Source Code

These source-code files derive from a printout of Luminary 116 (the Apollo 12 Lunar Module guidance computer program), from the personal library of original AGC developer Don Eyles, digitally photographed at archive.org, financially sponsored by Ron Burkey, and transcribed to source code by a team of volunteers. This colorized, syntax-highlighted form was created by assembling that transcribed source code. Note that the full page images are available on the Virtual AGC project page at archive.org, while reduced-size images are presented at the VirtualAGC project website. Report or fix any transcription errors at the Virtual AGC project code repository.

Notations on the program listing read, in part:

	GAP:  ASSEMBLE REVISION 116 OF AGC PROGRAM LUMINARY BY NASA 2021112-071
	19:09 AUG. 11,1969
Note that the date is the date of the printout, not the date of the program revision.

014239,000002:                                                                                                  ## Copyright:   Public domain.
014240,000003:                                                                                                  ## Filename:    ATTITUDE_MANEUVER_ROUTINE.agc
014241,000004:                                                                                                  ## Purpose:     A section of Luminary revision 116.
014242,000005:                                                                                                  ##              It is part of the source code for the Lunar Module's (LM) 
014243,000006:                                                                                                  ##              Apollo Guidance Computer (AGC) for Apollo 12.
014244,000007:                                                                                                  ##              This file is intended to be a faithful transcription, except
014245,000008:                                                                                                  ##              that the code format has been changed to conform to the
014246,000009:                                                                                                  ##              requirements of the yaYUL assembler rather than the
014247,000010:                                                                                                  ##              original YUL assembler.
014248,000011:                                                                                                  ## Reference:   pp. 343-364
014249,000012:                                                                                                  ## Assembler:   yaYUL
014250,000013:                                                                                                  ## Contact:     Ron Burkey <info@sandroid.org>.
014251,000014:                                                                                                  ## Website:     www.ibiblio.org/apollo/index.html
014252,000015:                                                                                                  ## Mod history: 2017-01-22 MAS  Created from Luminary 99.
014253,000016:                                                                                                  ##              2017-03-07 RSB  Transcribed, and then proofed comment-text using
014254,000017:                                                                                                  ##                              3-way diff vs Luminary 99 and Luminary 131.
014255,000018:                                                                                                  ##                              (Admittedly, the former is more for detecting errors
014256,000019:                                                                                                  ##                              in Luminary 99 than the other way around.)
014257,000020:                                                                                                  ##              2017-03-15 RSB  Comment-text fixes identified in 5-way
014258,000021:                                                                                                  ##                              side-by-side diff of Luminary 69/99/116/131/210.
014259,000022: 

Page 343

014261,000024:                                                                                                  #  BLOCK 2 LGC ATTITUDE MANEUVER ROUTINE - KALCMANU
014262,000025: 
014263,000026:                                                                                                  #  MOD 2         DATE 5/1/67     BY DON KEENE
014264,000027: 
014265,000028:                                                                                                  #  PROGRAM DESCRIPTION
014266,000029: 
014267,000030:                                                                                                  #       KALCMANU IS A ROUTINE WHICH GENERATES COMMANDS FOR THE LM DAP TO CHANGE THE ATTITUDE OF THE SPACECRAFT
014268,000031:                                                                                                  #  DURING FREE FALL.  IT IS DESIGNED TO MANEUVER THE SPACECRAFT FROM ITS INITIAL ORIENTATION TO SOME DESIRED
014269,000032:                                                                                                  #  ORIENTATION SPECIFIED BY THE PROGRAM WHICH CALLS KALCMANU, AVOIDING GIMBAL LOCK IN THE PROCESS.  IN THE 
014270,000033:                                                                                                  #  MOD 2 VERSION, THIS DESIRED ATTITUDE IS SPECIFIED BY A SET OF THREE COMMANDED CDU ANGLES STORED AS 2S COMPLEMENT
014271,000034:                                                                                                  #  SINGLE PRECISION ANGLES IN THE THREE CONSECUTIVE LOCATIONS, CPHI, CTHETA, CPSI, WHERE
014272,000035: 
014273,000036:                                                                                                  #        CPHI = COMMANDED OUTER GIMBAL ANGLE
014274,000037:                                                                                                  #        CTHETA = COMMANDED INNER GIMBAL ANGLE
014275,000038:                                                                                                  #        CPSI = COMMANDED MIDDLE GIMBAL ANGLE
014276,000039: 
014277,000040:                                                                                                  #      WHEN POINTING A SPACECRAFT AXIS (E.I. X, Y, Z, THE AOT, THRUST AXIS, ETC) THE SUBROUTINE VECPOINT MAY BE
014278,000041:                                                                                                  #  USED TO GENERATE THIS SET OF DESIRED CDU ANGLES (SEE DESCRIPTION IN R60)   -
014279,000042:                                                                                                  #   WITH THIS INFORMATION KALCMANU DETERMINES THE DIRECTION OF THE SINGLE EQUIVALENT ROTATION (COF ALSO U) AND THE
014280,000043:                                                                                                  #  MAGNITUDE OF THE ROTATION (AM) TO BRING THE S/C FROM ITS INITIAL ORIENTATION TO ITS FINAL ORIENTATION.
014281,000044:                                                                                                  #  THIS DIRECTION REMAINS FIXED BOTH IN INERTIAL COORDINATES AND IN COMMANDED S/C AXES THROUGHOUT THE 
014282,000045:                                                                                                  #                   -
014283,000046:                                                                                                  #  MANEUVER.  ONCE COF AND AM HAVE BEEN DETERMINED, KALCMANU THEN EXAMINES THE MANEUVER TO SEE IF IT WILL BRING
014284,000047:                                                                                                  #                                       -
014285,000048:                                                                                                  #  THE S/C THROUGH GIMBAL LOCK.  IF SO, COF AND AM ARE READJUSTED SO THAT THE S/C WILL JUST SKIM THE GIMBAL
014286,000049:                                                                                                  #  LOCK ZONE AND ALIGN THE X-AXIS.  IN GENERAL A FINAL YAW ABOUT X WILL BE NECESSARY TO COMPLETE THE MANEUVER.
014287,000050:                                                                                                  #  NEEDLESS TO SAY, NEITHER THE INITIAL NOR THE FINAL ORIENTATION CAN BE IN GIMBAL LOCK.
014288,000051: 
014289,000052:                                                                                                  #       FOR PROPER ATTITUDE CONTROL THE DIGITAL AUTOPILOT MUST BE GIVEN AN ATTITUDE REFERENCE WHICH IT CAN TRACK.
014290,000053:                                                                                                  #  KALCMANU DOES THIS BY GENERATING A REFERENCE OF DESIRED GIMBAL ANGLES (CDUXD, CDUYD, CDUZD) WHICH ARE UPDATED
014291,000054:                                                                                                  #  EVERY ONE SECOND DURING THE MANEUVER.  TO ACHIEVE A SMOOTHER SEQUENCE OF COMMANDS BETWEEN SUCCESSIVE UPDATES,
014292,000055:                                                                                                  #  THE PROGRAM ALSO GENERATES A SET OF INCREMENTAL CDU ANGLES (DELDCDU) TO BE ADDED TO CDU DESIRED BY THE DIGITAL
014293,000056:                                                                                                  #  AUTOPILOT.  KALCMANU ALSO CALCULATES THE COMPONENT MANEUVER RATES (OMEGAPD, OMEGAQD, OMEGARD), WHICH CAN
014294,000057:                                                                                                  #                                      -
014295,000058:                                                                                                  #  BE DETERMINED SIMPLY BY MULTIPLYING COF BY SOME SCALAR (ARATE) CORRESPONDING TO THE DESIRED ROTATIONAL RATE.
014296,000059: 
014297,000060:                                                                                                  #       AUTOMATIC MANEUVERS ARE TIMED WITH THE HELP OF WAITLIST SO THAT AFTER A SPECIFIED INTERVAL THE Y AND Z
014298,000061:                                                                                                  #  DESIRED RATES ARE SET TO ZERO AND THE DESIRED CDU ANGLES (CDUYD, CDUZD) ARE SET EQUAL TO THE FINAL DESIRED CDU
014299,000062:                                                                                                  #  ANGLES (CTHETA, CPSI).  IF ANY YAW REMAINS DUE TO GIMBAL LOCK AVOIDANCE, THE FINAL YAW MANEUVER IS
014300,000063:                                                                                                  #  CALCULATED AND THE DESIRED YAW RATE SET TO SOME FIXED VALUE (ROLLRATE = + OR - 2 DEGREES PER SEC).
014301,000064:                                                                                                  #  IN THIS CASE ONLY AN INCREMENTAL CDUX ANGLE (DELFROLL) IS SUPPLIED TO THE DAP.  AT THE END OF THE YAW
014302,000065:                                                                                                  #  MANEUVER OR IN THE EVENT THAT THERE WAS NO FINAL YAW, CDUXD IS SET EQUAL TO CPHI AND THE X-AXIS DESIRED
014303,000066:                                                                                                  #  RATE SET TO ZERO.  THUS, UPON COMPLETION OF THE MANEUVER THE S/C WILL FINISH UP IN A LIMIT CYCLE ABOUT THE
014304,000067:                                                                                                  #  DESIRED FINAL GIMBAL ANGLES.
014305,000068: 
014306,000069:                                                                                                  #  PROGRAM LOGIC FLOW
014307,000070: 
014308,000071:                                                                                                  #       KALCMANU IS CALLED AS A HIGH PRIORITY JOB WITH ENTRY POINTS AT KALCMAN3 AND VECPOINT.  IT FIRST PICKS
014309,000072:                                                                                                  #  UP THE CURRENT CDU ANGLES TO BE USED AS THE BASIS FOR ALL COMPUTATIONS INVOLVING THE INITIAL S/C ORIENTATION.

