# Copyright: Public domain. # Filename: ORBITAL_INTEGRATION.agc # Purpose: Part of the source code for Colossus 2A, AKA Comanche 055. # It is part of the source code for the Command Module's (CM) # Apollo Guidance Computer (AGC), for Apollo 11. # Assembler: yaYUL # Contact: Ron Burkey . # Website: www.ibiblio.org/apollo. # Pages: 1334-1354 # Mod history: 2009-05-14 RSB Adapted from the Colossus249/ file of the # same name, using Comanche055 page images. # 2009-05-20 RSB Corrections: DAT -> DAD in one place, # BWM -> BMN, DEFEQCNT -> DIFEQCNT. # # This source code has been transcribed or otherwise adapted from digitized # images of a hardcopy from the MIT Museum. The digitization was performed # by Paul Fjeld, and arranged for by Deborah Douglas of the Museum. Many # thanks to both. The images (with suitable reduction in storage size and # consequent reduction in image quality as well) are available online at # www.ibiblio.org/apollo. If for some reason you find that the images are # illegible, contact me at info@sandroid.org about getting access to the # (much) higher-quality images which Paul actually created. # # Notations on the hardcopy document read, in part: # # Assemble revision 055 of AGC program Comanche by NASA # 2021113-051. 10:28 APR. 1, 1969 # # This AGC program shall also be referred to as # Colossus 2A # Page 1334 # ORBITAL INTEGRATION # DELETE BANK 13 SETLOC ORBITAL BANK COUNT 11/ORBIT # DELETE KEPPREP LXA,2 SETPD PBODY 0 DLOAD* SQRT # SQRT(MU) (+18 OR +15) 0D PL 2D MUEARTH,2 PDVL UNIT # PL 8D RCV PDDL NORM # NORM R (+29 OR +27 - N1) 2D PL 4D 36D X1 PDVL DOT PDDL # F*SQRT(MU)(+7 OR +5) 4D PL 6D VCV TAU. # (+28) DSU NORM TC S1 SR1 DDV PDDL 2D DMP PUSH # FS(+6 +N1-N2) 6D PL 8D 4D DSQ PDDL # (FS)SQ(+12 +2(N1-N2)) 8D PL 10D 4D DSQ PDDL* # SSQ/MU(-2OR +2(N1-N2)) 10D PL 12D MUEARTH,2 SR3 SR4 PDVL VSQ # PREALIGN MU (+43 OR +37) 12D PL 14D VCV DMP BDSU # PL 12D 36D DDV DMP # PL 10D 2D # -(1/R-ALPHA)(+12 +3N1-2N2) DMP SL* DP2/3 0 -3,1 # 10L(1/R-ALPHA)(+13 +2(N1-N2)) XSU,1 DAD # 2(FS)SQ - ETCETERA PL 8D S1 # X1 = N2-N1 SL* DSU # -FS+2(FS)SQ ETC (+6 +N1-N2) PL 6D 8D,1 DMP DMP 0D 4D SL* SL* # Page 1335 8D,1 0,1 # S(-FS(1-2FS)-1/6...)