                                                                                                  #         8
015495,000230: 
015496,000231:                                                                                                  #  WHERE      X    =    OUTER GIMBAL ANGLE
015497,000232:                                                                                                  #             Y    =    INNER GIMBAL ANGLE
015498,000233:                                                                                                  #             Z    =    MIDDLE GIMBAL ANGLE
015499,000234: 
015500,000235:                                                                                                  #       THE INTERPRETATION OF THIS MATRIX IS AS FOLLOWS
015501,000236: 
015502,000237:                                                                                                  #       IF A , A , A  REPRESENT THE COMPONENTS OF A VECTOR IN S/C AXES THEN THE COMPONENTS OF THE SAME VECTOR IN
015503,000238:                                                                                                  #           X   Y   Z
015504,000239:                                                                                                  #  STABLE MEMBER AXES (B , B , B ) ARE
015505,000240:                                                                                                  #                       X   Y   Z
015506,000241: 
015507,000242:                                                                                                  #             (B )                (A )
015508,000243:                                                                                                  #             ( X)                ( X)
015509,000244:                                                                                                  #             (  )                (  )
015510,000245:                                                                                                  #             (  )           *    (  )
015511,000246:                                                                                                  #             (B )      =    M    (A )
015512,000247:                                                                                                  #             ( Y)                ( Y)
015513,000248:                                                                                                  #             (  )                (  )
015514,000249:                                                                                                  #             (B )                (A )
015515,000250:                                                                                                  #             ( Z)                ( Z)
015516,000251: 
015517,000252:                                                                                                  #      THE SUBROUTINE WILL STORE THIS MATRIX IN SEQUENTIAL LOCATIONS OF ERASABLE MEMORY AS SPECIFIED BY THE CALLING
015518,000253:                                                                                                  #                                                                                                              *
015519,000254:                                                                                                  #  PROGRAM.  TO DO THIS THE CALLING PROGRAM MUST FIRST LOAD X2 WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M.
015520,000255: 
015521,000256:                                                                                                  #       INTERNALLY, THE ROUTINE USES THE FIRST 16 LOCATIONS OF THE PUSH DOWN LIST, ALSO STEP REGISTER S1 AND INDEX
015522,000257:                                                                                                  #  REGISTER X2.
015523,000258: 
015524,000259: 
015525,000260:                                                                                                  #       DCM TO CDU
015526,000261:                                                                                                  #       ----------
015527,000262:                                                                                                  #                                                                            *
015528,000263:                                                                                                  #       THIS ROUTINE EXTRACTS THE CDU ANGLES FROM A DIRECTION COSINE MATRIX (M SCALED BY 2) RELATING S/C AXIS TO
015529,000264:                                                                                                  #                                                                                  *
015530,000265:                                                                                                  #  STABLE MEMBER AXES.  X1 MUST CONTAIN THE COMPLEMENT OF THE STARTING ADDRESS FOR M.  THE SUBROUTINE LEAVES THE
015531,000266:                                                                                                  #  CORRESPONDING GIMBAL ANGLES IN V(MPAC) AS DOUBLE PRECISION 1:S COMPLEMENT ANGLES SCALED BY 2PI.  THE FORMULAS
015532,000267:                                                                                                  #  FOR THIS CONVERSION ARE
015533,000268: 
015534,000269:                                                                                                  #        Z    =    ARCSIN (M )
015535,000270:                                                                                                  #                           3
015536,000271: 
015537,000272:                                                                                                  #        Y    =    ARCSIN (-M /COSZ)
015538,000273:                                                                                                  #                            6
015539,000274: 
015540,000275:                                                                                                  #  IF M  IS NEGATIVE, Y IS REPLACED BY PI SGN Y - Y
015541,000276:                                                                                                  #      0

Page 360

015543,000278:                                                                                                  #        X    =    ARCSIN (-M /COSZ)
015544,000279:                                                                                                  #                            5
015545,000280: 
015546,000281:                                                                                                  #  IF M  IS NEGATIVE X IS REPLACED BY PI SGN X - X
015547,000282:                                                                                                  #      4
015548,000283: 
015549,000284:                                                                                                  #       THIS ROUTINE DOES NOT SET THE PUSH DOWN POINTER, BUT USES THE NEXT 8 LOCATIONS OF THE PUSH DOWN LIST AND
015550,000285:                                                                                                  #  RETURNS THE POINTER TO ITS ORIGINAL SETTING.  THIS PROCEDURE ALLOWS THE CALLER TO STORE THE MATRIX AT THE TOP OF
015551,000286:                                                                                                  #  THE PUSH DOWN LIST.
015552,000287: 
015553,000288: 
015554,000289:                                                                                                  #       DELCOMP
015555,000290:                                                                                                  #       -------
015556,000291: 
015557,000292:                                                                                                  #                                                           *
015558,000293:                                                                                                  #       THIS ROUTINE COMPUTES THE DIRECTION COSINE MATRIX (DEL) RELATING ON
015559,000294:                                                                                                  #                                                                           -
015560,000295:                                                                                                  #  IS ROTATED WITH RESPECT TO THE FIRST BY AN ANGLE, A, ABOUT A UNIT VECTOR, U.  THE FORMULA FOR THIS MATRIX IS
015561,000296: 
015562,000297:                                                                                                  #        *         *           --T           *
015563,000298:                                                                                                  #        DEL  =    I  COSA  +  UU (1-COSA) + V SINA
015564,000299:                                                                                                  #                                             X
015565,000300: 
015566,000301:                                                                                                  #  WHERE      *         (1   0    0)
015567,000302:                                                                                                  #             I    =    (0   1    0)
015568,000303:                                                                                                  #                       (0   0    1)
015569,000304: 
015570,000305: 
015571,000306:                                                                                                  #                          2                             
015572,000307:                                                                                                  #                       (U        U U       U U )
015573,000308:                                                                                                  #                       ( X        X Y       X Z)
015574,000309:                                                                                                  #                       (                       )
015575,000310:                                                                                                  #             --T       (           2           )
015576,000311:                                                                                                  #             UU   =    (U U      U         U U )
015577,000312:                                                                                                  #                       ( Y X      Y         Y Z)
015578,000313:                                                                                                  #                       (                       )
015579,000314:                                                                                                  #                       (                     2 )
015580,000315:                                                                                                  #                       (U U      U U       U  )
015581,000316:                                                                                                  #                       ( Z X      Z Y       Z  )
015582,000317: 
015583,000318: 
015584,000319:                                                                                                  #                       (0        -U        U  )
015585,000320:                                                                                                  #                       (           Z        Y )
015586,000321:                                                                                                  #             *         (                      )
015587,000322:                                                                                                  #             V    =    (U        0         -U )
015588,000323:                                                                                                  #              X        ( Z                   X)
015589,000324:                                                                                                  #                       (                      )
015590,000325:                                                                                                  #                       (-U       U         0  )
015591,000326:                                                                                                  #                       (  Y       X           )
015592,000327: 