Page 344

014311,000074:                                                                                                  #  IT THEN DETERMINES THE DIRECTION COSINE MATRICES RELATING BOTH THE INITIAL AND FINAL S/C ORIENTATION TO STABLE
014312,000075:                                                                                                  #                *   *                                                                               *
014313,000076:                                                                                                  #  MEMBER AXES (MIS,MFS).  IT ALSO COMPUTES THE MATRIX RELATING FINAL S/C AXES TO INITIAL S/C AXES (MFI).  THE
014314,000077:                                                                                                  #  ANGLE OF ROTATION (AM) IS THEN EXTRACTED FROM THIS MATRIX, AND TESTS ARE MADE TO DETERMINE IF
014315,000078: 
014316,000079:                                                                                                  #        A)      AM LESS THAN .25 DEGREES (MINANG)
014317,000080:                                                                                                  #        B)      AM GREATER THAN 170 DEGREES (MAXANG)
014318,000081: 
014319,000082:                                                                                                  #  IF AM LESS THAN .25 DEGREES, NO COMPLICATED AUTOMATIC MANEUVERING IS NECESSARY.  THEREFORE WE CAN SIMPLY
014320,000083:                                                                                                  #  SET CDU DESIRED EQUAL TO THE FINAL CDU DESIRED ANGLES AND TERMINATE THE JOB.
014321,000084: 
014322,000085:                                                                                                  #  IF AM IS GREATER THAN .25 DEGREES BUT LESS THAN 170 DEGREES, THE AXES OF THE SINGLE EQUIVALENT ROTATION
014323,000086:                                                                                                  #    -                                                       *
014324,000087:                                                                                                  #  (COF) IS EXTRACTED FROM THE SKEW SYMMETRIC COMPONENTS OF MFI.                       *     *
014325,000088:                                                                                                  #  IF AM GREATER THAN 170 DEGREES AN ALTERNATE METHOD EMPLOYING THE SYMMETRIC PART OF MFI (MFISYM) IS USED
014326,000089:                                                                                                  #                -
014327,000090:                                                                                                  #  TO DETERMINE COF.
014328,000091: 
014329,000092:                                                                                                  #  THE PROGRAM THEN CHECKS TO SEE IF THE MANEUVER AS COMPUTED WILL BRING THE S/C THROUGH GIMBAL LOCK.  IF
014330,000093:                                                                                                  #  SO, A NEW MANEUVER IS CALCULATED WHICH WILL JUST SKIM THE GIMBAL LOCK ZONE AND ALIGN THE S/C X-AXIS.  THIS
014331,000094:                                                                                                  #  METHOD ASSURES THAT THE ADDITIONAL MANEUVERING TO AVOID GIMBAL LOCK WILL BE KEPT TO A MINIMUM.  SINCE A FINAL
014332,000095:                                                                                                  #  P AXIS YAW WILL BE NECESSARY, A SWITCH IS RESET (STATE SWITCH 31) TO ALLOW FOR THE COMPUTATION OF THIS FINAL
014333,000096:                                                                                                  #  YAW.
014334,000097: 
014335,000098:                                                                                                  #  AS STATED PREVIOUSLY KALCMANU GENERATES A SEQUENCE OF DESIRED GIMBAL ANGLES WHICH ARE UPDATED EVERY 
014336,000099:                                                                                                  #                                                                                               -
014337,000100:                                                                                                  #  SECOND.  THIS IS ACCOMPLISHED BY A SMALL ROTATION OF THE DESIRED S/C FRAME ABOUT THE VECTOR COF.  THE NEW
014338,000101:                                                                                                  #  DESIRED REFERENCE MATRIX IS THEN,
014339,000102:                                                                                                  #         *               *       *
014340,000103:                                                                                                  #        MIS     =       MIS     DEL
014341,000104:                                                                                                  #           N+1             N
014342,000105:                                                                                                  #         *
014343,000106:                                                                                                  #  WHERE DEL IS THE MATRIX CORRESPONDING TO THIS SMALL ROTATION.  THE NEW CDU ANGLES CAN THEN BE EXTRACTED
014344,000107:                                                                                                  #        *
014345,000108:                                                                                                  #  FROM MIS.
014346,000109: 
014347,000110:                                                                                                  #  AT THE BEGINNING OF THE MANEUVER THE AUTOPILOT DESIRED RATES (OMEGAPD, OMEGAQD, OMEGARD) AND THE 
014348,000111:                                                                                                  #  MANEUVER TIMINGS ARE ESTABLISHED.  ON THE FIRST PASS AND ON ALL SUBSEQUENT UPDATES THE CDU DESIRED
014349,000112:                                                                                                  #  ANGLES ARE LOADED WITH THE APPROPRIATE VALUES AND THE INCREMENTAL CDU ANGLES ARE COMPUTED.  THE AGC CLOCKS
014350,000113:                                                                                                  #  (TIME1 AND TIME2) ARE THAN CHECKED TO SEE IF THE MANEUVER WILL TERMINATE BEFORE THE NEXT UPDATE.  IF
014351,000114:                                                                                                  #  NOT, KALCMANU CALLS FOR ANOTHER UPDATE (RUN AS A JOB WITH PRIORITY TBD) IN ONE SECOND.  ANY DELAYS IN THIS
014352,000115:                                                                                                  #  CALLING SEQUENCE ARE AUTOMATICALLY COMPENSATED IN CALLING FOR THE NEXT UPDATE.
014353,000116: 
014354,000117:                                                                                                  #  IF IT IS FOUND THAT THE MANEUVER IS TO TERMINATE BEFORE THE NEXT UPDATE A ROUTINE IS CALLED (AS A WAIT-
014355,000118:                                                                                                  #  LIST TASK) TO STOP THE MANEUVER AT THE APPROPRIATE TIME AS EXPLAINED ABOVE.
014356,000119: 

Page 345

014358,000121:                                                                                                  #  CALLING SEQUENCE
014359,000122: 
014360,000123:                                                                                                  #  IN ORDER TO PERFORM A KALCMANU SUPERVISED MANEUVER, THE COMMANDED GIMBAL ANGLES MUST BE PRECOMPUTED AND
014361,000124:                                                                                                  #  STORED IN LOCATIONS CPHI, CTHETA, CPSI.  THE USER:S PROGRAM MUST THEN CLEAR STATE SWITCH NO 33 TO ALLOW THE 
014362,000125:                                                                                                  #  ATTITUDE MANEUVER ROUTINE TO PERFORM ANY FINAL P-AXIS YAW INCURRED BY AVOIDING GIMBAL LOCK.  THE MANEUVER IS
014363,000126:                                                                                                  #  THEN INITIATED BY ESTABLISHING THE FOLLOWING EXECUTIVE JOB
014364,000127: 
014365,000128:                                                                                                  #                       *
014366,000129:                                                                                                  #        CAF     PRIO XX
014367,000130:                                                                                                  #                     --
014368,000131:                                                                                                  #        INHINT
014369,000132:                                                                                                  #        TC      FINDVAC
014370,000133:                                                                                                  #        2CADR   KALCMAN3
014371,000134:                                                                                                  #        RELINT
014372,000135: 
014373,000136:                                                                                                  #  THE USER:S PROGRAM MAY EITHER CONTINUE OR WAIT FOR THE TERMINATION OF THE MANEUVER.  IF THE USER WISHES TO
014374,000137:                                                                                                  #  WAIT, HE MAY PUT HIS JOB TO SLEEP WITH THE FOLLOWING INSTRUCTIONS
014375,000138: 
014376,000139:                                                                                                  #        L       TC      BANKCALL
014377,000140:                                                                                                  #        L+1     CADR    ATTSTALL
014378,000141:                                                                                                  #        L+2     (BAD RETURN)
014379,000142:                                                                                                  #        L+3     (GOOD RETURN)
014380,000143: 
014381,000144:                                                                                                  #  UPON COMPLETION OF THE MANEUVER, THE PROGRAM WILL BE AWAKENED AT L+3 IF THE MANEUVER WAS COMPLETED
014382,000145:                                                                                                  #  SUCCESSFULLY, OR AT L+2 IF THE MANEUVER WAS ABORTED.  THIS ABORT WOULD OCCUR IF THE INITIAL OR FINAL ATTITUDE
014383,000146:                                                                                                  #  WAS IN GIMBAL LOCK.
014384,000147: 
014385,000148:                                                                                                  #  *** NOTA BENE ***  IT IS ASSUMED THAT THE DESIRED MANEUVERING RATE (0.5, 2, 5, 10, DEG/SEC) HAS BEEN SELECTED BY
014386,000149:                                                                                                  #  KEYBOARD ENTRY PRIOR TO THE EXECUTION OF KALCMANU.
014387,000150:                                                                                                  #  IT IS ALSO ASSUMED THAT THE AUTOPILOT IS IN THE AUTO MODE.  IF THE MODE SWITCH IS CHANGED DURING THE
014388,000151:                                                                                                  #  MANEUVER, KALCMANU WILL TERMINATE VIA GOODEND WITHIN 1 SECOND SO THAT R60 MAY REQUEST A TRIM OF THE S/C ATTITUDE
014389,000152:                                                                                                  #  THIS IS THE ONLY MEANS FOR MANUALLY TERMINATING A KALCMANU SUPERVISED MANEUVER.
014390,000153:                                                                                                  #  SUBROUTINES
014391,000154: 
014392,000155:                                                                                                  #  KALCMANU USES A NUMBER OF INTERPRETIVE SUBROUTINES WHICH MAY BE OF GENERAL INTEREST.  SINCE THESE ROUTINES
014393,000156:                                                                                                  #  WERE PROGRAMMED EXCLUSIVELY FOR KALCMANU, THEY ARE NOT, AS YET, GENERALLY AVAILABLE FOR USE BY OTHER PROGRAMS.
014394,000157: 
014395,000158:                                                                                                  #  MXM3
014396,000159:                                                                                                  #  ----
014397,000160: 
014398,000161:                                                                                                  #  THIS SUBROUTINE MULTIPLIES TWO 3X3 MATRICES AND LEAVES THE RESULT IN THE FIRST 18 LOCATIONS OF THE PUSH
014399,000162:                                                                                                  #  DOWN LIST, I.E.,
014400,000163:                                                                                                  #                        ( M     M     M  )
014401,000164:                                                                                                  #                        (  0     1     2 )
014402,000165:                                                                                                  #        *               (                )              *               *
014403,000166:                                                                                                  #        M       =       ( M     M     M  )      =       M1      X       M2
014404,000167:                                                                                                  #                        (  3     4     5 )
014405,000168:                                                                                                  #                        (                )
014406,000169:                                                                                                  #                        ( M     M     M  )

