### FILE="Main.annotation"

## Copyright: Public domain.

## Filename: CONIC_SUBROUTINES.agc

## Purpose: A section of Comanche revision 044.

## It is part of the reconstructed source code for the

## original release of the flight software for the Command

## Module's (CM) Apollo Guidance Computer (AGC) for Apollo 10.

## The code has been recreated from a copy of Comanche 055. It

## has been adapted such that the resulting bugger words

## exactly match those specified for Comanche 44 in NASA drawing

## 2021153D, which gives relatively high confidence that the

## reconstruction is correct.

## Assembler: yaYUL

## Contact: Ron Burkey <info@sandroid.org>.

## Website: www.ibiblio.org/apollo/index.html

## Mod history: 2020-12-03 MAS Created from Comanche 51.

## Page 1262

# PROGRAM DESCRIPTION - ENTIRE CONIC SUBROUTINE LOG SECTION DATE - 1 SEPTEMBER 1967

# MOD NO. - 0 LOG SECTION - CONIC SUBROUTINES

# MOD BY KRAUSE ASSEMBLY - COLOSSUS REVISION 88

#

# FUNCTIONAL DESCRIPTION -

# THE FOLLOWING SET OF SUBROUTINES SOLVE VARIOUS PROBLEMS INVOLVING THE TRAJECTORY PRODUCED BY A CENTRAL

# INVERSE-SQUARE FORCE ACTING ON A POINT MASS, AS OUTLINED IN THE CMC AND LGC LUNAR LANDING MISSION GSOP, SECTION

# 5.5.1.2. A GENERAL USAGE POINT-OF-VIEW WAS TAKEN IN FORMULATING, MECHANIZING, AND SCALING THE SUBROUTINES,

# RATHER THAN OPTIMIZING EACH FOR A PARTICULAR USE. THEREFORE, MULTIPLE USAGE CAN BE MADE OF THE SUBROUTINES

# INVOLVING ANY REALISTIC SET OF CONSTRAINTS. IT SHOULD BE NOTED THAT ONLY ONE SET OF CODING IS USED, WHETHER THE

# EARTH, MOON, OR ANY OTHER CELESTIAL BODY IS SPECIFIED AS THE CENTRAL BODY OF THE PROBLEM, PROVIDED ONE OBSERVES

# THE INHERENT SCALE CHANGE REQUIRED IN POSITION, VELOCITY, MU, AND TIME, AS OUTLINED IN MISSION PROGRAMMING

# DEFINITION MEMO NO. 10. THIS CAN BE ACCOMPLISHED BY SIMPLY ADDING TO THE MUTABLE AND INITIALIZING THE SUBROU-

# TINES APPROPRIATELY.

#

# DUE TO THE UNIFORMITY OF THE EQUATIONS INVOLVED, CODING WAS MINIMIZED BY TREATING INDIVIDUAL EQUATIONS AND

# BLOCKS OF EQUATIONS AS SUBROUTINES OF LOWER RANK WHENEVER POSSIBLE. AS A RESULT, THREE BY-PRODUCTS SUBROUTINES,

# DIRECTLY USABLE AS INDEPENDENT SUBROUTINES, WERE GENERATED.

#

# RESTRICTIONS -

# THE ONLY LIMITATION IN THE SCOPE OF PROBLEM WHICH CAN BE SOLVED BY A PARTICULAR SUBROUTINE IS THE SCALING

# LIMIT OF EACH PARAMETER AS SPECIFIED IN THE GSOP. THESE SCALING LIMITS WERE CHOSEN SO THAT ALL FEASIBLE TRAJEC-

# TORIES COULD BE HANDLED.