Page 361

015594,000329:                                                                                                  #             -
015595,000330:                                                                                                  #             U    =    UNIT ROTATION VECTOR RESOLVED INTO S/C AXES
015596,000331:                                                                                                  #             A    =    ROTATION ANGLE
015597,000332: 
015598,000333:                                                                                                  #                              *
015599,000334:                                                                                                  #       THE INTERPRETATION OF DEL IS AS FOLLOWS
015600,000335: 
015601,000336:                                                                                                  #       IF A , A , A  REPRESENT THE COMPONENT OF A VECTOR IN THE ROTATED FRAME, THEN THE COMPONENTS OF THE SAME
015602,000337:                                                                                                  #           X   Y   Z
015603,000338:                                                                                                  #  VECTOR IN THE ORIGINAL S/C AXES (B , B , B ) ARE
015604,000339:                                                                                                  #                                    X   Y   Z
015605,000340: 
015606,000341:                                                                                                  #             (B )                     (A )
015607,000342:                                                                                                  #             ( X)                     ( X)
015608,000343:                                                                                                  #             (  )            *        (  )
015609,000344:                                                                                                  #             (B )      =    DEL       (A )
015610,000345:                                                                                                  #             ( Y)                     ( Y)
015611,000346:                                                                                                  #             (  )                     (  )
015612,000347:                                                                                                  #             (B )                     (A )
015613,000348:                                                                                                  #             ( Z)                     ( Z)
015614,000349: 
015615,000350:                                                                                                  #       THE ROUTINE WILL STORE THIS MATRIX (SCALED UNITY) IN SEQUENTIAL LOCATIONS OF ERASABLE MEMORY BEGINNING WITH
015616,000351:                                                                                                  #                                                                                              -
015617,000352:                                                                                                  #  THE LOCATION CALLED DEL.  IN ORDER TO USE THE ROUTINE, THE CALLING PROGRAM MUST FIRST STORE U (A HALF UNIT
015618,000353:                                                                                                  #  DOUBLE PRECISION VECTOR) IN THE SET OF ERASABLE LOCATIONS BEGINNING WITH THE ADDRESS CALLED COF.  THE ANGLE, A,
015619,000354:                                                                                                  #  MUST THEN BE LOADED INTO D(MPAC).
015620,000355: 
015621,000356:                                                                                                  #       INTERNALLY, THE PROGRAM ALSO USES THE FIRST 10 LOCATIONS OF THE PUSH DOWN LIST.
015622,000357: 
015623,000358: 
015624,000359: 
015625,000360:                                                                                                  #       READCDUK
015626,000361:                                                                                                  #       --------
015627,000362: 
015628,000363:                                                                                                  #       THIS BASIC LANGUAGE SUBROUTINE LOADS T(MPAC) WITH THE THREE CDU ANGLES.
015629,000364: 
015630,000365: 
015631,000366: 
015632,000367:                                                                                                  #       SIGNMPAC
015633,000368:                                                                                                  #       --------
015634,000369: 
015635,000370:                                                                                                  #       THIS IS A BASIC LANGUAGE SUBROUTINE WHICH LIMITS THE MAGNITUDE OF D(MPAC) TO + OR - DPOSMAX ON OVERFLOW.
015636,000371: 
015637,000372: 
015638,000373: 
015639,000374:                                                                                                  #       PROGRAM STORAGE ALLOCATION
015640,000375: 
015641,000376:                                                                                                  #             1)   FIXED MEMORY                       1059 WORDS
015642,000377:                                                                                                  #             2)   ERASABLE MEMORY                      98
015643,000378:                                                                                                  #             3)   STATE SWITCHES                        3

Page 362

015645,000380:                                                                                                  #             4)   FLAGS                                 1
015646,000381: 
015647,000382: 
015648,000383:                                                                                                  #       JOB PRIORITIES
015649,000384: 
015650,000385:                                                                                                  #             1)   KALCMANU                            TBD
015651,000386:                                                                                                  #             2)   ONE SECOND UPDATE                   TBD
015652,000387: 
015653,000388: 
015654,000389:                                                                                                  #       SUMMARY OF STATE SWITCHES AND FLAGWORDS USED BY KALCMANU.
015655,000390: 
015656,000391:                                                                                                  #  STATE                FLAGWRD 2      SETTING             MEANING
015657,000392:                                                                                                  #  SWITCH NO.            BIT NO.
015658,000393: 
015659,000394:                                                                                                  #    *
015660,000395:                                                                                                  #  31                      14            0       MANEUVER WENT THROUGH GIMBAL LOCK
015661,000396:                                                                                                  #                                        1       MANEUVER DID NOT GO THROUGH GIMBAL LOCK
015662,000397:                                                                                                  #    *
015663,000398:                                                                                                  #  32                      13            0       CONTINUE UPDATE PROCESS
015664,000399:                                                                                                  #                                        1       START UPDATE PROCESS
015665,000400: 
015666,000401:                                                                                                  #  33                      12            0       PERFORM FINAL P-AXIS YAW IF REQUIRED
015667,000402:                                                                                                  #                                        1       IGNORE ANY FINAL P-AXIS YAW
015668,000403: 
015669,000404:                                                                                                  #  34                      11            0       SIGNAL END OF KALCMANU
015670,000405:                                                                                                  #                                        1       KALCMANU IN PROCESS       USER MUST SET SWITCH BEFORE INITIATING
015671,000406: 
015672,000407: 
015673,000408:                                                                                                  #          *  INTERNAL TO KALCMANU
015674,000409: 
015675,000410: 
015676,000411:                                                                                                  #       SUGGESTIONS FOR PROGRAM INTEGRATION
015677,000412: 
015678,000413:                                                                                                  #       THE FOLLOWING VARIABLES SHOULD BE ASSIGNED TO UNSWITCH ERASABLE
015679,000414: 
015680,000415:                                                                                                  #                       CPHI
015681,000416:                                                                                                  #                       CTHETA
015682,000417:                                                                                                  #                       CPSI
015683,000418:                                                                                                  #                       POINTVSM  +5
015684,000419:                                                                                                  #                       SCAXIS    +5
015685,000420:                                                                                                  #                       DELDCDU
015686,000421:                                                                                                  #                       DELDCDU1
015687,000422:                                                                                                  #                       DELDCDU2
015688,000423:                                                                                                  #                       RATEINDX
015689,000424: 
015690,000425:                                                                                                  #       THE FOLLOWING SUBROUTINES MAY BE PUT IN A DIFFERENT BANK
015691,000426: 
015692,000427:                                                                                                  #                       MXM3

Page 363

015694,000429:                                                                                                  #                       TRANSPOS
015695,000430:                                                                                                  #                       SIGNMPAC
015696,000431:                                                                                                  #                       READCDUK
015697,000432:                                                                                                  #                       CDUTODCM
015698,000433: 