(+17 OR +16) DAD PDDL # PL 6D XKEP DMP SL* # S(+17 OR +16) 0D 1,1 BOVB DAD TCDANZIG STADR STORE XKEPNEW STQ AXC,1 KEPRTN DEC 10 BON AXC,1 MOONFLAG KEPLERN DEC 2 GOTO KEPLERN # Page 1336 FBR3 LXA,1 SSP DIFEQCNT S1 DEC -13 DLOAD SR DT/2 9D TIX,1 ROUND +1 PUSH DAD TC STODL TAU. DAD TET STCALL TET KEPPREP # Page 1337 # AGC ROUTINE TO COMPUTE ACCELERATION COMPONENTS. ACCOMP LXA,1 LXA,2 PBODY PBODY VLOAD ZEROVEC STOVL FV ALPHAV VSL* VAD 0 -7,2 RCV STORE BETAV BOF XCHX,2 DIM0FLAG +5 DIFEQCNT STORE VECTAB,2 XCHX,2 DIFEQCNT VLOAD UNIT ALPHAV STODL ALPHAV 36D STORE ALPHAM CALL GAMCOMP VLOAD SXA,1 BETAV S2 STODL ALPHAV BETAM STORE ALPHAM BOF DLOAD MIDFLAG OBLATE TET CALL LSPOS AXT,2 LXA,1 2 S2 BOF MOONFLAG +3 VCOMP AXT,2 0 STORE BETAV STOVL RPQV # Page 1338 2D STORE RPSV BOF VLOAD DIM0FLAG GETRPSV ALPHAV VXSC VSR* ALPHAM 1,2 VSU XCHX,2 BETAV DIFEQCNT STORE VECTAB +6,2 XCHX,2 DIFEQCNT GETRPSV VLOAD INCR,1 RPQV 4 CLEAR BOF RPQFLAG MOONFLAG +5 VSR VAD 9D RPSV STORE RPSV CALL GAMCOMP AXT,2 INCR,1 4 4 VLOAD RPSV STCALL BETAV GAMCOMP GOTO OBLATE GAMCOMP VLOAD VSR1 BETAV VSQ SETPD 0 NORM ROUND 31D PDDL NORM # NORMED B SQUARED TO PD LIST ALPHAM # NORMALIZE (LESS ONE) LENGTH OF ALPHA 32D # SAVING NORM SCALE FACTOR IN X1 SR1 PDVL BETAV # C(PDL+2) = ALMOST NORMED ALPHA UNIT STODL BETAV # Page 1339 36D STORE BETAM NORM BDDV # FORM NORMALIZED QUOTIENT ALPHAM/BETAM 33D SR1R PUSH # C(PDL+2) = ALMOST NORMALIZED RHO. DLOAD* ASCALE,1 STORE S1 XCHX,2 XAD,2 S1 32D XSU,2 DLOAD 33D 2D SR* XCHX,2 0 -1,2 S1 PUSH SR1R # RHO/4 TO 4D PDVL DOT ALPHAV BETAV SL1R BDSU # (RHO/4) - 2(ALPHAV/2.BETAV/2) PUSH DMPR # TO PDL+6 4 SL1 PUSH DAD DQUARTER PUSH SQRT DMPR PUSH 10D SL1 DAD DQUARTER PDDL DAD # (1/4)+2((Q+1)/4) TO PD+14D 10D HALFDP DMPR SL1 8D DAD DDV THREE/8 14D DMPR VXSC 6 BETAV PDVL VSR3 # (G/2)(C(PD+4))B/2 TO PD+16D ALPHAV VAD PUSH # A12 + C(PD+16D) TO PD+16D DLOAD DMP 0 12D NORM ROUND # Page 1340 30D BDDV DMP* 2 MUEARTH,2 DCOMP VXSC XCHX,2 XAD,2 S1 S2 XSU,2 XSU,2 30D 31D BOV # CLEAR OVIND +1 VSR* XCHX,2 0 -1,2 S1 VAD FV STORE FV BOV RVQ # RETURN IF NO OVERFLOW +1 GOBAQUE VLOAD ABVAL TDELTAV BZE INT-ABRT DLOAD SR H 9D PUSH BDSU TC STODL TAU. TET DSU STADR STCALL TET KEPPREP CALL RECTIFY SETGO RPQFLAG TESTLOOP INT-ABRT EXIT TC POODOO OCT 00430 # Page 1341 # THE OBLATE ROUTINE COMPUTES THE ACCELERATION DUE TO OBLATENESS. IT USES THE UNIT OF THE VEHICLE # POSITION VECTOR FOUND IN ALPHAV AND THE DISTANCE TO THE CENTER IN ALPHAM. THIS IS ADDED TO THE SUM OF THE # DISTURBING ACCELERATIONS IN FV AND THE PROPER DIFEQ STAGE IS CALLED VIA X1. OBLATE LXA,2 DLOAD PBODY ALPHAM SETPD DSU* 0 RDE,2 BPL BOF # GET URPV NBRANCH MOONFLAG COSPHIE VLOAD PDDL ALPHAV TET PDDL CALL 3/5 R-TO-RP STORE URPV VLOAD VXV 504LM ZUNIT VAD VXM ZUNIT MMATRIX UNIT # POSSIBLY UNNECESSARY COMTERM STORE UZ DLOAD DMPR COSPHI/2 3/32 PDDL DSQ # P2/64 TO PD0 COSPHI/2 DMPR DSU 15/16 3/64 PUSH