#

# SINCE THE SUBROUTINES (EXCEPT KEPLER) USE COMMON SUBROUTINES OF LOWER RANK WHICH USE ERASABLE OTHER THAN

# THE PUSHLIST (DUE TO ITS LIMITED SIZE) AND COMMON INTERPRETIVE SWITCHES, THE CONIC SUBROUTINES CANNOT BE ALLOWED

# TO INTERRUPT EACH OTHER. IT IS UP TO THE USER TO GUARANTEE THIS CONDITION.

## Page 1263

# PROGRAM DESCRIPTION - KEPLER SUBROUTINE DATE - 11 OCTOBER 1967

# MOD NO. - 1 LOG SECTION - CONIC SUBROUTINES

# MOD BY KRAUSE ASSEMBLY - COLOSSUS 103 AND SUNDANCE 222

# MOD NO. - 2 (AUGUST 1968) BY ROBERTSON: TO PERMIT BACKDATING BY MORE THAN ONE ORBITAL PERIOD.

# MOD NO. - 3 (DEC 1968) BY ROBERTSON: SUPPRESSION OF X-MODULO-ING

# MOD. NO. - 4 (JAN 1969) BY ROBERTSON: CLEAR OVFIND AT KEPLER ENTRY

#

# FUNCTIONAL DESCRIPTION -

# THIS SUBROUTINE, GIVEN AN INITIAL STATE VECTOR AND THE DESIRED TRANSFER TIME THROUGH WHICH THE STATE IS TO

# BE UPDATED ALONG A CONIC TRAJECTORY, COMPUTES THE NEW, UPDATED STATE VECTOR. THE TRAJECTORY MAY BE ANY CONIC

# SECTION - CIRCULAR, ELLIPTIC, PARABOLIC, HYPERBOLIC, OR RECTILINEAR WITH RESPECT TO THE EARTH OR THE MOON. THE

# USE OF THE SUBROUTINE CAN BE EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT

# INTRODUCING ANY CODING CHANGES, ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY. AN ITERA-

# TION TECHNIQUE IS UTILIZED IN THE COMPUTATION.

#

# IF A NEGATIVE TIME-OF-FLIGHT IS INPUT, THE PROGRAM WILL SOLVE FOR THE STATE WHICH WOULD BE PRODUCED BY

# EXTRAPOLATING THE POSITION BACKWARD IN TIME.

#

# IF THE ABSOLUTE VALUE OF THE DESIRED TRANSFER TIME EXCEEDS THE ORBITAL PERIOD, THE SUBROUTINE, THROUGH A

# MODULAR TECHNIQUE, WILL COMPUTE THE STATE CORRESPONDING TO THE DESIRED TIME (WHETHER POSITIVE OR NEGATIVE).

#

# THE RESTRICTIONS ARE -

# 1. (PREVIOUS RESTRICTION ON THE NEGATIVE DESIRED TRANSFER TIME IS NOW DELETED.)

# 2. THE PARAMETERS IN THE PROBLEM CANNOT EXCEED THEIR SCALING LIMITS AS SPECIFIED IN THE GSOP. IF

# ANY OF THESE LIMITS ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS.

#

# THE NUMBER OF ITERATIONS AND, THEREFORE, THE COMPUTATION SPEED IS DEPENDENT ON THE ACCURACY OF THE

# GUESS, XKFPNEW. THE AGC COMPUTATION TIME IS APPROXIMATELY .061 SECONDS FOR INITIALIZATION, .065 SECONDS FOR THE

# FINAL COMPUTATIONS, PLUS .083 SECONDS FOR EACH ITERATION.

#

# REFERENCES -

# R-479, MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP, SECTION 5.5, SGA

# MEMO 67-4.

#

# INPUT - ERASABLE INITIALIZATION REQUIRED

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# RRECT * +29 FOR EARTH*DP INITIAL POSITION VECTOR IN METERS