Page 364

015700,000435: 15,2050                                           BANK     15                                    
015701,000436: 22,2000                                           SETLOC   KALCMON1                              
015702,000437: 22,2000                                           BANK                                           
015703,000438: 
015704,000439: 22,2004  E6,1674                                  EBANK=   BCDU                                  
015705,000440: 
015706,000441:                                                                                                  #  THE THREE DESIRED CDU ANGLES MUST BE STORED AS SINGLE PRECISION TWOS COMPLEMENT ANGLES IN THE THREE SUCCESSIVE
015707,000442:                                                                                                  #  LOCATIONS, CPHI, CTHETA, CPSI.
015708,000443: 
015709,000444: 22,2004                                           COUNT*   $$/KALC                               
015710,000445: 22,2004           06036        KALCMAN3           TC       INTPRET                               #  PICK UP THE CURRENT CDU ANGLES AND
015711,000446: 22,2005           77634                           RTB                                            #    COMPUTE THE MATRIX FROM INITIAL S/C
015712,000447: 22,2006           44403                                    READCDUK                              #    AXES TO FINAL S/C AXES
015713,000448: 22,2007           03275                           STORE    BCDU                                  #  STORE INITIAL S/C ANGLES
015714,000449: 22,2010           51535                           SLOAD    ABS                                   #  CHECK THE MAGNITUDE OF THE DESIRED
015715,000450: 22,2011           00324                                    CPSI                                  #  MIDDLE GIMBAL ANGLE
015716,000451: 22,2012           51025                           DSU      BPL                                   
015717,000452: 22,2013           04403                                    LOCKANGL                              #  IF GREATER THAN 70 DEG ABORT MANEUVER
015718,000453: 22,2014           44724                                    TOOBADF                               
015719,000454: 22,2015           72364                           AXC,2    TLOAD                                 
015720,000455: 22,2016           03244                                    MIS                                   
015721,000456: 22,2017           03275                                    BCDU                                  
015722,000457: 22,2020           77624                           CALL                                           #  COMPUTE THE TRANSFORMATION FROM INITIAL
015723,000458: 22,2021           44410                                    CDUTODCM                              #  S/C AXES TO STABLE MEMBER AXES
015724,000459: 22,2022           72364                           AXC,2    TLOAD                                 
015725,000460: 22,2023           02234                                    MFS                                   #  PREPARE TO CALCULATE ARRAY MFS
015726,000461: 22,2024           00322                                    CPHI                                  
015727,000462: 22,2025           77624                           CALL                                           
015728,000463: 22,2026           44410                                    CDUTODCM                              
015729,000464: 22,2027           45160        SECAD              AXC,1    CALL                                  #  MIS AND MFS ARRAYS CALCULATED        $2
015730,000465: 22,2030           03244                                    MIS                                   
015731,000466: 22,2031           44326                                    TRANSPOS                              
015732,000467: 22,2032           45575                           VLOAD    STADR                                 
015733,000468: 22,2033           50461                           STOVL    TMIS       +12D                       
015734,000469: 22,2034           77626                           STADR                                          
015735,000470: 22,2035           50467                           STOVL    TMIS       +6                         
015736,000471: 22,2036           77626                           STADR                                          
015737,000472: 22,2037           74475                           STORE    TMIS                                  #  TMIS = TRANSPOSE(MIS) SCALED BY 2
015738,000473: 22,2040           75160                           AXC,1    AXC,2                                 
015739,000474: 22,2041           03301                                    TMIS                                  
015740,000475: 22,2042           02234                                    MFS                                   
015741,000476: 22,2043           77624                           CALL                                           
015742,000477: 22,2044           44312                                    MXM3                                  
015743,000478: 22,2045           45575                           VLOAD    STADR                                 
015744,000479: 22,2046           51526                           STOVL    MFI        +12D                       
015745,000480: 22,2047           77626                           STADR                                          
015746,000481: 22,2050           51534                           STOVL    MFI        +6                         
015747,000482: 22,2051           77626                           STADR                                          
015748,000483: 22,2052           75542                           STORE    MFI                                   #  MFI = TMIS MFS (SCALED BY 4)
015749,000484: 22,2053           45001                           SETPD    CALL                                  #  TRANSPOSE MFI IN PD LIST

Page 365

015751,000486: 22,2054           00023                                    18D                                   
015752,000487: 22,2055           44335                                    TRNSPSPD                              
015753,000488: 22,2056           45575                           VLOAD    STADR                                 
015754,000489: 22,2057           50461                           STOVL    TMFI       +12D                       
015755,000490: 22,2060           77626                           STADR                                          
015756,000491: 22,2061           50467                           STOVL    TMFI       +6                         
015757,000492: 22,2062           77626                           STADR                                          
015758,000493: 22,2063           74475                           STORE    TMFI                                  #  TMFI = TRANSPOSE (MFI)  SCALED BY 4
015759,000494:                                                                                                  #                 
015760,000495:                                                                                                  #  CALCULATE COFSKEW AND MFISYM
015761,000496: 
015762,000497: 22,2064           45345                           DLOAD    DSU                                   
015763,000498: 22,2065           03304                                    TMFI       +2                         
015764,000499: 22,2066           02237                                    MFI        +2                         
015765,000500: 22,2067           45325                           PDDL     DSU                                   #  CALCULATE COF SCALED BY 2/SIN(AM)
015766,000501: 22,2070           02241                                    MFI        +4                         
015767,000502: 22,2071           03306                                    TMFI       +4                         
015768,000503: 22,2072           45325                           PDDL     DSU                                   
015769,000504: 22,2073           03314                                    TMFI       +10D                       
015770,000505: 22,2074           02247                                    MFI        +10D                       
015771,000506: 22,2075           77666                           VDEF                                           
015772,000507: 22,2076           03324                           STORE    COFSKEW                               #  EQUALS MFISKEW
015773,000508:                                                                                                  #                 
015774,000509:                                                                                                  #  CALCULATE AM AND PROCEED ACCORDING TO ITS MAGNITUDE
015775,000510: 
015776,000511: 22,2077           43345                           DLOAD    DAD                                   
015777,000512: 22,2100           02235                                    MFI                                   
015778,000513: 22,2101           02255                                    MFI        +16D                       
015779,000514: 22,2102           43225                           DSU      DAD                                   
015780,000515: 22,2103           06414                                    DP1/4TH                               
015781,000516: 22,2104           02245                                    MFI        +8D                        
015782,000517: 22,2105           03332                           STORE    CAM                                   #  CAM = (MFI0+MFI4+MFI8-1)/2 HALF SCALE
015783,000518: 22,2106           77726                           ARCCOS                                         
015784,000519: 22,2107           03334                           STORE    AM                                    #  AM=ARCCOS(CAM)  (AM SCALED BY 2)
015785,000520: 22,2110           51025                           DSU      BPL                                   
015786,000521: 22,2111           04363                                    MINANG                                
015787,000522: 22,2112           44117                                    CHECKMAX                              
015788,000523: 22,2113           77751                           TLOAD                                          #  MANEUVER LESS THAN .25 DEGREES
015789,000524: 22,2114           00322                                    CPHI                                  #  GO DIRECTLY INTO ATTITUDE HOLD
015790,000525: 22,2115           37234                           STCALL   CDUXD                                 #  ABOUT COMMANDED ANGLES
015791,000526: 22,2116           44742                                    TOOBADI                               #  STOP RATE AND EXIT
015792,000527: 
015793,000528: 22,2117           45345        CHECKMAX           DLOAD    DSU                                   
015794,000529: 22,2120           03334                                    AM                                    
015795,000530: 22,2121           04365                                    MAXANG                                
015796,000531: 22,2122           77244                           BPL      VLOAD                                 
015797,000532: 22,2123           44131                                    ALTCALC                               #  UNIT
015798,000533: 22,2124           03324                                    COFSKEW                               #  COFSKEW
015799,000534: 22,2125           77656                           UNIT                                           
015800,000535: 22,2126           03267                           STORE    COF                                   #  COF IS THE MANEUVER AXIS