Page 346

014408,000171:                                                                                                  #                        (  6     7     8 )
014409,000172:                                                                                                  #                                                                                   *
014410,000173:                                                                                                  #  INDEX REGISTER X1 MUST BE LOADED WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M1, AND X2 MUST BE
014411,000174:                                                                                                  #                                                         *
014412,000175:                                                                                                  #  LOADED WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M2.  THE ROUTINE USES THE FIRST 20 LOCATIONS OF THE PUSH
014413,000176:                                                                                                  #  DOWN LIST.  THE FIRST ELEMENT OF THE MATRIX APPEARS IN PDO.  PUSH UP FOR M .
014414,000177:                                                                                                  #                                                                            8
014415,000178:                                                                                                  #  TRANSPOS
014416,000179:                                                                                                  #  --------
014417,000180: 
014418,000181:                                                                                                  #  THIS ROUTINE TRANSPOSES A 3X3 MATRIX AND LEAVES THE RESULT IN THE PUSH DOWN LIST, I.E.,
014419,000182:                                                                                                  #  
014420,000183:                                                                                                  #        *               * T
014421,000184:                                                                                                  #        M       =       M1
014422,000185: 
014423,000186:                                                                                                  #  INDEX REGISTER X1 MUST CONTAIN THE COMPLEMENT OF THE STARTING ADDRESS FOR M1.  PUSH UP FOR THE FIRST AND SUB-
014424,000187:                                                                                                  #                        *
014425,000188:                                                                                                  #  SEQUENT COMPONENTS OF M.  THIS SUBROUTINE ALSO USES THE FIRST 20 LOCATIONS OF THE PUSH DOWN LIST.
014426,000189: 
014427,000190:                                                                                                  #  CDU TO DCM
014428,000191:                                                                                                  #  ----------
014429,000192: 
014430,000193:                                                                                                  #  THIS SUBROUTINE CONVERTS THREE CDU ANGLES IN T(MPAC) TO A DIRECTION COSINE MATRIX (SCALED BY 2) RELATING
014431,000194:                                                                                                  #  THE CORRESPONDING S/C ORIENTATIONS TO THE STABLE MEMBER FRAME.  THE FORMULAS FOR THIS CONVERSION ARE
014432,000195: 
014433,000196:                                                                                                  #        M       =       COSY COSZ
014434,000197:                                                                                                  #         0
014435,000198: 
014436,000199:                                                                                                  #        M       =       -COSY SINZ COSX + SINY SINX
014437,000200:                                                                                                  #         1
014438,000201: 
014439,000202:                                                                                                  #        M       =       COSY SINZ SINX + SINY COSX
014440,000203:                                                                                                  #         2
014441,000204: 
014442,000205:                                                                                                  #        M       =       SINZ
014443,000206:                                                                                                  #         3
014444,000207: 
014445,000208:                                                                                                  #        M       =       COSZ COSX
014446,000209:                                                                                                  #         4
014447,000210: 
014448,000211:                                                                                                  #        M       =       -COSZ SINX
014449,000212:                                                                                                  #         5
014450,000213: 
014451,000214:                                                                                                  #        M       =       -SINY COSZ
014452,000215:                                                                                                  #         6
014453,000216:                                                                                                  #        
014454,000217:                                                                                                  #        M       =       SINY SINZ COSX + COSY SINX
014455,000218:                                                                                                  #         7

Page 347

014457,000220:                                                                                                  #        M       =       -SINY SINZ SINX + COSY COSX
014458,000221:                                                                                                  #         8
014459,000222: 
014460,000223:                                                                                                  #  WHERE         X       =       OUTER GIMBAL ANGLE
014461,000224:                                                                                                  #                Y       =       INNER GIMBAL ANGLE
014462,000225:                                                                                                  #                Z       =       MIDDLE GIMBAL ANGLE
014463,000226: 
014464,000227:                                                                                                  #  THE INTERPRETATION OF THIS MATRIX IS AS FOLLOWS
014465,000228: 
014466,000229:                                                                                                  #  IF A , A , A  REPRESENT THE COMPONENTS OF A VECTOR IN S/C AXES THEN THE COMPONENTS OF THE SAME VECTOR IN
014467,000230:                                                                                                  #      X   Y   Z
014468,000231:                                                                                                  #  STABLE MEMBER AXES (B , B , B ) ARE
014469,000232:                                                                                                  #                       X   Y   Z
014470,000233: 
014471,000234:                                                                                                  #        ( B  )                  ( A  )
014472,000235:                                                                                                  #        (  X )                  (  X )
014473,000236:                                                                                                  #        (    )                  (    )
014474,000237:                                                                                                  #        (    )            *     (    )
014475,000238:                                                                                                  #        ( B  )     =      M     ( A  )
014476,000239:                                                                                                  #        (  Y )                  (  Y )
014477,000240:                                                                                                  #        (    )                  (    )
014478,000241:                                                                                                  #        ( B  )                  ( A  )
014479,000242:                                                                                                  #        (  Z )                  (  Z )
014480,000243: 
014481,000244:                                                                                                  #  THE SUBROUTINE WILL STORE THIS MATRIX IN SEQUENTIAL LOCATIONS OF ERASABLE MEMORY AS SPECIFIED BY THE CALLING
014482,000245:                                                                                                  #                                                                                                              *
014483,000246:                                                                                                  #  PROGRAM.  TO DO THIS THE CALLING PROGRAM MUST FIRST LOAD X2 WITH THE COMPLEMENT OF THE STARTING ADDRESS FOR M.
014484,000247: 
014485,000248:                                                                                                  #  INTERNALLY, THE ROUTINE USES THE FIRST 16 LOCATIONS OF THE PUSH DOWN LIST, ALSO STEP REGISTER S1 AND INDEX
014486,000249:                                                                                                  #  REGISTER X2.
014487,000250: 
014488,000251:                                                                                                  #  DCM TO CDU
014489,000252:                                                                                                  #  ----------
014490,000253:                                                                                                  #                                                                       *
014491,000254:                                                                                                  #  THIS ROUTINE EXTRACTS THE CDU ANGLES FROM A DIRECTION COSINE MATRIX (M SCALED BY 2) RELATING S/C AXIS TO
014492,000255:                                                                                                  #                                                                                  *
014493,000256:                                                                                                  #  STABLE MEMBER AXES.  X1 MUST CONTAIN THE COMPLEMENT OF THE STARTING ADDRESS FOR M.  THE SUBROUTINE LEAVES THE
014494,000257:                                                                                                  #  CORRESPONDING GIMBAL ANGLES IN V(MPAC) AS DOUBLE PRECISION 1:S COMPLEMENT ANGLES SCALED BY 2PI.  THE FORMULAS
014495,000258:                                                                                                  #  FOR THIS CONVERSION ARE
014496,000259: 
014497,000260:                                                                                                  #        Z       =       ARCSIN (M  )
014498,000261:                                                                                                  #                                 3
014499,000262: 
014500,000263:                                                                                                  #        Y       =       ARCSIN (-M /COSZ)
014501,000264:                                                                                                  #                                  6
014502,000265: 
014503,000266:                                                                                                  #  IF M  IS NEGATIVE, Y IS REPLACED BY PI SGN Y - Y
014504,000267:                                                                                                  #      0

Page 348

014506,000269:                                                                                                  #        X       =       ARCSIN (-M /COSZ)
014507,000270:                                                                                                  #                                  5
014508,000271: 
014509,000272:                                                                                                  #  IF M  IS NEGATIVE X IS REPLACED BY PI SGN X - X
014510,000273:                                                                                                  #      4
014511,000274: 
014512,000275:                                                                                                  #  THIS ROUTINE DOES NOT SET THE PUSH DOWN POINTER, BUT USES THE NEXT 8 LOCATIONS OF THE PUSH DOWN LIST AND
014513,000276:                                                                                                  #  RETURNS THE POINTER TO ITS ORIGINAL SETTING.  THIS PROCEDURE ALLOWS THE CALLER TO STORE THE MATRIX AT THE TOP OF
014514,000277:                                                                                                  #  THE PUSH DOWN LIST.
014515,000278: 
014516,000279:                                                                                                  #  DELCOMP
014517,000280:                                                                                                  #  -------
014518,000281:                                                                                                  #                                                      *
014519,000282:                                                                                                  #  THIS ROUTINE COMPUTES THE DIRECTION COSINE MATRIX (DEL) RELATING ON
014520,000283:                                                                                                  #                                                                           -
014521,000284:                                                                                                  #  IS ROTATED WITH RESPECT TO THE FIRST BY AN ANGLE, A, ABOUT A UNIT VECTOR, U.  THE FORMULA FOR THIS MATRIX IS
014522,000285: 
014523,000286:                                                                                                  #         *              *        - -T              *
014524,000287:                                                                                                  #        DEL     =       I COSA + U U  (1 - COSA) + V  SINA
014525,000288:                                                                                                  #                                                    X
014526,000289: 
014527,000290:                                                                                                  #  WHERE         *               ( 1    0    0 )
014528,000291:                                                                                                  #                I       =       ( 0    1    0 )
014529,000292:                                                                                                  #                                ( 0    0    1 )
014530,000293: 
014531,000294:                                                                                                  #                                     2                             
014532,000295:                                                                                                  #                                (  U           U  U          U  U  )
014533,000296:                                                                                                  #                                (   X           X  Y          X  Z )
014534,000297:                                                                                                  #                                (                                  )
014535,000298:                                                                                                  #                - -T            (                 2                )
014536,000299:                                                                                                  #                U U     =       ( U  U          U            U  U  )
014537,000300:                                                                                                  #                                (  Y  X          Y            Y  Z )
014538,000301:                                                                                                  #                                (                                  )
014539,000302:                                                                                                  #                                (                               2  )
014540,000303:                                                                                                  #                                ( U  U         U  U           U    )
014541,000304:                                                                                                  #                                (  Z  X         Z  Y           Z   )
014542,000305: 
014543,000306: 
014544,000307:                                                                                                  #                                (   0           -U               U  )
014545,000308:                                                                                                  #                                (                 Z               Y )
014546,000309:                                                                                                  #                *               (                                   )
014547,000310:                                                                                                  #                V       =       (  U             0              -U  )
014548,000311:                                                                                                  #                 X              (   Z                             X )
014549,000312:                                                                                                  #                                (                                   )
014550,000313:                                                                                                  #                                ( -U             U               0  )
014551,000314:                                                                                                  #                                (   Y             X                 )
014552,000315: 

