ORBITAL_INTEGRATION.agc
### FILE="Main.annotation"
## Copyright: Public domain.
## Filename: ORBITAL_INTEGRATION.agc
## Purpose: A section of Luminary 1C, revision 131.
## It is part of the source code for the Lunar Module's (LM)
## Apollo Guidance Computer (AGC) for Apollo 13.
## This file is intended to be a faithful transcription, except
## that the code format has been changed to conform to the
## requirements of the yaYUL assembler rather than the
## original YUL assembler.
## Reference: pp. 1220-1240
## Contact: Ron Burkey <info@sandroid.org>.
## Website: www.ibiblio.org/apollo/index.html
## Mod history: 06/02/03 RSB. Began transcribing.
## 05/14/05 RSB Corrected website reference above.
## 2017-01-06 RSB Page numbers now agree with those on the
## original hardcopy, as opposed to the PDF page
## numbers in 1701.pdf.
## 2017-02-27 RSB Proofed comment text using octopus/ProoferComments.
## 2017-03-13 RSB Comment-text fixes noted in proofing Luminary 116.
## 2017-03-16 RSB Comment-text fixes identified in 5-way
## side-by-side diff of Luminary 69/99/116/131/210.
## 2017-03-17 RSB Comment-text fixes identified in diff'ing
## Luminary 99 vs Comanche 55.
## Page 1220
# DELETE
BANK 13
SETLOC ORBITAL
BANK
COUNT* $$/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 (-2 OR +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 - ETCETRA 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 1221
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 1222
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 1223
# 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
STCALL ALPHAM
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
2D
## Page 1224
STORE RPSV
SLOAD DSU
MODREG
OCT27
BHIZ BOF
+3
DIM0FLAG
GETRPSV
VLOAD VXSC
ALPHAV
ALPHAM
VSR* VSU
1,2
BETAV
XCHX,2
DIFEQCNT
STORE VECTAB +6,2
STORE RQVV
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
## Page 1225
32D # SAVING NORM SCALE FACTOR IN X1
SR1 PDVL
BETAV # C(PDL+2) = ALMOST NORMED ALPHA
UNIT
STODL BETAV
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
## Page 1226
VAD PUSH # A12 + C(PD+16D) TO PD+16D
DLOAD DMP
0
12D
NORM ROUND
30D
BDDV DMP*
2
MUEARTH,2
DCOMP VXSC
XCHX,2 XAD,2
S1
S2
XSU,2 XSU,2
30D
31D
BOVB VSR*
TCDANZIG
0 -1,2
XCHX,2 VAD
S1
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 20430
## Page 1227
# 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
STOVL URPV # RP/R B-1 IN PLANETARY COORDINATES
ZUNIT
PUSH CALL # ZUNIT B-1 IN PLANETARY COORDL AT 00D
MATRIX
PDVL # UZ B-2 IN INERT COORD AT 00D
XUNIT
PUSH CALL # XUNIT B-1 IN PLANETARY COORD. AT 06D
MATRIX
VSL1
STOVL 32D # UX B-1 IN INERT. COORD AT 32D
VSL1
COMTERM STODL UZ # UZ B-1 IN INERTIAL COORD AT 20D
COSPHI/2 # ' Z-COMPONENT OF URPV
DMPR PDDL # P B-6, 3COSPHI/64 AT 00D
3/32 # 2
COSPHI/2
DSQ DMPR
15/16 # ' 2
DSU PUSH # P B-5, (1/2)(15COSPHI -3) AT 02D
3/64 # 3
DMPR DMP
COSPHI/2
7/12
SL1R PDDL
0D
DMPR BDSU
2/3 # ' ' '
PUSH DMPR # P B-7, (1/3)(7COSPHI P -4P ) AT 04D
COSPHI/2 # 4 3 2
DMPR PDDL
9/16
## Page 1228
2D # ' ' '
DMPR BDSU # P B-10, (1/4)(9COSPHI P -5P )
5/128 # 5 4 3
DMP* DDV # '
J4REQ/J3,2 # B- , (J RP/J R)P
ALPHAM # 4 3 5
DAD DMPR*
4D # 2 2 ' '
2J3RE/J2,2 # B , (2J RP /J2 R )P +(2J RP/J2R)P
DDV DAD # 4 5 3 4
ALPHAM # - 2 ' 2 ' '
2D # (R/R)(J RP P /R + 2J RP P / + J P )
VXSC # 4 5 3 4 2 2 3
ALPHAV # 4 2 ' -
STODL TVEC # B-6,(SUM((J /R )P (COSPHI))UR)
DMP* SR1 # I=2 I I+1
J4REQ/J3,2 # '
DDV DAD # (J RP/J R)P
ALPHAM # 4 3 4
DMPR* SR3 # 2 2 ' '
2J3RE/J2,2 # (2J RP /J R )P +(2J RP/J R)P