Page 366

015802,000537: 22,2127           77650                           GOTO                                           #  SEE IF MANEUVER GOES THRU GIMBAL LOCK
015803,000538: 22,2130           44744                                    LOCSKIRT                              
015804,000539: 22,2131           53375        ALTCALC            VLOAD    VAD                                   #  IF AM GREATER THAN 170 DEGREES
015805,000540: 22,2132           02235                                    MFI                                   
015806,000541: 22,2133           03302                                    TMFI                                  
015807,000542: 22,2134           77762                           VSR1                                           
015808,000543: 22,2135           27302                           STOVL    MFISYM                                
015809,000544: 22,2136           02243                                    MFI        +6                         
015810,000545: 22,2137           74455                           VAD      VSR1                                  
015811,000546: 22,2140           03310                                    TMFI       +6                         
015812,000547: 22,2141           27310                           STOVL    MFISYM     +6                         
015813,000548: 22,2142           02251                                    MFI        +12D                       
015814,000549: 22,2143           74455                           VAD      VSR1                                  
015815,000550: 22,2144           03316                                    TMFI       +12D                       
015816,000551: 22,2145           03316                           STORE    MFISYM     +12D                       #  MFISYM=(MFI+TMFI)/2  SCALED BY 4
015817,000552: 
015818,000553: 
015819,000554:                                                                                                  #  CALCULATE COF
015820,000555: 
015821,000556: 
015822,000557: 22,2146           70545                           DLOAD    SR1                                   
015823,000558: 22,2147           03332                                    CAM                                   
015824,000559: 22,2150           45325                           PDDL     DSU                                   #  PDO CAM                               $4
015825,000560: 22,2151           06422                                    DPHALF                                
015826,000561: 22,2152           03332                                    CAM                                   
015827,000562: 22,2153           65204                           BOVB     PDDL                                  #  PD2 1 - CAM                           $2
015828,000563: 22,2154           21664                                    SIGNMPAC                              
015829,000564: 22,2155           03322                                    MFISYM     +16D                       
015830,000565: 22,2156           56225                           DSU      DDV                                   
015831,000566: 22,2157           00001                                    0                                     
015832,000567: 22,2160           00003                                    2                                     
015833,000568: 22,2161           65366                           SQRT     PDDL                                  #  COFZ = SQRT(MFISYM8-CAM)/1-CAM)
015834,000569: 22,2162           03312                                    MFISYM     +8D                        #                                $ ROOT 2
015835,000570: 22,2163           56225                           DSU      DDV                                   
015836,000571: 22,2164           00001                                    0                                     
015837,000572: 22,2165           00003                                    2                                     
015838,000573: 22,2166           65366                           SQRT     PDDL                                  #  COFY = SQRT(MFISYM4-CAM)/(1-CAM)  $ROOT2
015839,000574: 22,2167           03302                                    MFISYM                                
015840,000575: 22,2170           56225                           DSU      DDV                                   
015841,000576: 22,2171           00001                                    0                                     
015842,000577: 22,2172           00003                                    2                                     
015843,000578: 22,2173           55566                           SQRT     VDEF                                  #  COFX = SQRT(MFISYM-CAM)/(1-CAM)  $ROOT 2
015844,000579: 22,2174           77656                           UNIT                                           
015845,000580: 22,2175           03267                           STORE    COF                                   
015846,000581:                                                                                                  #                 
015847,000582:                                                                                                  #  DETERMINE LARGEST COF AND ADJUST ACCORDINGLY
015848,000583: 
015849,000584: 22,2176           45345        COFMAXGO           DLOAD    DSU                                   
015850,000585: 22,2177           03267                                    COF                                   
015851,000586: 22,2200           03271                                    COF        +2                         
015852,000587: 22,2201           71240                           BMN      DLOAD                                 #  COFY G COFX

Page 367

015854,000589: 22,2202           44211                                    COMP12                                
015855,000590: 22,2203           03267                                    COF                                   
015856,000591: 22,2204           50025                           DSU      BMN                                   
015857,000592: 22,2205           03273                                    COF        +4                         
015858,000593: 22,2206           44266                                    METHOD3                               #  COFZ G COFX OR COFY
015859,000594: 22,2207           77650                           GOTO                                           
015860,000595: 22,2210           44242                                    METHOD1                               #  COFX G COFY OR COFZ
015861,000596: 22,2211           45345        COMP12             DLOAD    DSU                                   
015862,000597: 22,2212           03271                                    COF        +2                         
015863,000598: 22,2213           03273                                    COF        +4                         
015864,000599: 22,2214           77640                           BMN                                            
015865,000600: 22,2215           44266                                    METHOD3                               #  COFZ G COFY OR COFX
015866,000601: 
015867,000602: 22,2216           51145        METHOD2            DLOAD    BPL                                   #  COFY MAX
015868,000603: 22,2217           03326                                    COFSKEW    +2                         #  UY
015869,000604: 22,2220           44224                                    U2POS                                 
015870,000605: 22,2221           57575                           VLOAD    VCOMP                                 
015871,000606: 22,2222           03267                                    COF                                   
015872,000607: 22,2223           03267                           STORE    COF                                   
015873,000608: 22,2224           51145        U2POS              DLOAD    BPL                                   
015874,000609: 22,2225           03304                                    MFISYM     +2                         #  UX UY
015875,000610: 22,2226           44232                                    OKU21                                 
015876,000611: 22,2227           57545                           DLOAD    DCOMP                                 #  SIGN OF UX OPPOSITE TO UY
015877,000612: 22,2230           03267                                    COF                                   
015878,000613: 22,2231           03267                           STORE    COF                                   
015879,000614: 22,2232           51145        OKU21              DLOAD    BPL                                   
015880,000615: 22,2233           03314                                    MFISYM     +10D                       #  UY UZ
015881,000616: 22,2234           44744                                    LOCSKIRT                              
015882,000617: 22,2235           57545                           DLOAD    DCOMP                                 #  SIGN OF UZ OPPOSITE TO UY
015883,000618: 22,2236           03273                                    COF        +4                         
015884,000619: 22,2237           03273                           STORE    COF        +4                         
015885,000620: 22,2240           77650                           GOTO                                           
015886,000621: 22,2241           44744                                    LOCSKIRT                              
015887,000622: 22,2242           51145        METHOD1            DLOAD    BPL                                   #  COFX MAX
015888,000623: 22,2243           03324                                    COFSKEW                               #  UX
015889,000624: 22,2244           44250                                    U1POS                                 
015890,000625: 22,2245           57575                           VLOAD    VCOMP                                 
015891,000626: 22,2246           03267                                    COF                                   
015892,000627: 22,2247           03267                           STORE    COF                                   
015893,000628: 22,2250           51145        U1POS              DLOAD    BPL                                   
015894,000629: 22,2251           03304                                    MFISYM     +2                         #  UX UY
015895,000630: 22,2252           44256                                    OKU12                                 
015896,000631: 22,2253           57545                           DLOAD    DCOMP                                 
015897,000632: 22,2254           03271                                    COF        +2                         #  SIGN OF UY OPPOSITE TO UX
015898,000633: 22,2255           03271                           STORE    COF        +2                         
015899,000634: 22,2256           51145        OKU12              DLOAD    BPL                                   
015900,000635: 22,2257           03306                                    MFISYM     +4                         #  UX UZ
015901,000636: 22,2260           44744                                    LOCSKIRT                              
015902,000637: 22,2261           57545                           DLOAD    DCOMP                                 #  SIGN OF UZ OPPOSITE TO UY
015903,000638: 22,2262           03273                                    COF        +4                         