DMPR # P3/32 TO PD2 COSPHI/2 DMP SL1R 7/12 PDDL DMPR 0 2/3 BDSU PUSH # P4/128 TO PD4 DMPR DMPR COSPHI/2 # BEGIN COMPUTING P5/1024 9/16 PDDL DMPR 2 5/128 # Page 1342 BDSU DMP* J4REQ/J3,2 DDV DAD # -3 ALPHAM # (((P5/256)B 2 /R+P4/32) /R+P3/8)ALPHAV 4 # 4 3 DMPR* DDV 2J3RE/J2,2 ALPHAM DAD VXSC 2 ALPHAV STODL TVEC DMP* SR1 J4REQ/J3,2 DDV DAD ALPHAM # -3 DMPR* SR3 2J3RE/J2,2 # 3 4 DDV DAD ALPHAM VXSC VSL1 UZ BVSU TVEC STODL TVEC ALPHAM NORM DSQ X1 DSQ NORM S1 # 4 PUSH BDDV* # NORMED R TO 0D J2REQSQ,2 VXSC BOV TVEC +1 # (RESET OVERFLOW INDICATOR) XAD,1 XAD,1 X1 X1 XAD,1 VSL* S1 0 -22D,1 VAD BOV FV GOBAQUE STCALL FV QUALITY1 QUALITY3 DSQ # J22 TERM X R**4 IN 2D. SCALED B61 # AS VECTOR. PUSH DMP # STORE COSPHI**2 SCALED B2 IN 8D # Page 1343 5/8 # 5 SCALED B3 PDDL SR2 # PUT 5 COSPHI**2, D5, IN 8D. GET # COSPHI**2 D2 FROM 8D DAD BDSU # END UP WITH (1-7 COSPHI**2), B5 8D # ADDING COSPHI**2 B4 SAME AS COSPHI**2 # X 2 D5 D1/32 # 1 SCALED B5 DMP DMP URPV # X COMPONENT 5/8 # 5 SCALED B3 VXSC VSL5 # AFTER SHIFT, SCALED B5 URPV # VECTOR, B1. PDDL # VECTOR INTO 8D, 10D, 12D, SCALED B5. # GET 5 COSPHI**2 OUT OF 8D DSU DAD D1/32 # 1 B5 8D # X COMPONENT (SAME AS MULTIPLYING # BY UNITX) STODL 8D URPV # X COMPONENT DMP DMP URPV +4 # Z COMPONENT 5/8 # 5 B3 ANSWER B5 SL1 DAD # FROM 12D FOR Z COMPONENT (SL1 GIVES 10 # INSTEAD OF 5 FOR COEFFICIENT) PDDL NORM # BACK INTO 12D FOR Z COMPONENT. ALPHAM # SCALED B27 FOR MOON X2 PUSH SLOAD # STORE IN 14D, DESTROYING URPV # X COMPONENT E32C31RM DDV VXSC # IF X2 = 0, DIVISION GIVES B53, VXSC # OUT OF 8D B5 GIVES B58 VSL* VAD # SHIFT MAKES B61, FOR ADDITION OF # VECTOR IN 2D 0 -3,2 VSL* V/SC # OPERAND FROM 0D, B108 FOR X1 = 0 0 -27D,1 # FOR X1 = 0, MAKES B88, GIVING B-20 # FOR RESULT. PDDL PDDL TET 5/8 # ANY NON-ZERO CONSTANT LXA,2 CALL # POSITION IN 0D, TIME IN 6D. X2 LEFT # ALONE. PBODY RP-TO-R VAD BOV # OVERFLOW INDICATOR RESET IN "RP-TO-R" FV GOBAQUE STORE FV # Page 1344 NBRANCH SLOAD LXA,1 DIFEQCNT MPAC DMP CGOTO -1/12 MPAC DIFEQTAB COSPHIE DLOAD ALPHAV +4 STOVL COSPHI/2 ZUNIT GOTO COMTERM DIFEQTAB CADR DIFEQ+0 CADR DIFEQ+1 CADR DIFEQ+2 TIMESTEP BOF CALL MIDFLAG RECTEST # SKIP ORIGIN CHANGE LOGIC CHKSWTCH BMN DOSWITCH RECTEST VLOAD ABVAL # RECTIFY IF TDELTAV BOV CALLRECT DSU BPL # 1) EITHER TDELTAV OR TNUV EQUALS OR 3/4 # EXCEEDS 3/4 IN MAGNITUDE CALLRECT # DAD SL* # OR 3/4 # 0 -7,2 # 2) ABVAL(TDELTAV) EQUALS OR EXCEEDS DDV DSU # .01(ABVAL(RCV)) 10D RECRATIO BPL VLOAD CALLRECT TNUV ABVAL DSU 3/4 BOV CALLRECT BMN INTGRATE CALLRECT CALL RECTIFY INTGRATE VLOAD