Page 349

014554,000317:                                                                                                  #        -
014555,000318:                                                                                                  #        U       =       UNIT ROTATION VECTOR RESOLVED INTO S/C AXES
014556,000319:                                                                                                  #        A       =       ROTATION ANGLE
014557,000320: 
014558,000321:                                                                                                  #                         *
014559,000322:                                                                                                  #  THE INTERPRETATION OF DEL IS AS FOLLOWS
014560,000323: 
014561,000324:                                                                                                  #  IF A , A , A  REPRESENT THE COMPONENT OF A VECTOR IN THE ROTATED FRAME, THEN THE COMPONENTS OF THE SAME
014562,000325:                                                                                                  #      X   Y   Z
014563,000326:                                                                                                  #  VECTOR IN THE ORIGINAL S/C AXES (B , B , B ) ARE
014564,000327:                                                                                                  #                                    X   Y   Z
014565,000328: 
014566,000329:                                                                                                  #        ( B  )                  ( A  )
014567,000330:                                                                                                  #        (  X )                  (  X )
014568,000331:                                                                                                  #        (    )            *     (    )
014569,000332:                                                                                                  #        ( B  )     =     DEL    ( A  )
014570,000333:                                                                                                  #        (  Y )                  (  Y )
014571,000334:                                                                                                  #        (    )                  (    )
014572,000335:                                                                                                  #        ( B  )                  ( A  )
014573,000336:                                                                                                  #        (  Z )                  (  Z )
014574,000337: 
014575,000338:                                                                                                  #  THE ROUTINE WILL STORE THIS MATRIX (SCALED UNITY) IN SEQUENTIAL LOCATIONS OF ERASABLE MEMORY BEGINNING WITH
014576,000339:                                                                                                  #                                                                                              -
014577,000340:                                                                                                  #  THE LOCATION CALLED DEL.  IN ORDER TO USE THE ROUTINE, THE CALLING PROGRAM MUST FIRST STORE U (A HALF UNIT
014578,000341:                                                                                                  #  DOUBLE PRECISION VECTOR) IN THE SET OF ERASABLE LOCATIONS BEGINNING WITH THE ADDRESS CALLED COF.  THE ANGLE, A,
014579,000342:                                                                                                  #  MUST THEN BE LOADED INTO D(MPAC).
014580,000343:                                                                                                  #  
014581,000344:                                                                                                  #  INTERNALLY, THE PROGRAM ALSO USES THE FIRST 10 LOCATIONS OF THE PUSH DOWN LIST.
014582,000345: 
014583,000346:                                                                                                  #  READCDUK
014584,000347:                                                                                                  #  --------
014585,000348: 
014586,000349:                                                                                                  #  THIS BASIC LANGUAGE SUBROUTINE LOADS T(MPAC) WITH THE THREE CDU ANGLES.
014587,000350: 
014588,000351:                                                                                                  #  SIGNMPAC
014589,000352:                                                                                                  #   --------
014590,000353: 
014591,000354:                                                                                                  #  THIS IS A BASIC LANGUAGE SUBROUTINE WHICH LIMITS THE MAGNITUDE OF D(MPAC) TO + OR - DPOSMAX ON OVERFLOW.
014592,000355: 
014593,000356:                                                                                                  #  PROGRAM STORAGE ALLOCATION
014594,000357: 
014595,000358:                                                                                                  #        1)      FIXED MEMORY            1059 WORDS
014596,000359:                                                                                                  #        2)      ERASABLE MEMORY           98
014597,000360:                                                                                                  #        3)      STATE SWITCHES             3

Page 350

014599,000362:                                                                                                  #        4)      FLAGS                      1
014600,000363: 
014601,000364:                                                                                                  #  JOB PRIORITIES
014602,000365: 
014603,000366:                                                                                                  #        1)      KALCMANU                TBD
014604,000367:                                                                                                  #        2)      ONE SECOND UPDATE       TBD
014605,000368: 
014606,000369:                                                                                                  #  SUMMARY OF STATE SWITCHES AND FLAGWORDS USED BY KALCMANU.
014607,000370: 
014608,000371:                                                                                                  #        STATE        FLAGWRD 2        SETTING                    MEANING
014609,000372:                                                                                                  #        SWITCH NO.    BIT NO.
014610,000373: 
014611,000374:                                                                                                  #          *
014612,000375:                                                                                                  #        31              14              0               MANEUVER WENT THROUGH GIMBAL LOCK
014613,000376:                                                                                                  #                                        1               MANEUVER DID NOT GO THROUGH GIMBAL LOCK
014614,000377:                                                                                                  #          *
014615,000378:                                                                                                  #        32              13              0               CONTINUE UPDATE PROCESS
014616,000379:                                                                                                  #                                        1               START UPDATE PROCESS
014617,000380: 
014618,000381:                                                                                                  #        33              12              0               PERFORM FINAL P-AXIS YAW IF REQUIRED
014619,000382:                                                                                                  #                                        1               IGNORE ANY FINAL P-AXIS YAW
014620,000383: 
014621,000384:                                                                                                  #        34              11              0               SIGNAL END OF KALCMANU
014622,000385:                                                                                                  #                                        1               KALCMANU IN PROCESS     USER MUST SET SWITCH BEFORE INITIATING
014623,000386: 
014624,000387:                                                                                                  #        * INTERNAL TO KALCMANU
014625,000388: 
014626,000389:                                                                                                  #  SUGGESTIONS FOR PROGRAM INTEGRATION
014627,000390: 
014628,000391:                                                                                                  #  THE FOLLOWING VARIABLES SHOULD BE ASSIGNED TO UNSWITCH ERASABLE
014629,000392: 
014630,000393:                                                                                                  #        CPHI
014631,000394:                                                                                                  #        CTHETA
014632,000395:                                                                                                  #        CPSI
014633,000396:                                                                                                  #        POINTVSM +5
014634,000397:                                                                                                  #        SCAXIS   +5
014635,000398:                                                                                                  #        DELDCDU
014636,000399:                                                                                                  #        DELDCDU1
014637,000400:                                                                                                  #        DELDCDU2
014638,000401:                                                                                                  #        RATEINDX
014639,000402: 
014640,000403:                                                                                                  #  THE FOLLOWING SUBROUTINES MAY BE PUT IN A DIFFERENT BANK
014641,000404: 
014642,000405:                                                                                                  #        MXM3

Page 351

014644,000407:                                                                                                  #        TRANSPOS
014645,000408:                                                                                                  #        SIGNMPAC
014646,000409:                                                                                                  #        READCDUK
014647,000410:                                                                                                  #        CDUTODCM
014648,000411: 

Page 352

014650,000413: 15,2050                                           BANK     15                                    
014651,000414: 22,2000                                           SETLOC   KALCMON1                              
014652,000415: 22,2000                                           BANK                                           
014653,000416: 
014654,000417: 22,2004  E6,1676                                  EBANK=   BCDU                                  
014655,000418: 
014656,000419:                                                                                                  #  THE THREE DESIRED CDU ANGLES MUST BE STORED AS SINGLE PRECISION TWOS COMPLEMENT ANGLES IN THE THREE SUCCESSIVE
014657,000420:                                                                                                  #  LOCATIONS, CPHI, CTHETA, CPSI.
014658,000421: 
014659,000422: 22,2004                                           COUNT*   $$/KALC                               
014660,000423: 22,2004           06042        KALCMAN3           TC       INTPRET                               #  PICK UP THE CURRENT CDU ANGLES AND
014661,000424: 22,2005           77634                           RTB                                            #    COMPUTE THE MATRIX FROM INITIAL S/C
014662,000425: 22,2006           44403                                    READCDUK                              #    AXES TO FINAL S/C AXES
014663,000426: 22,2007           03277                           STORE    BCDU                                  #  STORE INITIAL S/C ANGLES
014664,000427: 22,2010           51535                           SLOAD    ABS                                   #  CHECK THE MAGNITUDE OF THE DESIRED
014665,000428: 22,2011           00324                                    CPSI                                  #  MIDDLE GIMBAL ANGLE
014666,000429: 22,2012           51025                           DSU      BPL                                   
014667,000430: 22,2013           04403                                    LOCKANGL                              #  IF GREATER THAN 70 DEG ABORT MANEUVER
014668,000431: 22,2014           44724                                    TOOBADF                               
014669,000432: 22,2015           72364                           AXC,2    TLOAD                                 
014670,000433: 22,2016           03246                                    MIS                                   
014671,000434: 22,2017           03277                                    BCDU                                  
014672,000435: 22,2020           77624                           CALL                                           #  COMPUTE THE TRANSFORMATION FROM INITIAL
014673,000436: 22,2021           44410                                    CDUTODCM                              #  S/C AXES TO STABLE MEMBER AXES
014674,000437: 22,2022           72364                           AXC,2    TLOAD                                 
014675,000438: 22,2023           02230                                    MFS                                   #  PREPARE TO CALCULATE ARRAY MFS
014676,000439: 22,2024           00322                                    CPHI                                  
014677,000440: 22,2025           77624                           CALL                                           
014678,000441: 22,2026           44410                                    CDUTODCM                              
014679,000442: 22,2027           45160        SECAD              AXC,1    CALL                                  #  MIS AND MFS ARRAYS CALCULATED         $2
014680,000443: 22,2030           03246                                    MIS                                   
014681,000444: 22,2031           44326                                    TRANSPOS                              
014682,000445: 22,2032           45575                           VLOAD    STADR                                 
014683,000446: 22,2033           50457                           STOVL    TMIS       +12D                       
014684,000447: 22,2034           77626                           STADR                                          
014685,000448: 22,2035           50465                           STOVL    TMIS       +6                         
014686,000449: 22,2036           77626                           STADR                                          
014687,000450: 22,2037           74473                           STORE    TMIS                                  #  TMIS = TRANSPOSE(MIS) SCALED BY 2
014688,000451: 22,2040           75160                           AXC,1    AXC,2                                 
014689,000452: 22,2041           03303                                    TMIS                                  
014690,000453: 22,2042           02230                                    MFS                                   
014691,000454: 22,2043           77624                           CALL                                           
014692,000455: 22,2044           44312                                    MXM3                                  
014693,000456: 22,2045           45575                           VLOAD    STADR                                 
014694,000457: 22,2046           51532                           STOVL    MFI        +12D                       
014695,000458: 22,2047           77626                           STADR                                          
014696,000459: 22,2050           51540                           STOVL    MFI        +6                         
014697,000460: 22,2051           77626                           STADR                                          
014698,000461: 22,2052           75546                           STORE    MFI                                   #  MFI = TMIS MFS (SCALED BY 4)
014699,000462: 22,2053           45001                           SETPD    CALL                                  #  TRANSPOSE MFI IN PD LIST