Page 368

015905,000640: 22,2263           03273                           STORE    COF        +4                         
015906,000641: 22,2264           77650                           GOTO                                           
015907,000642: 22,2265           44744                                    LOCSKIRT                              
015908,000643: 22,2266           51145        METHOD3            DLOAD    BPL                                   #  COFZ MAX
015909,000644: 22,2267           03330                                    COFSKEW    +4                         #  UZ
015910,000645: 22,2270           44274                                    U3POS                                 
015911,000646: 22,2271           57575                           VLOAD    VCOMP                                 
015912,000647: 22,2272           03267                                    COF                                   
015913,000648: 22,2273           03267                           STORE    COF                                   
015914,000649: 22,2274           51145        U3POS              DLOAD    BPL                                   
015915,000650: 22,2275           03306                                    MFISYM     +4                         #  UX UZ
015916,000651: 22,2276           44302                                    OKU31                                 
015917,000652: 22,2277           57545                           DLOAD    DCOMP                                 
015918,000653: 22,2300           03267                                    COF                                   #  SIGN OF UX OPPOSITE TO UZ
015919,000654: 22,2301           03267                           STORE    COF                                   
015920,000655: 22,2302           51145        OKU31              DLOAD    BPL                                   
015921,000656: 22,2303           03314                                    MFISYM     +10D                       #  UY UZ
015922,000657: 22,2304           44744                                    LOCSKIRT                              
015923,000658: 22,2305           57545                           DLOAD    DCOMP                                 
015924,000659: 22,2306           03271                                    COF        +2                         #  SIGN OF UY OPPOSITE TO UZ
015925,000660: 22,2307           03271                           STORE    COF        +2                         
015926,000661: 22,2310           77650                           GOTO                                           
015927,000662: 22,2311           44744                                    LOCSKIRT                              

Page 369

015929,000664:                                                                                                  #  MATRIX OPERATIONS
015930,000665: 
015931,000666: 13,2207                                           BANK     13                                    
015932,000667: 22,2000                                           SETLOC   KALCMON2                              
015933,000668: 22,2000                                           BANK                                           
015934,000669: 
015935,000670: 22,2312  E6,1674                                  EBANK=   BCDU                                  
015936,000671: 
015937,000672: 22,2312           76601        MXM3               SETPD    VLOAD*                                #  MXM3 MULTIPLIES 2 3X3 MATRICES
015938,000673: 22,2313           00001                                    0                                     #  AND LEAVES RESULT IN PD LIST
015939,000674: 22,2314           00001                                    0,1                                   #  AND MPAC
015940,000675: 22,2315           62703                           VXM*     PDVL*                                 
015941,000676: 22,2316           77776                                    0,2                                   
015942,000677: 22,2317           00007                                    6,1                                   
015943,000678: 22,2320           62703                           VXM*     PDVL*                                 
015944,000679: 22,2321           77776                                    0,2                                   
015945,000680: 22,2322           00015                                    12D,1                                 
015946,000681: 22,2323           41503                           VXM*     PUSH                                  
015947,000682: 22,2324           77776                                    0,2                                   
015948,000683: 22,2325           77616                           RVQ                                            
015949,000684: 
015950,000685: 
015951,000686:                                                                                                  #                           RETURN WITH M1XM2 IN PD LIST
015952,000687: 
015953,000688: 22,2326           76601        TRANSPOS           SETPD    VLOAD*                                #  TRANSPOS TRANSPOSES A 3X3 MATRIX
015954,000689: 22,2327           00001                                    0                                     #   AND LEAVES RESULT IN PD LIST
015955,000690: 22,2330           00001                                    0,1                                   #  MATRIX ADDRESS IN XR1
015956,000691: 22,2331           62713                           PDVL*    PDVL*                                 
015957,000692: 22,2332           00007                                    6,1                                   
015958,000693: 22,2333           00015                                    12D,1                                 
015959,000694: 22,2334           77606                           PUSH                                           #  MATRIX IN PD
015960,000695: 22,2335           77776        TRNSPSPD           EXIT                                           #  ENTER WITH MATRIX AT 0 IN PD LIST
015961,000696: 22,2336           50120                           INDEX    FIXLOC                                
015962,000697: 22,2337           52013                           DXCH     12                                    
015963,000698: 22,2340           50120                           INDEX    FIXLOC                                
015964,000699: 22,2341           52017                           DXCH     16                                    
015965,000700: 22,2342           50120                           INDEX    FIXLOC                                
015966,000701: 22,2343           52013                           DXCH     12                                    
015967,000702: 22,2344           50120                           INDEX    FIXLOC                                
015968,000703: 22,2345           52015                           DXCH     14                                    
015969,000704: 22,2346           50120                           INDEX    FIXLOC                                
015970,000705: 22,2347           52005                           DXCH     4                                     
015971,000706: 22,2350           50120                           INDEX    FIXLOC                                
015972,000707: 22,2351           52015                           DXCH     14                                    
015973,000708: 22,2352           50120                           INDEX    FIXLOC                                
015974,000709: 22,2353           52003                           DXCH     2                                     
015975,000710: 22,2354           50120                           INDEX    FIXLOC                                
015976,000711: 22,2355           52007                           DXCH     6                                     
015977,000712: 22,2356           50120                           INDEX    FIXLOC                                
015978,000713: 22,2357           52003                           DXCH     2                                     