# * +27 FOR MOON *

## Page 1264

# VRECT * +7 FOR EARTH *DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND

# * +5 FOR MOON *

# X1 (38D)* NONE *INDEX REGISTER SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON,

# * *RESPECTIVELY, IS THE CENTRAL BODY

# TAU. * +28 *DESIRED TRANSFER TIME IN CENTISECONDS (DP)

# * * MAY BE POS OR NEG AND ABSOLUTE VALUE MAY BE GREATER OR LESS THAN ONE ORBITAL PERIOD.

# XKEPNEW * +17 FOR EARTH*DP GUESS OF ROOT X OF KEPLERS EQN IN SQRT(METERS).SIGN SHOULD AGREE WITH THAT OF TAU.

# * +16 FOR MOON * AND ABS VALUE SHOULD BE LESS THAN THAT CORRESPONDING TO A PERIOD, VIZ, 2PI SQRT(SEMI-

# * * MAJOR AXIS), FOR SPEED OF CONVERGENCE, BUT IF EITHER CONDITION FAILS, XKEPNEW IS RESET

# * * BY KEPLER TO A POOR BUT VALID GUESS.

# TC * +28 *DP PREV. VALUE OF TIME IN CENTISECS. MUST BE LESS THAN ONE ORBITAL PERIOD.

# XPREV * +17 FOR EARTH*DP PREV. VALUE OF X IN SQRT(METERS). MUST BE LESS THAN AN X CORRESPONDING TO ONE

# * +16 FOR MOON * ORBITAL PERIOD, VIZ, 2PI SQRT(SEMI-MAJOR AXIS)

#

# SUBROUTINES CALLED -

# DELTIME

#

# CALLING SEQUENCE AND NORMAL EXIT MODES -

# KEPRTN-2 GOTO MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY.

# KEPRTN-1 KEPLER RETURNS WITH XPREV IN MPAC. PL IS AT 0.

# KEPRTN ... CONTINUE

#

# KEPLER MUST NOT BE CALLED DIRECTLY SINCE AN INTERRUPTION OF IT WOULD DESTROY THE ERASABLES IT NEEDS TO COMPLETE

# THE INTERRUPTED JOB. THEREFORE THE USER MUST CALL CSMCONIC OR LEMCONIC WHICH GUARANTEES NO INTERRUPTS AND WHICH

# ALSO CALLS KEPPREP TO COMPUTE A GUESS OF XKEPNEW.

#

# ABORT EXIT MODES -

# NONE

#

# OUTPUT -

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# RCV * +29 FOR EARTH*DP TERMINAL POSITION VECTOR IN METERS

# * +27 FOR MOON *

# VCV * +7 FOR EARTH *DP TERMINAL VELOCITY VECTOR IN METERS/CENTISEC

# * +5 FOR MOON *

# TC * +28 *DP TRANSFER TIME IN CENTISECS TO WHICH KEPLER CONVERGED. ALWAYS LESS THAN ONE PERIOD.

# XPREV * +17 FOR EARTH*DP VALUE OF X IN SQRT(METERS) TO WHCIH KEPLER CONVERGED. ALWAYS LESS THAN THE X

# * +16 FOR MOON * CORRESPONDING TO ONE PERIOD.

## Page 1265

# FOR OTHER OUTPUT WHICH MAY BE OF USE, SEE DEBRIS.

#

# DEBRIS -

# PARAMETERS WHICH MAY BE OF USE -

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# URRECT * +1 *DP UNIT VECTOR OF INITIAL POSITION