Page 353

014701,000464: 22,2054           00023                                    18D                                   
014702,000465: 22,2055           44335                                    TRNSPSPD                              
014703,000466: 22,2056           45575                           VLOAD    STADR                                 
014704,000467: 22,2057           50457                           STOVL    TMFI       +12D                       
014705,000468: 22,2060           77626                           STADR                                          
014706,000469: 22,2061           50465                           STOVL    TMFI       +6                         
014707,000470: 22,2062           77626                           STADR                                          
014708,000471: 22,2063           74473                           STORE    TMFI                                  #  TMFI = TRANSPOSE (MFI) SCALED BY 4
014709,000472: 
014710,000473:                                                                                                  #  CALCULATE COFSKEW AND MFISYM
014711,000474: 
014712,000475: 22,2064           45345                           DLOAD    DSU                                   
014713,000476: 22,2065           03306                                    TMFI       +2                         
014714,000477: 22,2066           02233                                    MFI        +2                         
014715,000478: 22,2067           45325                           PDDL     DSU                                   #  CALCULATE COF SCALED BY 2/SIN(AM)
014716,000479: 22,2070           02235                                    MFI        +4                         
014717,000480: 22,2071           03310                                    TMFI       +4                         
014718,000481: 22,2072           45325                           PDDL     DSU                                   
014719,000482: 22,2073           03316                                    TMFI       +10D                       
014720,000483: 22,2074           02243                                    MFI        +10D                       
014721,000484: 22,2075           77666                           VDEF                                           
014722,000485: 22,2076           03326                           STORE    COFSKEW                               #  EQUALS MFISKEW
014723,000486: 
014724,000487:                                                                                                  #  CALCULATE AM AND PROCEED ACCORDING TO ITS MAGNITUDE
014725,000488: 
014726,000489: 22,2077           43345                           DLOAD    DAD                                   
014727,000490: 22,2100           02231                                    MFI                                   
014728,000491: 22,2101           02251                                    MFI        +16D                       
014729,000492: 22,2102           43225                           DSU      DAD                                   
014730,000493: 22,2103           06514                                    DP1/4TH                               
014731,000494: 22,2104           02241                                    MFI        +8D                        
014732,000495: 22,2105           03334                           STORE    CAM                                   #  CAM = (MFI0+MFI4+MFI8-1)/2 HALF SCALE
014733,000496: 22,2106           77726                           ARCCOS                                         
014734,000497: 22,2107           03336                           STORE    AM                                    #  AM=ARCCOS(CAM)        (AM SCALED BY 2)
014735,000498: 22,2110           51025                           DSU      BPL                                   
014736,000499: 22,2111           04363                                    MINANG                                
014737,000500: 22,2112           44117                                    CHECKMAX                              
014738,000501: 22,2113           77751                           TLOAD                                          #  MANEUVER LESS THAN .25 DEGREES
014739,000502: 22,2114           00322                                    CPHI                                  #  GO DIRECTLY INTO ATTITUDE HOLD
014740,000503: 22,2115           37236                           STCALL   CDUXD                                 #  ABOUT COMMANDED ANGLES
014741,000504: 22,2116           44742                                    TOOBADI                               #  STOP RATE AND EXIT
014742,000505: 
014743,000506: 22,2117           45345        CHECKMAX           DLOAD    DSU                                   
014744,000507: 22,2120           03336                                    AM                                    
014745,000508: 22,2121           04365                                    MAXANG                                
014746,000509: 22,2122           77244                           BPL      VLOAD                                 
014747,000510: 22,2123           44131                                    ALTCALC                               #  UNIT
014748,000511: 22,2124           03326                                    COFSKEW                               #  COFSKEW
014749,000512: 22,2125           77656                           UNIT                                           
014750,000513: 22,2126           03271                           STORE    COF                                   #  COF IS THE MANEUVER AXIS

Page 354

014752,000515: 22,2127           77650                           GOTO                                           #  SEE IF MANEUVER GOES THRU GIMBAL LOCK
014753,000516: 22,2130           44744                                    LOCSKIRT                              
014754,000517: 22,2131           53375        ALTCALC            VLOAD    VAD                                   #  IF AM GREATER THAN 170 DEGREES
014755,000518: 22,2132           02231                                    MFI                                   
014756,000519: 22,2133           03304                                    TMFI                                  
014757,000520: 22,2134           77762                           VSR1                                           
014758,000521: 22,2135           27304                           STOVL    MFISYM                                
014759,000522: 22,2136           02237                                    MFI        +6                         
014760,000523: 22,2137           74455                           VAD      VSR1                                  
014761,000524: 22,2140           03312                                    TMFI       +6                         
014762,000525: 22,2141           27312                           STOVL    MFISYM     +6                         
014763,000526: 22,2142           02245                                    MFI        +12D                       
014764,000527: 22,2143           74455                           VAD      VSR1                                  
014765,000528: 22,2144           03320                                    TMFI       +12D                       
014766,000529: 22,2145           03320                           STORE    MFISYM     +12D                       #  MFISYM=(MFI+TMFI)/2   SCALED BY 4
014767,000530: 
014768,000531:                                                                                                  #  CALCULATE COF
014769,000532: 
014770,000533: 22,2146           70545                           DLOAD    SR1                                   
014771,000534: 22,2147           03334                                    CAM                                   
014772,000535: 22,2150           45325                           PDDL     DSU                                   #  PDO CAM                               $4
014773,000536: 22,2151           06522                                    DPHALF                                
014774,000537: 22,2152           03334                                    CAM                                   
014775,000538: 22,2153           65204                           BOVB     PDDL                                  #  PD2 1 - CAM                           $2
014776,000539: 22,2154           21713                                    SIGNMPAC                              
014777,000540: 22,2155           03324                                    MFISYM     +16D                       
014778,000541: 22,2156           56225                           DSU      DDV                                   
014779,000542: 22,2157           00001                                    0                                     
014780,000543: 22,2160           00003                                    2                                     
014781,000544: 22,2161           65366                           SQRT     PDDL                                  #  COFZ = SQRT(MFISYM8-CAM)/1-CAM)
014782,000545: 22,2162           03314                                    MFISYM     +8D                        #                                $ ROOT 2
014783,000546: 22,2163           56225                           DSU      DDV                                   
014784,000547: 22,2164           00001                                    0                                     
014785,000548: 22,2165           00003                                    2                                     
014786,000549: 22,2166           65366                           SQRT     PDDL                                  #  COFY = SQRT(MFISYM4-CAM)/(1-CAM)  $ROOT2
014787,000550: 22,2167           03304                                    MFISYM                                
014788,000551: 22,2170           56225                           DSU      DDV                                   
014789,000552: 22,2171           00001                                    0                                     
014790,000553: 22,2172           00003                                    2                                     
014791,000554: 22,2173           55566                           SQRT     VDEF                                  #  COFX = SQRT(MFISYM-CAM)/(1-CAM)  $ROOT 2
014792,000555: 22,2174           77656                           UNIT                                           
014793,000556: 22,2175           03271                           STORE    COF                                   
014794,000557: 
014795,000558:                                                                                                  #  DETERMINE LARGEST COF AND ADJUST ACCORDINGLY
014796,000559: 
014797,000560: 22,2176           45345        COFMAXGO           DLOAD    DSU                                   
014798,000561: 22,2177           03271                                    COF                                   
014799,000562: 22,2200           03273                                    COF        +2                         
014800,000563: 22,2201           71240                           BMN      DLOAD                                 #  COFY G COFX

Page 355

014802,000565: 22,2202           44211                                    COMP12                                
014803,000566: 22,2203           03271                                    COF                                   
014804,000567: 22,2204           50025                           DSU      BMN                                   
014805,000568: 22,2205           03275                                    COF        +4                         
014806,000569: 22,2206           44266                                    METHOD3                               #  COFZ G COFX OR COFY
014807,000570: 22,2207           77650                           GOTO                                           
014808,000571: 22,2210           44242                                    METHOD1                               #  COFX G COFY OR COFZ
014809,000572: 22,2211           45345        COMP12             DLOAD    DSU                                   
014810,000573: 22,2212           03273                                    COF        +2                         
014811,000574: 22,2213           03275                                    COF        +4                         
014812,000575: 22,2214           77640                           BMN                                            
014813,000576: 22,2215           44266                                    METHOD3                               #  COFZ G COFY OR COFX
014814,000577: 
014815,000578: 22,2216           51145        METHOD2            DLOAD    BPL                                   #  COFY MAX
014816,000579: 22,2217           03330                                    COFSKEW    +2                         #  UY
014817,000580: 22,2220           44224                                    U2POS                                 
014818,000581: 22,2221           57575                           VLOAD    VCOMP                                 
014819,000582: 22,2222           03271                                    COF                                   
014820,000583: 22,2223           03271                           STORE    COF                                   
014821,000584: 22,2224           51145        U2POS              DLOAD    BPL                                   
014822,000585: 22,2225           03306                                    MFISYM     +2                         #  UX UY
014823,000586: 22,2226           44232                                    OKU21                                 
014824,000587: 22,2227           57545                           DLOAD    DCOMP                                 #  SIGN OF UX OPPOSITE TO UY
014825,000588: 22,2230           03271                                    COF                                   
014826,000589: 22,2231           03271                           STORE    COF                                   
014827,000590: 22,2232           51145        OKU21              DLOAD    BPL                                   
014828,000591: 22,2233           03316                                    MFISYM     +10D                       #  UY UZ
014829,000592: 22,2234           44744                                    LOCSKIRT                              
014830,000593: 22,2235           57545                           DLOAD    DCOMP                                 #  SIGN OF UZ OPPOSITE TO UY
014831,000594: 22,2236           03275                                    COF        +4                         
014832,000595: 22,2237           03275                           STORE    COF        +4                         
014833,000596: 22,2240           77650                           GOTO                                           
014834,000597: 22,2241           44744                                    LOCSKIRT                              
014835,000598: 22,2242           51145        METHOD1            DLOAD    BPL                                   #  COFX MAX
014836,000599: 22,2243           03326                                    COFSKEW                               #  UX
014837,000600: 22,2244           44250                                    U1POS                                 
014838,000601: 22,2245           57575                           VLOAD    VCOMP                                 
014839,000602: 22,2246           03271                                    COF                                   
014840,000603: 22,2247           03271                           STORE    COF                                   
014841,000604: 22,2250           51145        U1POS              DLOAD    BPL                                   
014842,000605: 22,2251           03306                                    MFISYM     +2                         #  UX UY
014843,000606: 22,2252           44256                                    OKU12                                 
014844,000607: 22,2253           57545                           DLOAD    DCOMP                                 
014845,000608: 22,2254           03273                                    COF        +2                         #  SIGN OF UY OPPOSITE TO UX
014846,000609: 22,2255           03273                           STORE    COF        +2                         
014847,000610: 22,2256           51145        OKU12              DLOAD    BPL                                   
014848,000611: 22,2257           03310                                    MFISYM     +4                         #  UX UZ
014849,000612: 22,2260           44744                                    LOCSKIRT                              
014850,000613: 22,2261           57545                           DLOAD    DCOMP                                 #  SIGN OF UZ OPPOSITE TO UY
014851,000614: 22,2262           03275                                    COF        +4                         