Page 370

015980,000715: 22,2360           06036                           TC       INTPRET                               
015981,000716: 22,2361           77616                           RVQ                                            
015982,000717: 
015983,000718: 15,2050                                           BANK     15                                    
015984,000719: 22,2000                                           SETLOC   KALCMON1                              
015985,000720: 22,2000                                           BANK                                           
015986,000721: 
015987,000722: 22,2362  E6,1674                                  EBANK=   BCDU                                  
015988,000723: 
015989,000724: 22,2362           00013 13563  MINANG             2DEC     0.00069375                            
015990,000725: 
015991,000726: 22,2364           17070 34343  MAXANG             2DEC     0.472222222                            
015992,000727: 
015993,000728:                                                                                                  #           GIMBAL LOCK CONSTANTS
015994,000729: 
015995,000730:                                                                                                  #  D = MGA CORRESPONDING TO GIMBAL LOCK = 60 DEGREES
015996,000731:                                                                                                  #           NGL = BUFFER ANGLE (TO AVOID DIVISIONS BY ZERO) = 2 DEGREES
015997,000732: 
015998,000733: 22,2366           15666 20443  SD                 2DEC     .433015                               #  = SIN(D)                        $2
015999,000734: 
016000,000735: 22,2370           33555 01106  K3S1               2DEC     .86603                                #  = SIN(D)                        $1
016001,000736: 
016002,000737: 22,2372           67777 77777  K4                 2DEC     -.25                                  #  = -COS(D)                       $2
016003,000738: 
016004,000739: 22,2374           04000 00000  K4SQ               2DEC     .125                                  #  = COS(D)COS(D)                  $2
016005,000740: 
016006,000741: 22,2376           00216 36323  SNGLCD             2DEC     .008725                               #  = SIN(NGL)COS(D)                $2
016007,000742: 
016008,000743: 22,2400           17773 00057  CNGL               2DEC     .499695                               #  COS(NGL)                        $2
016009,000744: 
016010,000745: 22,2402           14344        LOCKANGL           DEC      .388889                               #  = 70 DEGREES
016011,000746:                                                                                                  #  INTERPRETIVE SUBROUTINE TO READ THE CDU ANGLES
016012,000747: 
016013,000748: 22,2403           30034        READCDUK           CA       CDUZ                                  #  LOAD T(MPAC) WITH CDU ANGLES
016014,000749: 22,2404           54156                           TS       MPAC       +2                         
016015,000750: 22,2405           00006                           EXTEND                                         
016016,000751: 22,2406           30033                           DCA      CDUX                                  #  AND CHANGE MODE TO TRIPLE PRECISION
016017,000752: 22,2407           16475                           TCF      TLOAD      +6                         
016018,000753: 
016019,000754: 22,2410           66370        CDUTODCM           AXT,1    SSP                                   
016020,000755: 22,2411           00003                           OCT      3                                     
016021,000756: 22,2412           00051                                    S1                                    
016022,000757: 22,2413           00001                           OCT      1                                     #  SET XR1, S1, AND PD FOR LOOP
016023,000758: 22,2414           00010                           STORE    7                                     
016024,000759: 22,2415           77601                           SETPD                                          
016025,000760: 22,2416           00001                                    0                                     
016026,000761: 22,2417           47133        LOOPSIN            SLOAD*   RTB                                   
016027,000762: 22,2420           00013                                    10D,1                                 
016028,000763: 22,2421           21465                                    CDULOGIC                              

Page 371

016030,000765: 22,2422           00013                           STORE    10D                                   #  LOAD PD WITH  0 SIN(PHI)
016031,000766: 22,2423           65356                           SIN      PDDL                                  #                2 COS(PHI)
016032,000767: 22,2424           00013                                    10D                                   #                4 SIN(THETA)
016033,000768: 22,2425           41546                           COS      PUSH                                  #                6 COS(THETA)
016034,000769: 22,2426           71300                           TIX,1    DLOAD                                 #                8 SIN(PSI)
016035,000770: 22,2427           44417                                    LOOPSIN                               #               10 COS(PSI)
016036,000771: 22,2430           00007                                    6                                     
016037,000772: 22,2431           72405                           DMP      SL1                                   
016038,000773: 22,2432           00013                                    10D                                   
016039,000774: 22,2433           10001                           STORE    0,2                                   #  C0=COS(THETA)COS(PSI)
016040,000775: 22,2434           41345                           DLOAD    DMP                                   
016041,000776: 22,2435           00005                                    4                                     
016042,000777: 22,2436           00001                                    0                                     
016043,000778: 22,2437           41325                           PDDL     DMP                                   #  (PD6 SIN(THETA)SIN(PHI))
016044,000779: 22,2440           00007                                    6                                     
016045,000780: 22,2441           00011                                    8D                                    
016046,000781: 22,2442           72405                           DMP      SL1                                   
016047,000782: 22,2443           00003                                    2                                     
016048,000783: 22,2444           72421                           BDSU     SL1                                   
016049,000784: 22,2445           00015                                    12D                                   
016050,000785: 22,2446           10003                           STORE    2,2                                   #  C1=-COS(THETA)SIN(PSI)COS(PHI)
016051,000786: 22,2447           41345                           DLOAD    DMP                                   
016052,000787: 22,2450           00003                                    2                                     
016053,000788: 22,2451           00005                                    4                                     
016054,000789: 22,2452           41325                           PDDL     DMP                                   #  (PD7 COS(PHI)SIN(THETA)) SCALED 4
016055,000790: 22,2453           00007                                    6                                     
016056,000791: 22,2454           00011                                    8D                                    
016057,000792: 22,2455           72405                           DMP      SL1                                   
016058,000793: 22,2456           00001                                    0                                     
016059,000794: 22,2457           72415                           DAD      SL1                                   
016060,000795: 22,2460           00017                                    14D                                   
016061,000796: 22,2461           10005                           STORE    4,2                                   #  C2=COS(THETA)SIN(PSI)SIN(PHI)
016062,000797: 22,2462           77745                           DLOAD                                          
016063,000798: 22,2463           00011                                    8D                                    
016064,000799: 22,2464           10007                           STORE    6,2                                   #  C3=SIN(PSI)
016065,000800: 22,2465           77745                           DLOAD                                          
016066,000801: 22,2466           00013                                    10D                                   
016067,000802: 22,2467           72405                           DMP      SL1                                   
016068,000803: 22,2470           00003                                    2                                     
016069,000804: 22,2471           10011                           STORE    8D,2                                  #  C4=COS(PSI)COS(PHI)
016070,000805: 22,2472           41345                           DLOAD    DMP                                   
016071,000806: 22,2473           00013                                    10D                                   
016072,000807: 22,2474           00001                                    0                                     
016073,000808: 22,2475           72476                           DCOMP    SL1                                   
016074,000809: 22,2476           10013                           STORE    10D,2                                 #  C5=-COS(PSI)SIN(PHI)
016075,000810: 22,2477           41345                           DLOAD    DMP                                   
016076,000811: 22,2500           00005                                    4                                     
016077,000812: 22,2501           00013                                    10D                                   
016078,000813: 22,2502           72476                           DCOMP    SL1                                   
016079,000814: 22,2503           10015                           STORE    12D,2                                 #  C6=-SIN(THETA)COS(PSI)