DDV DAD # 4 2 4 3 2 3
ALPHAM
VXSC VSL1 # 4 ' -
UZ # B-6 SUM(P (COSPHI))UZ
BVSU # I=2 I
TVEC # 4 I-2 ' -
STODL TVEC # SUM((MU J (RP/R) )(P (COSPHI)UR -
ALPHAM # I=2 I I+2
NORM DSQ # P (COSPHI)UZ)) B-6 AT 20D
X1 # I
DSQ NORM
S1 # 4
PUSH BDDV* # NORMALIZED R AT 00D
J2REQSQ,2
VXSC BOV
TVEC
+1 # B+38 FOR EARTH , B+42 FOR MOON
XAD,1 XAD,1
X1
X1
XAD,1 VSL*
S1
0 -22D,1
VAD BOV
FV
GOBAQUE
STODL FV # B+16 FOR EARTH , B+20 FOR MOON
URPV # B-1 X-COMPONENT OF POSITION IN
BOF PUSH # PLANETORY COORD. AT 02D
## Page 1229
MOONFLAG
NBRANCH # 2
DSQ PDDL # B-2 X AT 04D
URPV +2 # B-1 Y-COMPONENT
DSQ DSU
DMP VXSC
5/8 # 2 2 -
ALPHAV # B-6 5(Y -X )UR 2 2 -
VSL3 PDDL # B-3 5(Y -X )UR AT 02D
VXSC VAD
32D # 2 2 - 2 -
PDVL VXV # (5(Y.-X )UR/R ) +(2X/R)UX AT 02D
32D # B-1 UX
UZ # B-2 -UY =(UX * UZ)
VSL1 VXSC # B-3 -(2Y/R)UY
URPV +2 # 2 2 - 2 -
VAD PUSH # B-3 (5(X -Y )UR/R )+(2X/R)UX -(
DLOAD # -
COSPHI/2 # 2Y/R)UY AT 02D
DSQ PUSH # B-2 (Z.COMPONENT) AT 08D
DMP PDDL # 2
5/8 # B-5 5COSPHI /2 AT 08D
SR2 DAD
08D
BDSU DMP # 2
D1/32 # B-5 (1 - 7COSPHI )
URPV
DMP VXSC
5/8
ALPHAV # 2 -
VSL5 PDDL # B-5 (5X/R)(1-7COSPHI )UR AT 08D
DSU VXSC
D1/32
32D
VSL1 VAD # 2 - -
PDDL DMP # B-5 (5X/R)(1-7COSPHI )UR +(5COSPHI
URPV # -
URPV +4 # -1)UX AT 08D
DMP VXSC
5/8 # B-5 5X Y
UZ # M M
VSL2 VAD # 2 - 2
PDDL NORM # B-5 (5X/R)(1-7COSPHI )UR +(5COSPHI
ALPHAM # - 2 -
X2 # -1)UX +(10XZ/R )UZ AT 08D
PUSH SLOAD
E32C31RM
DDV VXSC
VSL* PDVL
0 -3,2
## Page 1230
PUSH SLOAD
E3J22R2M
VXSC VAD
VSL* V/SC
0 -27D,1 # B+16 OR B+20 (J + C )
VAD BOV # 22 31
FV
GOBAQUE
STORE FV
LXA,2
PBODY
NBRANCH SLOAD LXA,1
DIFEQCNT
MPAC
DMP CGOTO
-1/12
MPAC
DIFEQTAB
COSPHIE DLOAD
ALPHAV +4
STOVL COSPHI/2
ZUNIT
GOTO
COMTERM
MATRIX VXV VCOMP
504LM # ROUTINE TRANSLATES FROM PLANETARY
VAD # TO INERTIAL COORDINATES
VXM RVQ
MMATRIX
DIFEQTAB CADR DIFEQ+0
CADR DIFEQ+1
CADR DIFEQ+2
TIMESTEP BOF VLOAD
MIDFLAG
RECTEST
RCV
DOT DMP
VCV
DT/2 # (R.V) X (DELTA T)
BMN
RECTEST
BON BOF
MOONFLAG
LUNSPH
RPQFLAG
EARSPH
DLOAD CALL
TET
LSPOS # RPQV IN MPAC
STORE RPQV # RPQV
## Page 1231
LXA,2
PBODY
INLUNCHK BVSU ABVAL
RCV
DSU BMN
RSPHERE
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
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
EARSPH VLOAD GOTO
## Page 1232
RPQV
INLUNCHK
LUNSPH DLOAD SR2
10D
DSU BMN
RSPHERE
RECTEST
BOF DLOAD
RPQFLAG
DOSWITCH
TET
CALL
LUNPOS
VCOMP
STORE RPQV
DOSWITCH CALL
ORIGCHNG
GOTO
INTGRATE
ORIGCHNG STQ CALL
ORIGEX
RECTIFY
VLOAD VSL*
RCV
0,2
VSU VSL*
RPQV
2,2
STORE RRECT
STORE RCV
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 1233
# THE RECTIFY SUBROUTINE IS CALLED BY THE INTEGRATION PROGRAM AND OCCASIONALLY BY THE MEASUREMENT INCORPORATION
# ROUTINES TO ESTABLISH A NEW CONIC.
BANK 13
SETLOC ORBITAL2
BANK
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
BANK 11
SETLOC ORBITAL
BANK
## Page 1234
# THE THREE DIFEQ ROUTINES - DIFEQ+0, DIFEQ+12, AND DIFEQ+24 - ARE ENTERED TO 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 1235
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 1236
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 1237
GOTO
TESTLOOP # FINISH INTEGRATING STATE VECTOR
## Page 1238
# 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 SOLVE THE 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 1239
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
BANK 05
SETLOC ORBITAL3
BANK
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
## Page 1240
DEC -4
ASCALE DEC -7
DEC -6
5/8 2DEC 5 B-3
-1/12 2DEC -.1
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