Page 356

014853,000616: 22,2263           03275                           STORE    COF        +4                         
014854,000617: 22,2264           77650                           GOTO                                           
014855,000618: 22,2265           44744                                    LOCSKIRT                              
014856,000619: 22,2266           51145        METHOD3            DLOAD    BPL                                   #  COFZ MAX
014857,000620: 22,2267           03332                                    COFSKEW    +4                         #  UZ
014858,000621: 22,2270           44274                                    U3POS                                 
014859,000622: 22,2271           57575                           VLOAD    VCOMP                                 
014860,000623: 22,2272           03271                                    COF                                   
014861,000624: 22,2273           03271                           STORE    COF                                   
014862,000625: 22,2274           51145        U3POS              DLOAD    BPL                                   
014863,000626: 22,2275           03310                                    MFISYM     +4                         #  UX UZ
014864,000627: 22,2276           44302                                    OKU31                                 
014865,000628: 22,2277           57545                           DLOAD    DCOMP                                 
014866,000629: 22,2300           03271                                    COF                                   #  SIGN OF UX OPPOSITE TO UZ
014867,000630: 22,2301           03271                           STORE    COF                                   
014868,000631: 22,2302           51145        OKU31              DLOAD    BPL                                   
014869,000632: 22,2303           03316                                    MFISYM     +10D                       #  UY UZ
014870,000633: 22,2304           44744                                    LOCSKIRT                              
014871,000634: 22,2305           57545                           DLOAD    DCOMP                                 
014872,000635: 22,2306           03273                                    COF        +2                         #  SIGN OF UY OPPOSITE TO UZ
014873,000636: 22,2307           03273                           STORE    COF        +2                         
014874,000637: 22,2310           77650                           GOTO                                           
014875,000638: 22,2311           44744                                    LOCSKIRT                              

Page 357

014877,000640:                                                                                                  #  MATRIX OPERATIONS
014878,000641: 
014879,000642: 13,2207                                           BANK     13                                    
014880,000643: 22,2000                                           SETLOC   KALCMON2                              
014881,000644: 22,2000                                           BANK                                           
014882,000645: 
014883,000646: 22,2312  E6,1676                                  EBANK=   BCDU                                  
014884,000647: 
014885,000648: 22,2312           76601        MXM3               SETPD    VLOAD*                                #  MXM3 MULTIPLIES 2 3X3 MATRICES
014886,000649: 22,2313           00001                                    0                                     #  AND LEAVES RESULT IN PD LIST
014887,000650: 22,2314           00001                                    0,1                                   #  AND MPAC
014888,000651: 22,2315           62703                           VXM*     PDVL*                                 
014889,000652: 22,2316           77776                                    0,2                                   
014890,000653: 22,2317           00007                                    6,1                                   
014891,000654: 22,2320           62703                           VXM*     PDVL*                                 
014892,000655: 22,2321           77776                                    0,2                                   
014893,000656: 22,2322           00015                                    12D,1                                 
014894,000657: 22,2323           41503                           VXM*     PUSH                                  
014895,000658: 22,2324           77776                                    0,2                                   
014896,000659: 22,2325           77616                           RVQ                                            
014897,000660: 
014898,000661:                                                                                                  #  RETURN WITH M1XM2 IN PD LIST
014899,000662: 
014900,000663: 22,2326           76601        TRANSPOS           SETPD    VLOAD*                                #  TRANSPOS TRANSPOSES A 3X3 MATRIX
014901,000664: 22,2327           00001                                    0                                     #        AND LEAVES RESULT IN PD LIST
014902,000665: 22,2330           00001                                    0,1                                   #  MATRIX ADDRESS IN XR1
014903,000666: 22,2331           62713                           PDVL*    PDVL*                                 
014904,000667: 22,2332           00007                                    6,1                                   
014905,000668: 22,2333           00015                                    12D,1                                 
014906,000669: 22,2334           77606                           PUSH                                           #  MATRIX IN PD
014907,000670: 22,2335           77776        TRNSPSPD           EXIT                                           #  ENTER WITH MATRIX AT 0 IN PD LIST
014908,000671: 22,2336           50120                           INDEX    FIXLOC                                
014909,000672: 22,2337           52013                           DXCH     12                                    
014910,000673: 22,2340           50120                           INDEX    FIXLOC                                
014911,000674: 22,2341           52017                           DXCH     16                                    
014912,000675: 22,2342           50120                           INDEX    FIXLOC                                
014913,000676: 22,2343           52013                           DXCH     12                                    
014914,000677: 22,2344           50120                           INDEX    FIXLOC                                
014915,000678: 22,2345           52015                           DXCH     14                                    
014916,000679: 22,2346           50120                           INDEX    FIXLOC                                
014917,000680: 22,2347           52005                           DXCH     4                                     
014918,000681: 22,2350           50120                           INDEX    FIXLOC                                
014919,000682: 22,2351           52015                           DXCH     14                                    
014920,000683: 22,2352           50120                           INDEX    FIXLOC                                
014921,000684: 22,2353           52003                           DXCH     2                                     
014922,000685: 22,2354           50120                           INDEX    FIXLOC                                
014923,000686: 22,2355           52007                           DXCH     6                                     
014924,000687: 22,2356           50120                           INDEX    FIXLOC                                
014925,000688: 22,2357           52003                           DXCH     2                                     

Page 358

014927,000690: 22,2360           06042                           TC       INTPRET                               
014928,000691: 22,2361           77616                           RVQ                                            
014929,000692: 
014930,000693: 15,2050                                           BANK     15                                    
014931,000694: 22,2000                                           SETLOC   KALCMON1                              
014932,000695: 22,2000                                           BANK                                           
014933,000696: 
014934,000697: 22,2362  E6,1676                                  EBANK=   BCDU                                  
014935,000698: 
014936,000699: 22,2362           00013 13563  MINANG             2DEC     0.00069375                            
014937,000700: 
014938,000701: 22,2364           17070 34343  MAXANG             2DEC     0.472222222                            
014939,000702: 
014940,000703:                                                                                                  #  GIMBAL LOCK CONSTANTS
014941,000704: 
014942,000705:                                                                                                  #  D = MGA CORRESPONDING TO GIMBAL LOCK = 60 DEGREES
014943,000706:                                                                                                  #           NGL = BUFFER ANGLE (TO AVOID DIVISIONS BY ZERO) = 2 DEGREES
014944,000707: 
014945,000708: 22,2366           15666 20443  SD                 2DEC     .433015                               #  = SIN(D)                      $2
014946,000709: 
014947,000710: 22,2370           33555 01106  K3S1               2DEC     .86603                                #  = SIN(D)                      $1
014948,000711: 
014949,000712: 22,2372           67777 77777  K4                 2DEC     -.25                                  #  = -COS(D)                     $2
014950,000713: 
014951,000714: 22,2374           04000 00000  K4SQ               2DEC     .125                                  #  = COS(D)COS(D)                $2
014952,000715: 
014953,000716: 22,2376           00216 36323  SNGLCD             2DEC     .008725                               #  = SIN(NGL)COS(D)              $2
014954,000717: 
014955,000718: 22,2400           17773 00057  CNGL               2DEC     .499695                               #  COS(NGL)                      $2
014956,000719: 
014957,000720: 22,2402           14344        LOCKANGL           DEC      .388889                               #  = 70 DEGREES
014958,000721:                                                                                                  #  INTERPRETIVE SUBROUTINE TO READ THE CDU ANGLES
014959,000722: 
014960,000723: 22,2403           30034        READCDUK           CA       CDUZ                                  #  LOAD T(MPAC) WITH CDU ANGLES
014961,000724: 22,2404           54156                           TS       MPAC       +2                         
014962,000725: 22,2405           00006                           EXTEND                                         
014963,000726: 22,2406           30033                           DCA      CDUX                                  #  AND CHANGE MODE TO TRIPLE PRECISION
014964,000727: 22,2407           16501                           TCF      TLOAD      +6                         
014965,000728: 
014966,000729: 22,2410           66370        CDUTODCM           AXT,1    SSP                                   
014967,000730: 22,2411           00003                           OCT      3                                     
014968,000731: 22,2412           00051                                    S1                                    
014969,000732: 22,2413           00001                           OCT      1                                     #  SET XR1, S1, AND PD FOR LOOP
014970,000733: 22,2414           00010                           STORE    7                                     
014971,000734: 22,2415           77601                           SETPD                                          
014972,000735: 22,2416           00001                                    0                                     
014973,000736: 22,2417           47133        LOOPSIN            SLOAD*   RTB                                   
014974,000737: 22,2420           00013                                    10D,1                                 
014975,000738: 22,2421           21577                                    CDULOGIC                              