Page 372

016081,000816: 22,2504           77745                           DLOAD                                          
016082,000817: 22,2505           72405                           DMP      SL1                                   #   (PUSH UP 7)
016083,000818: 22,2506           00011                                    8D                                    
016084,000819: 22,2507           41325                           PDDL     DMP                                   #   (PD7 COS(PHI)SIN(THETA)SIN(PSI)) SCALE4
016085,000820: 22,2510           00007                                    6                                     
016086,000821: 22,2511           00001                                    0                                     
016087,000822: 22,2512           72415                           DAD      SL1                                   #   (PUSH UP 7)
016088,000823: 22,2513           77626                           STADR                                          #  C7=COS(PHI)SIN(THETA)SIN(PSI)
016089,000824: 22,2514           67760                           STORE    14D,2                                 #   +COS(THETA)SIN(PHI)
016090,000825: 22,2515           77745                           DLOAD                                          
016091,000826: 22,2516           72405                           DMP      SL1                                   #  (PUSH UP 6)
016092,000827: 22,2517           00011                                    8D                                    
016093,000828: 22,2520           41325                           PDDL     DMP                                   #  (PD6 SIN(THETA)SIN(PHI)SIN(PSI)) SCALE4
016094,000829: 22,2521           00007                                    6                                     
016095,000830: 22,2522           00003                                    2                                     
016096,000831: 22,2523           72425                           DSU      SL1                                   #  (PUSH UP 6)
016097,000832: 22,2524           77626                           STADR                                          
016098,000833: 22,2525           67756                           STORE    16D,2                                 #  C8=-SIN(THETA)SIN(PHI)SIN(PSI)
016099,000834: 22,2526           77616                           RVQ                                            #   +COS(THETA)COS(PHI)
016100,000835: 
016101,000836:                                                                                                  #  CALCULATION OF THE MATRIX DEL......
016102,000837: 
016103,000838:                                                                                                  #           *          *           --T           *
016104,000839:                                                                                                  #           DEL = (IDMATRIX)COS(A)+UU (1-COS(A))+UX SIN(A)         SCALED 1
016105,000840: 
016106,000841:                                                                                                  #                 -
016107,000842:                                                                                                  #           WHERE U IS A UNIT VECTOR (DP SCALED 2) ALONG THE AXIS OF ROTATION.
016108,000843:                                                                                                  #           A IS THE ANGLE OF ROTATION (DP SCALED 2)
016109,000844:                                                                                                  #                                              -
016110,000845:                                                                                                  #           UPON ENTRY THE STARTING ADDRESS OF U IS COF, AND A IS IN MPAC
016111,000846: 
016112,000847: 22,2527           41401        DELCOMP            SETPD    PUSH                                  #  MPAC CONTAINS THE ANGLE A
016113,000848: 22,2530           00001                                    0                                     
016114,000849: 22,2531           65356                           SIN      PDDL                                  #  PD0 = SIN(A)
016115,000850: 22,2532           41546                           COS      PUSH                                  #  PD2 = COS(A)
016116,000851: 22,2533           65302                           SR2      PDDL                                  #  PD2 = COS(A)                         $8
016117,000852: 22,2534           41021                           BDSU     BOVB                                  
016118,000853: 22,2535           06422                                    DPHALF                                
016119,000854: 22,2536           21664                                    SIGNMPAC                              
016120,000855: 22,2537           77725                           PDDL                                           #  PD4 = 1-COS(A)
016121,000856: 
016122,000857:                                                                                                  #  COMPUTE THE DIAGONAL COMPONENTS OF DEL
016123,000858: 
016124,000859: 22,2540           03267                                    COF                                   
016125,000860: 22,2541           41316                           DSQ      DMP                                   
016126,000861: 22,2542           00005                                    4                                     
016127,000862: 22,2543           52415                           DAD      SL3                                   
016128,000863: 22,2544           00003                                    2                                     
016129,000864: 22,2545           77604                           BOVB                                           
016130,000865: 22,2546           21664                                    SIGNMPAC                              

Page 373

016132,000867: 22,2547           16235                           STODL    KEL                                   #  UX UX(1-COS(A)) +COS(A)              $1
016133,000868: 22,2550           03271                                    COF        +2                         
016134,000869: 22,2551           41316                           DSQ      DMP                                   
016135,000870: 22,2552           00005                                    4                                     
016136,000871: 22,2553           52415                           DAD      SL3                                   
016137,000872: 22,2554           00003                                    2                                     
016138,000873: 22,2555           77604                           BOVB                                           
016139,000874: 22,2556           21664                                    SIGNMPAC                              
016140,000875: 22,2557           16245                           STODL    KEL        +8D                        #  UY UY(1-COS(A)) +COS(A)              $1
016141,000876: 22,2560           03273                                    COF        +4                         
016142,000877: 22,2561           41316                           DSQ      DMP                                   
016143,000878: 22,2562           00005                                    4                                     
016144,000879: 22,2563           52415                           DAD      SL3                                   
016145,000880: 22,2564           00003                                    2                                     
016146,000881: 22,2565           77604                           BOVB                                           
016147,000882: 22,2566           21664                                    SIGNMPAC                              
016148,000883: 22,2567           02255                           STORE    KEL        +16D                       #  UZ UZ(1-COS(A)) +COS(A)              $1
016149,000884: 
016150,000885:                                                                                                  #  COMPUTE THE OFF DIAGONAL TERMS OF DEL
016151,000886: 
016152,000887: 22,2570           41345                           DLOAD    DMP                                   
016153,000888: 22,2571           03267                                    COF                                   
016154,000889: 22,2572           03271                                    COF        +2                         
016155,000890: 22,2573           72405                           DMP      SL1                                   
016156,000891: 22,2574           00005                                    4                                     
016157,000892: 22,2575           41325                           PDDL     DMP                                   #  D6  UX UY (1-COS A)                  $4
016158,000893: 22,2576           03273                                    COF        +4                         
016159,000894: 22,2577           00001                                    0                                     
016160,000895: 22,2600           43206                           PUSH     DAD                                   #  D8  UZ SIN A                         $4
016161,000896: 22,2601           00007                                    6                                     
016162,000897: 22,2602           41112                           SL2      BOVB                                  
016163,000898: 22,2603           21664                                    SIGNMPAC                              
016164,000899: 22,2604           16243                           STODL    KEL        +6                         
016165,000900: 22,2605           62421                           BDSU     SL2                                   
016166,000901: 22,2606           77604                           BOVB                                           
016167,000902: 22,2607           21664                                    SIGNMPAC                              
016168,000903: 22,2610           16237                           STODL    KEL        +2                         
016169,000904: 22,2611           03267                                    COF                                   
016170,000905: 22,2612           41205                           DMP      DMP                                   
016171,000906: 22,2613           03273                                    COF        +4                         
016172,000907: 22,2614           00005                                    4                                     
016173,000908: 22,2615           65352                           SL1      PDDL                                  #  D6  UX UZ (1-COS A)                  $4
016174,000909: 22,2616           03271                                    COF        +2                         
016175,000910: 22,2617           41405                           DMP      PUSH                                  #  D8  UY SIN(A)
016176,000911: 22,2620           00001                                    0                                     
016177,000912: 22,2621           62415                           DAD      SL2                                   
016178,000913: 22,2622           00007                                    6                                     
016179,000914: 22,2623           77604                           BOVB                                           
016180,000915: 22,2624           21664                                    SIGNMPAC                              
016181,000916: 22,2625           16241                           STODL    KEL        +4                         #  UX UZ (1-COS(A))+UY SIN(A)