TNUV # Page 1345 STOVL ZV TDELTAV STORE YV CLEAR JSWITCH DIFEQ0 VLOAD SSP YV DIFEQCNT 0 STODL ALPHAV DPZERO STORE H # START H AT ZERO. GOES 0(DELT/2)DELT. BON GOTO JSWITCH DOW.. ACCOMP CHKSWTCH STQ BOF ORIGEX RPQFLAG RPQOK # MOON POSITION IS AVAILABLE DLOAD CALL TET LUNPOS # GET MOON POSITION BOF VCOMP MOONFLAG +1 STORE RPQV RPQOK LXA,2 VLOAD # RESTORE X2 AFTER USING LUNPOS PBODY TDELTAV # _ VSL* VAD # |RQC|-RSPHERE WHEN OUTSIDE THE SPHERE. 0 -7,2 # _ _ _ RCV # R = RDEVIATION + RCONIC BOF ABVAL MOONFLAG EARSPH SR2 BDSU # INSIDE RSPHERE GOTO ORIGEX EARSPH VSU ABVAL # OUTSIDE RPQV DSU GOTO RSPHERE ORIGEX DOSWITCH CALL ORIGCHNG GOTO INTGRATE # Page 1346 ORIGCHNG STQ CALL ORIGEX RECTIFY VLOAD VSL* RCV 0,2 VSU VSL* RPQV 2,2 STORE RRECT STODL RCV TET CALL LUNVEL BOF VCOMP MOONFLAG +1 PDVL VSL* VCV 0,2 VSU VSL* 0 +2,2 STORE VRECT STORE VCV LXA,2 SXA,2 ORIGEX QPRET BON GOTO MOONFLAG CLRMOON SETMOON # Page 1347 # THE RECTIFY SUBROUTINE IS CALLED BY THE INTEGRATION PROGRAM AND OCCASIONALLY BY THE MEASUREMENT INCORPORATION # ROUTINES TO ESTABLISH A NEW CONIC. RECTIFY LXA,2 VLOAD PBODY TDELTAV VSL* VAD 0 -7,2 RCV STORE RRECT STOVL RCV TNUV VSL* VAD 0 -4,2 VCV MINIRECT STORE VRECT STOVL VCV ZEROVEC STORE TDELTAV STODL TNUV ZEROVEC STORE TC STORE XKEP RVQ # Page 1348 # THE THREE DIFEQ ROUTINES - DIFEQ+0, DIFEQ+12, DIFEQ+24 - ARE ENTEREDTO PROCESS THE CONTRIBUTIONS AT THE # BEGINNING, MIDDLE, AND END OF THE TIMESTEP, RESPECTIVELY. THE UPDATING IS DONE BY THE NYSTROM METHOD. DIFEQ+0 VLOAD VSR3 FV STCALL PHIV DIFEQCOM DIFEQ+1 VLOAD VSR1 FV PUSH VAD PHIV STOVL PSIV VSR1 VAD PHIV STCALL PHIV DIFEQCOM DIFEQ+2 DLOAD DMPR H DP2/3 PUSH VXSC PHIV VSL1 VAD ZV VXSC VAD H YV STOVL YV FV VSR3 VAD PSIV VXSC VSL1 VAD ZV STORE ZV BOFF CALL JSWITCH ENDSTATE GRP2PC LXA,2 VLOAD COLREG ZV VSL3 # ADJUST W-POSITION FOR STORAGE STORE W +54D,2 VLOAD YV VSL3 BOV WMATEND STORE W,2 CALL GRP2PC # Page 1349 LXA,2 SSP COLREG S2 0 INCR,2 SXA,2 6 YV TIX,2 CALL RELOADSV GRP2PC LXA,2 SXA,2 YV COLREG NEXTCOL CALL GRP2PC LXA,2 VLOAD* COLREG W,2 VSR3 # ADJUST W-POSITION FOR INTEGRATION STORE YV VLOAD* AXT,1 W +54D,2 0 VSR3 # ADJUST W-VELOCITY FOR INTEGRATION STCALL ZV DIFEQ0 ENDSTATE BOV VLOAD GOBAQUE ZV STOVL TNUV YV STORE TDELTAV BON BOFF MIDAVFLG CKMID2 # CHECK FOR MID2 BEFORE GOING TO TIMEINC DIM0FLAG TESTLOOP EXIT TC PHASCHNG OCT 04022 # PHASE 1 TC UPFLAG # PHASE CHANGE HAS OCCURRED BETWEEN ADRES REINTFLG # INTSTALL AND INTWAKE TC INTPRET SSP QPRET AMOVED BON GOTO VINTFLAG # Page 1350 ATOPCSM ATOPLEM AMOVED SET SSP JSWITCH