Page 359

014977,000740: 22,2422           00013                           STORE    10D                                   #  LOAD PD WITH  0 SIN(PHI)
014978,000741: 22,2423           65356                           SIN      PDDL                                  #                2 COS(PHI)
014979,000742: 22,2424           00013                                    10D                                   #                4 SIN(THETA)
014980,000743: 22,2425           41546                           COS      PUSH                                  #                6 COS(THETA)
014981,000744: 22,2426           71300                           TIX,1    DLOAD                                 #                8 SIN(PSI)
014982,000745: 22,2427           44417                                    LOOPSIN                               #               10 COS(PSI)
014983,000746: 22,2430           00007                                    6                                     
014984,000747: 22,2431           72405                           DMP      SL1                                   
014985,000748: 22,2432           00013                                    10D                                   
014986,000749: 22,2433           10001                           STORE    0,2                                   #  C0 = COS(THETA)COS(PSI)
014987,000750: 22,2434           41345                           DLOAD    DMP                                   
014988,000751: 22,2435           00005                                    4                                     
014989,000752: 22,2436           00001                                    0                                     
014990,000753: 22,2437           41325                           PDDL     DMP                                   #  (PD6 SIN(THETA)SIN(PHI))
014991,000754: 22,2440           00007                                    6                                     
014992,000755: 22,2441           00011                                    8D                                    
014993,000756: 22,2442           72405                           DMP      SL1                                   
014994,000757: 22,2443           00003                                    2                                     
014995,000758: 22,2444           72421                           BDSU     SL1                                   
014996,000759: 22,2445           00015                                    12D                                   
014997,000760: 22,2446           10003                           STORE    2,2                                   #  C1=-COS(THETA)SIN(PSI)COS(PHI)
014998,000761: 22,2447           41345                           DLOAD    DMP                                   
014999,000762: 22,2450           00003                                    2                                     
015000,000763: 22,2451           00005                                    4                                     
015001,000764: 22,2452           41325                           PDDL     DMP                                   #  (PD7 COS(PHI)SIN(THETA)) SCALED 4
015002,000765: 22,2453           00007                                    6                                     
015003,000766: 22,2454           00011                                    8D                                    
015004,000767: 22,2455           72405                           DMP      SL1                                   
015005,000768: 22,2456           00001                                    0                                     
015006,000769: 22,2457           72415                           DAD      SL1                                   
015007,000770: 22,2460           00017                                    14D                                   
015008,000771: 22,2461           10005                           STORE    4,2                                   #  C2=COS(THETA)SIN(PSI)SIN(PHI)
015009,000772: 22,2462           77745                           DLOAD                                          
015010,000773: 22,2463           00011                                    8D                                    
015011,000774: 22,2464           10007                           STORE    6,2                                   #  C3=SIN(PSI)
015012,000775: 22,2465           77745                           DLOAD                                          
015013,000776: 22,2466           00013                                    10D                                   
015014,000777: 22,2467           72405                           DMP      SL1                                   
015015,000778: 22,2470           00003                                    2                                     
015016,000779: 22,2471           10011                           STORE    8D,2                                  #  C4=COS(PSI)COS(PHI)
015017,000780: 22,2472           41345                           DLOAD    DMP                                   
015018,000781: 22,2473           00013                                    10D                                   
015019,000782: 22,2474           00001                                    0                                     
015020,000783: 22,2475           72476                           DCOMP    SL1                                   
015021,000784: 22,2476           10013                           STORE    10D,2                                 #  C5=-COS(PSI)SIN(PHI)
015022,000785: 22,2477           41345                           DLOAD    DMP                                   
015023,000786: 22,2500           00005                                    4                                     
015024,000787: 22,2501           00013                                    10D                                   
015025,000788: 22,2502           72476                           DCOMP    SL1                                   
015026,000789: 22,2503           10015                           STORE    12D,2                                 #  C6=-SIN(THETA)COS(PSI)

Page 360

015028,000791: 22,2504           77745                           DLOAD                                          
015029,000792: 22,2505           72405                           DMP      SL1                                   #   (PUSH UP 7)
015030,000793: 22,2506           00011                                    8D                                    
015031,000794: 22,2507           41325                           PDDL     DMP                                   #   (PD7 COS(PHI)SIN(THETA)SIN(PSI)) SCALE 4
015032,000795: 22,2510           00007                                    6                                     
015033,000796: 22,2511           00001                                    0                                     
015034,000797: 22,2512           72415                           DAD      SL1                                   #   (PUSH UP 7)
015035,000798: 22,2513           77626                           STADR                                          #  C7=COS(PHI)SIN(THETA)SIN(PSI)
015036,000799: 22,2514           67760                           STORE    14D,2                                 #   +COS(THETA)SIN(PHI)
015037,000800: 22,2515           77745                           DLOAD                                          
015038,000801: 22,2516           72405                           DMP      SL1                                   #   (PUSH UP 6)
015039,000802: 22,2517           00011                                    8D                                    
015040,000803: 22,2520           41325                           PDDL     DMP                                   #   (PD6 SIN(THETA)SIN(PHI)SIN(PSI)) SCALE 4
015041,000804: 22,2521           00007                                    6                                     
015042,000805: 22,2522           00003                                    2                                     
015043,000806: 22,2523           72425                           DSU      SL1                                   #   (PUSH UP 6)
015044,000807: 22,2524           77626                           STADR                                          
015045,000808: 22,2525           67756                           STORE    16D,2                                 #  C8=-SIN(THETA)SIN(PHI)SIN(PSI)
015046,000809: 22,2526           77616                           RVQ                                            #   +COS(THETA)COS(PHI)
015047,000810: 
015048,000811:                                                                                                  #  CALCULATION OF THE MATRIX DEL......
015049,000812: 
015050,000813:                                                                                                  #         *         *           --T           *
015051,000814:                                                                                                  #        DEL = (IDMATRIX)COS(A)+UU (1-COS(A))+UX SIN(A)          SCALED 1
015052,000815:                                                                                                  #              -
015053,000816:                                                                                                  #        WHERE U IS A UNIT VECTOR (DP SCALED 2) ALONG THE AXIS OF ROTATION.
015054,000817:                                                                                                  #        A IS THE ANGLE OF ROTATION (DP SCALED 2)
015055,000818:                                                                                                  #                                            -
015056,000819:                                                                                                  #        UPON ENTRY THE STARTING ADDRESS OF U IS COF, AND A IS IN MPAC
015057,000820: 
015058,000821: 22,2527           41401        DELCOMP            SETPD    PUSH                                  #  MPAC CONTAINS THE ANGLE A
015059,000822: 22,2530           00001                                    0                                     
015060,000823: 22,2531           65356                           SIN      PDDL                                  #  PD0 = SIN(A)
015061,000824: 22,2532           41546                           COS      PUSH                                  #  PD2 = COS(A)
015062,000825: 22,2533           65302                           SR2      PDDL                                  #  PD2 = COS(A)                          $8
015063,000826: 22,2534           41021                           BDSU     BOVB                                  
015064,000827: 22,2535           06522                                    DPHALF                                
015065,000828: 22,2536           21713                                    SIGNMPAC                              
015066,000829: 22,2537           77725                           PDDL                                           #  PD4 = 1-COS(A)
015067,000830: 
015068,000831:                                                                                                  #  COMPUTE THE DIAGONAL COMPONENTS OF DEL
015069,000832: 
015070,000833: 22,2540           03271                                    COF                                   
015071,000834: 22,2541           41316                           DSQ      DMP                                   
015072,000835: 22,2542           00005                                    4                                     
015073,000836: 22,2543           52415                           DAD      SL3                                   
015074,000837: 22,2544           00003                                    2                                     
015075,000838: 22,2545           77604                           BOVB                                           
015076,000839: 22,2546           21713                                    SIGNMPAC                              

Page 361

015078,000841: 22,2547           16231                           STODL    KEL                                   #  UX UX(1-COS(A)) +COS(A)               $1
015079,000842: 22,2550           03273                                    COF        +2                         
015080,000843: 22,2551           41316                           DSQ      DMP                                   
015081,000844: 22,2552           00005                                    4                                     
015082,000845: 22,2553           52415                           DAD      SL3                                   
015083,000846: 22,2554           00003                                    2                                     
015084,000847: 22,2555           77604                           BOVB                                           
015085,000848: 22,2556           21713                                    SIGNMPAC                              
015086,000849: 22,2557           16241                           STODL    KEL        +8D                        #  UY UY(1-COS(A)) +COS(A)               $1
015087,000850: 22,2560           03275                                    COF        +4                         
015088,000851: 22,2561           41316                           DSQ      DMP                                   
015089,000852: 22,2562           00005                                    4                                     
015090,000853: 22,2563           52415                           DAD      SL3                                   
015091,000854: 22,2564           00003                                    2                                     
015092,000855: 22,2565           77604                           BOVB                                           
015093,000856: 22,2566           21713                                    SIGNMPAC                              
015094,000857: 22,2567           02251                           STORE    KEL        +16D                       #  UZ UZ(1-COS(A)) +COS(A)               $1
015095,000858: 
015096,000859:                                                                                                  #  COMPUTE THE OFF DIAGONAL TERMS OF DEL
015097,000860: 
015098,000861: 22,2570           41345                           DLOAD    DMP                                   
015099,000862: 22,2571           03271                                    COF                                   
015100,000863: 22,2572           03273                                    COF        +2                         
015101,000864: 22,2573           72405                           DMP      SL1                                   
015102,000865: 22,2574           00005                                    4                                     
015103,000866: 22,2575           41325                           PDDL     DMP                                   #  D6     UX UY (1-COS A)                $4
015104,000867: 22,2576           03275                                    COF        +4                         
015105,000868: 22,2577           00001                                    0                                     
015106,000869: 22,2600           43206                           PUSH     DAD                                   #  D8    UZ SIN A                        $4
015107,000870: 22,2601           00007                                    6                                     
015108,000871: 22,2602           41112                           SL2      BOVB                                  
015109,000872: 22,2603           21713                                    SIGNMPAC                              
015110,000873: 22,2604           16237                           STODL    KEL        +6                         
015111,000874: 22,2605           62421                           BDSU     SL2                                   
015112,000875: 22,2606           77604                           BOVB                                           
015113,000876: 22,2607           21713                                    SIGNMPAC                              
015114,000877: 22,2610           16233                           STODL    KEL        +2                         
015115,000878: 22,2611           03271                                    COF                                   
015116,000879: 22,2612           41205                           DMP      DMP                                   
015117,000880: 22,2613           03275                                    COF        +4                         
015118,000881: 22,2614           00005                                    4                                     
015119,000882: 22,2615           65352                           SL1      PDDL                                  #  D6    UX UZ (1-COS A)                 $4
015120,000883: 22,2616           03273                                    COF        +2                         
015121,000884: 22,2617           41405                           DMP      PUSH                                  #  D8    UY SIN(A)
015122,000885: 22,2620           00001                                    0                                     
015123,000886: 22,2621           62415                           DAD      SL2                                   
015124,000887: 22,2622           00007                                    6                                     
015125,000888: 22,2623           77604                           BOVB                                           
015126,000889: 22,2624           21713                                    SIGNMPAC                              
015127,000890: 22,2625           16235                           STODL    KEL        +4                         #  UX UZ (1-COS(A))+UY SIN(A)