Page 374

016183,000918: 22,2626           62421                           BDSU     SL2                                   
016184,000919: 22,2627           77604                           BOVB                                           
016185,000920: 22,2630           21664                                    SIGNMPAC                              
016186,000921: 22,2631           16251                           STODL    KEL        +12D                       #  UX UZ (1-COS(A))-UY SIN(A)
016187,000922: 22,2632           03271                                    COF        +2                         
016188,000923: 22,2633           41205                           DMP      DMP                                   
016189,000924: 22,2634           03273                                    COF        +4                         
016190,000925: 22,2635           00005                                    4                                     
016191,000926: 22,2636           65352                           SL1      PDDL                                  #  D6  UY UZ (1-COS(A))                $ 4
016192,000927: 22,2637           03267                                    COF                                   
016193,000928: 22,2640           41405                           DMP      PUSH                                  #  D8  UX SIN(A)
016194,000929: 22,2641           00001                                    0                                     
016195,000930: 22,2642           62415                           DAD      SL2                                   
016196,000931: 22,2643           00007                                    6                                     
016197,000932: 22,2644           77604                           BOVB                                           
016198,000933: 22,2645           21664                                    SIGNMPAC                              
016199,000934: 22,2646           16253                           STODL    KEL        +14D                       #  UY UZ(1-COS(A)) +UX SIN(A)
016200,000935: 22,2647           62421                           BDSU     SL2                                   
016201,000936: 22,2650           77604                           BOVB                                           
016202,000937: 22,2651           21664                                    SIGNMPAC                              
016203,000938: 22,2652           02247                           STORE    KEL        +10D                       #  UY UZ (1-COS(A)) -UX SIN(A)
016204,000939: 22,2653           77616                           RVQ                                            
016205,000940: 
016206,000941: 
016207,000942:                                                                                                  #  DIRECTION COSINE MATRIX TO CDU ANGLE ROUTINE
016208,000943:                                                                                                  #  X1 CONTAINS THE COMPLEMENT OF THE STARTING ADDRESS FOR MATRIX (SCALED 2)
016209,000944:                                                                                                  #  LEAVES CDU ANGLES SCALED 2PI IN V(MPAC)
016210,000945:                                                                                                  #  COS(MGA) WILL BE LEFT IN S1 (SCALED 1)
016211,000946: 
016212,000947:                                                                                                  #  THE DIRECTION COSINE MATRIX RELATING S/C AXES TO STABLE MEMBER AXES CAN BE WRITTEN AS***
016213,000948: 
016214,000949:                                                                                                  #           C =COS(THETA)COS(PSI)
016215,000950:                                                                                                  #            0
016216,000951:                                                                                                  #           C =-COS(THETA)SIN(PSI)COS(PHI)+SI (THETA)SIN(PHI)
016217,000952:                                                                                                  #            1
016218,000953:                                                                                                  #           C =COS(THETA)SIN(PSI)SIN(PHI) + S N(THETA)COS(PHI)
016219,000954:                                                                                                  #            2
016220,000955:                                                                                                  #           C =SIN(PSI)
016221,000956:                                                                                                  #            3
016222,000957:                                                                                                  #           C =COS(PSI)COS(PHI)
016223,000958:                                                                                                  #            4
016224,000959:                                                                                                  #           C =-COS(PSI)SIN(PHI)
016225,000960:                                                                                                  #            5
016226,000961:                                                                                                  #           C =-SIN(THETA)COS(PSI)
016227,000962:                                                                                                  #            6
016228,000963:                                                                                                  #           C =SIN(THETA)SIN(PSI)COS(PHI)+COS THETA)SIN(PHI)
016229,000964:                                                                                                  #            7
016230,000965:                                                                                                  #           C =-SIN(THETA)SIN(PSI)SIN(PHI)+CO (THETA)COS(PHI)
016231,000966:                                                                                                  #            8

Page 375

016233,000968:                                                                                                  #           WHERE PHI = OGA
016234,000969:                                                                                                  #                 THETA = IGA
016235,000970:                                                                                                  #                 PSI = MGA
016236,000971: 
016237,000972: 22,2654           67543        DCMTOCDU           DLOAD*   ARCSIN                                
016238,000973: 22,2655           00007                                    6,1                                   
016239,000974: 22,2656           71406                           PUSH     COS                                   #  PD +0   PSI
016240,000975: 22,2657           41152                           SL1      BOVB                                  
016241,000976: 22,2660           21664                                    SIGNMPAC                              
016242,000977: 22,2661           00051                           STORE    S1                                    
016243,000978: 22,2662           57543                           DLOAD*   DCOMP                                 
016244,000979: 22,2663           00015                                    12D,1                                 
016245,000980: 22,2664           67471                           DDV      ARCSIN                                
016246,000981: 22,2665           00051                                    S1                                    
016247,000982: 22,2666           51123                           PDDL*    BPL                                   #  PD +2  THETA
016248,000983: 22,2667           00001                                    0,1                                   #  MUST CHECK THE SIGN OF COS(THETA)
016249,000984: 22,2670           44702                                    OKTHETA                               #  TO DETERMINE THE PROPER QUADRANT
016250,000985: 22,2671           57545                           DLOAD    DCOMP                                 
016251,000986: 22,2672           43244                           BPL      DAD                                   
016252,000987: 22,2673           44677                                    SUHALFA                               
016253,000988: 22,2674           06422                                    DPHALF                                
016254,000989: 22,2675           77650                           GOTO                                           
016255,000990: 22,2676           44701                                    CALCPHI                               
016256,000991: 22,2677           77625        SUHALFA            DSU                                            
016257,000992: 22,2700           06422                                    DPHALF                                
016258,000993: 22,2701           77606        CALCPHI            PUSH                                           
016259,000994: 22,2702           57543        OKTHETA            DLOAD*   DCOMP                                 
016260,000995: 22,2703           00013                                    10D,1                                 
016261,000996: 22,2704           67471                           DDV      ARCSIN                                
016262,000997: 22,2705           00051                                    S1                                    
016263,000998: 22,2706           51123                           PDDL*    BPL                                   #  PUSH DOWN PHI
016264,000999: 22,2707           00011                                    8D,1                                  
016265,001000: 22,2710           44722                                    OKPHI                                 
016266,001001: 22,2711           57545                           DLOAD    DCOMP                                 #  PUSH UP PHI
016267,001002: 22,2712           43244                           BPL      DAD                                   
016268,001003: 22,2713           44717                                    SUHALFAP                              
016269,001004: 22,2714           06422                                    DPHALF                                
016270,001005: 22,2715           77650                           GOTO                                           
016271,001006: 22,2716           44723                                    VECOFANG                              
016272,001007: 22,2717           52025        SUHALFAP           DSU      GOTO                                  
016273,001008: 22,2720           06422                                    DPHALF                                
016274,001009: 22,2721           44723                                    VECOFANG                              
016275,001010: 22,2722           77745        OKPHI              DLOAD                                          #  PUSH UP PHI
016276,001011: 22,2723           43466        VECOFANG           VDEF     RVQ                                   

Page 376

016278,001013:                                                                                                  #  ROUTINES FOR TERMINATING THE AUTOMATIC MANEUVER AND RETURNING TO USER
016279,001014: 
016280,001015: 22,2724           77776        TOOBADF            EXIT                                           
016281,001016: 22,2725           05567                           TC       ALARM                                 
016282,001017: 22,2726           00401                           OCT      00401                                 
016283,001018: 
016284,001019: 22,2727           12732                           TCF      NOGO                                  #  DO NOT ZERO ATTITUDE ERRORS
016285,001020: 
016286,001021: 22,2730           04616                           TC       BANKCALL                              
016287,001022: 22,2731           40153                           CADR     ZATTEROR                              #  ZERO ATTITUDE ERRORS
016288,001023: 
016289,001024: 22,2732           04616        NOGO               TC       BANKCALL                              
016290,001025: 22,2733           40165                           CADR     STOPRATE                              #  STOP RATES
016291,001026: 
016292,001027: 22,2734           34752                           CAF      TWO                                   
016293,001028: 22,2735           00004                           INHINT                                         #  ALL RETURNS ARE NOW MADE VIA GOODEND
016294,001029: 22,2736           05203                           TC       WAITLIST                              
016295,001030: 22,2737  E6,1674                                  EBANK=   BCDU                                  
016296,001031: 22,2737           03234 44066                     2CADR    GOODMANU                              
016297,001032: 
016298,001033: 22,2741           15155                           TCF      ENDOFJOB                              
016299,001034: 
016300,001035: 22,2742           77776        TOOBADI            EXIT                                           
016301,001036: 22,2743           12732                           TCF      NOGO                                  

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