COLREG DEC -30 BOFF SSP D6OR9FLG NEXTCOL COLREG DEC -48 GOTO NEXTCOL RELOADSV DLOAD # RELOAD TEMPORARY STATE VECTOR TDEC # FROM PERMANENT IN CASE OF STCALL TDEC1 INTEGRV2 # BY STARTING AT INTEGRV2. DIFEQCOM DLOAD DAD # INCREMENT H AND DIFEQCNT. DT/2 H INCR,1 SXA,1 DEC -12 DIFEQCNT # DIFEQCNT SET FOR NEXT ENTRY. STORE H VXSC VSR1 FV VAD VXSC ZV H VAD YV STORE ALPHAV BON GOTO JSWITCH DOW.. FBR3 WMATEND CLEAR CLEAR DIM0FLAG # DONT INTEGRATE W THIS TIME ORBWFLAG # INVALIDATE W CLEAR RENDWFLG SET EXIT STATEFLG # PICK UP STATE VECTOR UPDATE TC ALARM OCT 421 TC INTPRET # Page 1351 GOTO TESTLOOP # FINISH INTEGRATING STATE VECTOR # Page 1352 # ORBITAL ROUTINE FOR EXTRAPOLATION OF THE W MATRIX. IT COMPUTES THE SECOND DERIVATIVE OF EACH COLUMN POSITION # VECTOR OF THE MATRIX AND CALLS THE NYSTROM INTEGRATION ROUTINES TO SOLVETHE DIFFERENTIAL EQUATIONS. THE PROGRAM # USES A TABLE OF VEHICLE POSITION VECTORS COMPUTED DURING THE INTEGRATION OF THE VEHICLES POSITION AND VELOCITY. DOW.. LXA,2 DLOAD* PBODY MUEARTH,2 STCALL BETAM DOW..1 STORE FV BOF INCR,1 MIDFLAG NBRANCH DEC -6 LXC,2 DLOAD* PBODY MUEARTH -2,2 STCALL BETAM DOW..1 BON VSR6 MOONFLAG +1 VAD FV STCALL FV NBRANCH DOW..1 VLOAD VSR4 ALPHAV PDVL* UNIT VECTAB,1 PDVL VPROJ ALPHAV VXSC VSU 3/4 PDDL NORM 36D S2 PUSH DSQ DMP NORM PDDL 34D BETAM SR1 DDV VXSC LXA,2 XAD,2 S2 S2 XAD,2 XAD,2 S2 34D VSL* RVQ # Page 1353 0 -8D,2 SETLOC ORBITAL1 BANK 3/5 2DEC .6 B-2 THREE/8 2DEC .375 .3D 2DEC .3 B-2 3/64 2DEC 3 B-6 DP1/4 2DEC .25 DQUARTER EQUALS DP1/4 POS1/4 EQUALS DP1/4 3/32 2DEC 3 B-5 15/16 2DEC 15. B-4 3/4 2DEC 3.0 B-2 7/12 2DEC .5833333333 9/16 2DEC 9 B-4 5/128 2DEC 5 B-7 DPZERO EQUALS ZEROVEC DP2/3 2DEC .6666666667 2/3 EQUALS DP2/3 OCT27 OCT 27 BANK 13 SETLOC ORBITAL2 BANK # IT IS VITAL THAT THE FOLLOWING CONSTANTS NOT BE SHUFFLED DEC -11 DEC -2 DEC -9 DEC -6 DEC -2 DEC -2 DEC 0 DEC -12 DEC -9 DEC -4 ASCALE DEC -7 DEC -6 # Page 1354 2DEC* 1.32715445 E16 B-54* # S 2DEC* 4.9027780 E8 B-30* # M MUEARTH 2DEC* 3.986032 E10 B-36* 2DEC 0 J4REQ/J3 2DEC* .4991607391 E7 B-26* 2DEC -176236.02 B-25 2J3RE/J2 2DEC* -.1355426363 E5 B-27* 2DEC* .3067493316 E18 B-60* J2REQSQ 2DEC* 1.75501139 E21 B-72* 3J22R2MU 2DEC* 9.20479048 E16 B-58* 5/8 2DEC 5 B-3 -1/12 2DEC -.1 MUM = MUEARTH -2 RECRATIO 2DEC .01 RSPHERE 2DEC 64373.76 E3 B-29 RDM 2DEC 16093.44 E3 B-27 RDE 2DEC 80467.20 E3 B-29 RATT EQUALS 00 VATT EQUALS 6D TAT EQUALS 12D RATT1 EQUALS 14D VATT1 EQUALS 20D MU(P) EQUALS 26D TDEC1 EQUALS 32D URPV EQUALS 14D COSPHI/2 EQUALS URPV +4 UZ EQUALS 20D TVEC EQUALS 26D