Page 362

015129,000892: 22,2626           62421                           BDSU     SL2                                   
015130,000893: 22,2627           77604                           BOVB                                           
015131,000894: 22,2630           21713                                    SIGNMPAC                              
015132,000895: 22,2631           16245                           STODL    KEL        +12D                       #  UX UZ (1-COS(A))-UY SIN(A)
015133,000896: 22,2632           03273                                    COF        +2                         
015134,000897: 22,2633           41205                           DMP      DMP                                   
015135,000898: 22,2634           03275                                    COF        +4                         
015136,000899: 22,2635           00005                                    4                                     
015137,000900: 22,2636           65352                           SL1      PDDL                                  #  D6    UY UZ (1-COS(A))                $ 4
015138,000901: 22,2637           03271                                    COF                                   
015139,000902: 22,2640           41405                           DMP      PUSH                                  #  D8    UX SIN(A)
015140,000903: 22,2641           00001                                    0                                     
015141,000904: 22,2642           62415                           DAD      SL2                                   
015142,000905: 22,2643           00007                                    6                                     
015143,000906: 22,2644           77604                           BOVB                                           
015144,000907: 22,2645           21713                                    SIGNMPAC                              
015145,000908: 22,2646           16247                           STODL    KEL        +14D                       #  UY UZ(1-COS(A)) +UX SIN(A)
015146,000909: 22,2647           62421                           BDSU     SL2                                   
015147,000910: 22,2650           77604                           BOVB                                           
015148,000911: 22,2651           21713                                    SIGNMPAC                              
015149,000912: 22,2652           02243                           STORE    KEL        +10D                       #  UY UZ (1-COS(A)) -UX SIN(A)
015150,000913: 22,2653           77616                           RVQ                                            
015151,000914: 
015152,000915:                                                                                                  #  DIRECTION COSINE MATRIX TO CDU ANGLE ROUTINE
015153,000916:                                                                                                  #  X1 CONTAINS THE COMPLEMENT OF THE STARTING ADDRESS FOR MATRIX (SCALED 2)
015154,000917:                                                                                                  #  LEAVES CDU ANGLES SCALED 2PI IN V(MPAC)
015155,000918:                                                                                                  #  COS(MGA) WILL BE LEFT IN S1 (SCALED 1)
015156,000919: 
015157,000920:                                                                                                  #  THE DIRECTION COSINE MATRIX RELATING S/C AXES TO STABLE MEMBER AXES CAN BE WRITTEN AS***
015158,000921: 
015159,000922:                                                                                                  #        C  = COS(THETA) COS(PSI)
015160,000923:                                                                                                  #         0
015161,000924: 
015162,000925:                                                                                                  #        C  = -COS(THETA) SIN(PSI) COS(PHI) + SI (THETA) SIN(PHI)
015163,000926:                                                                                                  #         1
015164,000927: 
015165,000928:                                                                                                  #        C  = COS(THETA) SIN(PSI) SIN(PHI) + S N(THETA) COS(PHI)
015166,000929:                                                                                                  #         2
015167,000930: 
015168,000931:                                                                                                  #        C  = SIN(PSI)
015169,000932:                                                                                                  #         3
015170,000933: 
015171,000934:                                                                                                  #        C  = COS(PSI) COS(PHI)
015172,000935:                                                                                                  #         4
015173,000936: 
015174,000937:                                                                                                  #        C  = -COS(PSI) SIN(PHI)
015175,000938:                                                                                                  #         5
015176,000939: 
015177,000940:                                                                                                  #        C  = -SIN(THETA) COS(PSI)
015178,000941:                                                                                                  #         6
015179,000942: 
015180,000943:                                                                                                  #        C  = SIN(THETA) SIN(PSI) COS(PHI) + COS THETA) SIN(PHI)
015181,000944:                                                                                                  #         7
015182,000945: 
015183,000946:                                                                                                  #        C  = -SIN(THETA) SIN(PSI) SIN(PHI) + CO (THETA)COS(PHI)
015184,000947:                                                                                                  #         8

Page 363

015186,000949: 
015187,000950:                                                                                                  #  WHERE PHI = OGA
015188,000951:                                                                                                  #        THETA = IGA
015189,000952:                                                                                                  #        PSI = MGA
015190,000953: 
015191,000954: 22,2654           67543        DCMTOCDU           DLOAD*   ARCSIN                                
015192,000955: 22,2655           00007                                    6,1                                   
015193,000956: 22,2656           71406                           PUSH     COS                                   #  PD +0         PSI
015194,000957: 22,2657           41152                           SL1      BOVB                                  
015195,000958: 22,2660           21713                                    SIGNMPAC                              
015196,000959: 22,2661           00051                           STORE    S1                                    
015197,000960: 22,2662           57543                           DLOAD*   DCOMP                                 
015198,000961: 22,2663           00015                                    12D,1                                 
015199,000962: 22,2664           67471                           DDV      ARCSIN                                
015200,000963: 22,2665           00051                                    S1                                    
015201,000964: 22,2666           51123                           PDDL*    BPL                                   #  PD +2         THETA
015202,000965: 22,2667           00001                                    0,1                                   #  MUST CHECK THE SIGN OF COS(THETA)
015203,000966: 22,2670           44702                                    OKTHETA                               #  TO DETERMINE THE PROPER QUADRANT
015204,000967: 22,2671           57545                           DLOAD    DCOMP                                 
015205,000968: 22,2672           43244                           BPL      DAD                                   
015206,000969: 22,2673           44677                                    SUHALFA                               
015207,000970: 22,2674           06522                                    DPHALF                                
015208,000971: 22,2675           77650                           GOTO                                           
015209,000972: 22,2676           44701                                    CALCPHI                               
015210,000973: 22,2677           77625        SUHALFA            DSU                                            
015211,000974: 22,2700           06522                                    DPHALF                                
015212,000975: 22,2701           77606        CALCPHI            PUSH                                           
015213,000976: 22,2702           57543        OKTHETA            DLOAD*   DCOMP                                 
015214,000977: 22,2703           00013                                    10D,1                                 
015215,000978: 22,2704           67471                           DDV      ARCSIN                                
015216,000979: 22,2705           00051                                    S1                                    
015217,000980: 22,2706           51123                           PDDL*    BPL                                   #  PUSH DOWN PHI
015218,000981: 22,2707           00011                                    8D,1                                  
015219,000982: 22,2710           44722                                    OKPHI                                 
015220,000983: 22,2711           57545                           DLOAD    DCOMP                                 #  PUSH UP PHI
015221,000984: 22,2712           43244                           BPL      DAD                                   
015222,000985: 22,2713           44717                                    SUHALFAP                              
015223,000986: 22,2714           06522                                    DPHALF                                
015224,000987: 22,2715           77650                           GOTO                                           
015225,000988: 22,2716           44723                                    VECOFANG                              
015226,000989: 22,2717           52025        SUHALFAP           DSU      GOTO                                  
015227,000990: 22,2720           06522                                    DPHALF                                
015228,000991: 22,2721           44723                                    VECOFANG                              
015229,000992: 22,2722           77745        OKPHI              DLOAD                                          #  PUSH UP PHI
015230,000993: 22,2723           43466        VECOFANG           VDEF     RVQ                                   

Page 364

015232,000995:                                                                                                  #  ROUTINES FOR TERMINATING THE AUTOMATIC MANEUVER AND RETURNING TO USER
015233,000996: 
015234,000997: 22,2724           77776        TOOBADF            EXIT                                           
015235,000998: 22,2725           05567                           TC       ALARM                                 
015236,000999: 22,2726           00401                           OCT      00401                                 
015237,001000: 
015238,001001: 22,2727           12732                           TCF      NOGO                                  #  DO NOT ZERO ATTITUDE ERRORS
015239,001002: 
015240,001003: 22,2730           04616                           TC       BANKCALL                              
015241,001004: 22,2731           40154                           CADR     ZATTEROR                              #  ZERO ATTITUDE ERRORS
015242,001005: 
015243,001006: 22,2732           04616        NOGO               TC       BANKCALL                              
015244,001007: 22,2733           40166                           CADR     STOPRATE                              #  STOP RATES
015245,001008: 
015246,001009: 22,2734           34752                           CAF      TWO                                   
015247,001010: 22,2735           00004                           INHINT                                         #  ALL RETURNS ARE NOW MADE VIA GOODEND
015248,001011: 22,2736           05203                           TC       WAITLIST                              
015249,001012: 22,2737  E6,1676                                  EBANK=   BCDU                                  
015250,001013: 22,2737           03234 44066                     2CADR    GOODMANU                              
015251,001014: 
015252,001015: 22,2741           15155                           TCF      ENDOFJOB                              
015253,001016: 
015254,001017: 22,2742           77776        TOOBADI            EXIT                                           
015255,001018: 22,2743           12732                           TCF      NOGO                                  
015256,001019: 
015257,001020: 

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