# R1 * +29 FOR EARTH*DP MAGNITUDE OF INITIAL POSITION IN METERS

# * +27 FOR MOON *

# ALPHA * -22 FOR EARTH*DP INVERSE OF SEMIMAJOR AXIS IN 1/METERS

# * -20 FOR MOON *

# TMODULO * +28 *DP INTEGRAL NUMBER OF PERIODS IN CENTISECS. WHICH WAS SUBTRACTED FROM TAU. TO PRODUCE A

# * *TAU. OF LESS THAN ONE PERIOD.

#

# PARAMETERS OF NO USE -

# DP PARAMETERS - EPSILONT, DELX, DELT, RCNORM, XMODULO, PLUS PUSHLIST REGISTERS 0 THROUGH 39D.

## Page 1266

# PROGRAM DESCRIPTION - LAMBERT SUBROUTINE DATE - 1 SEPTEMBER 1967

# MOD NO. - 0 LOG SECTION - CONIC SUBROUTINES

# MOD BY KRAUSE ASSEMBLY - COLOSSUS REVISION 88

#

# FUNCTIONAL DESCRIPTION -

# THIS SUBROUTINE CALCULATES THE INITIAL VELOCITY REQUIRED TO TRANSFER A POINT-MASS ALONG A CONIC TRAJECTORY

# FROM AN INITIAL POSITION TO A TERMINAL POSITION IN A PRESCRIBED TIME INTERVAL. THE RESULTING TRAJECTORY MAY BE

# A SECTION OF A CIRCLE, ELLIPSE, PARABOLA, OR HYPERBOLA WITH RESPECT TO THE EARTH OR THE MOON. THE USE OF THE

# SUBROUTINE CAN BE EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT INTRODUCING ANY

# CODING CHANGES, ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY. AN ITERATION TECHNIQUE IS

# UTILIZED IN THE COMPUTATION.

#

# THE RESTRICTIONS ARE -

# 1. RECTILINEAR TRAJECTORIES CANNOT BE COMPUTED.

# 2. AN ACCURACY DEGRADATION OCCURS AS THE COSINE OF THE TRUE ANOMALY DIFFERENCE APPROACHES +1.0.

# 3. THE ANGLE BETWEEN ANY POSITION VECTOR AND ITS VELOCITY VECTOR MUST BE GREATER THAN 1 DEGREE 47.5 MINUTES

# AND LESS THAN 178 DEGREES 12.5 MINUTES.

# 4. NEGATIVE TRANSFER TIME IS AMBIGUOUS AND WILL RESULT IN NO SOLUTION.

# 5. THE PARAMETERS IN THE PROBLEM MUST NOT EXCEED THEIR SCALING LIMITS SPECIFIED IN THE GSOP. IF THE

# LIMITS ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS.

#

# THE NUMBER OF ITERATIONS AND, THEREFORE, THE COMPUTATIONS SPEED IS DEPENDENT ON THE ACCURACY OF THE FIRST

# GUESS OF THE INDEPENDENT VARIABLE, COGA. THE AGC COMPUTATION TIME IS APPROXIMATE-

# LY .105 SECONDS FOR INITIALIZATION, .069 SECONDS FOR FINAL COMPUTATIONS, PLUS .205 SECONDS FOR EACH ITERATION.

#

# REFERENCES -

# R-479, MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP - SECTION 5.5, SGA MEMO 67-8,

# SGA MEMO 67-4.

#

# INPUT - ERASABLE INITIALIZATION REQUIRED

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# R1VEC * +29 FOR EARTH*DP INITIAL POSITION VECTOR IN METERS

# * +27 FOR MOON *

# R2VEC * +29 FOR EARTH*DP TARGET OR TERMINAL POSITION VECTOR IN METERS

# * +27 FOR MOON *

# TDESIRED* +28 *DP DESIRED TRANSFER TIME IN CENTISECONDS

# X1 (38D)* NONE *INDEX REGISTER SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON,

# * *RESPECTIVELY, IS THE CENTRAL BODY

# GEOMSGN * NONE *SP +.5 IF DESIRED TRANSFER ANGLE IS LESS THAN 180 DEGREES, -.5 IF GREATER THAN 180 DEG.

# GUESSW * NONE *AN INTERPRETER SWITCH TO BE SET IF NO GUESS OF COGA IS AVAILABLE, CLEAR IF A GUESS OF

## Page 1267

# * *COGA IS TO BE USED BY LAMBERT

# COGA * +5 *DP GUESS OF COTANGNT OF FLIGHT PATH ANGLE (MEASURED FROM VERTICAL). THIS WILL BE

# *IGNORED IF GUESSW IS SET.

# NORMSW * NONE *AN INTERPRETER SWITCH TO BE SET IF UN IS TO BE AN INPUT TO THE SUBROUTINE, CLEAR IF

# * *LAMBERT IS TO COMPUTE ITS OWN NORMAL (UN).

# UN * +1 *DP UNIT NORMAL TO THE DESIRED ORBIT PLANE IN THE DIRECTION OF THE RESULTING ANGULAR

# * *MOMENTUM VECTOR. THIS WILL BE IGNORED IF NORMSW IS CLEAR.

# VTARGTAG* NONE *A S.P. TAG TO BE SET TO ZERO IF LAMBERT IS TO COMPUTE THE VELOCITY AT R2VEC AS WELL AS

# * *AT R1VEC.

#

# SUBROUTINES CALLED -

# GEOM, GETX, DELTIME, ITERATOR, LAMENTER (PART OF NEWSTATE)

#

# CALLING SEQUENCE AND NORMAL EXIT MODES -

# L CALL MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY.

# L+1 LAMBERT RETURNS WITH PL AT 0 AND WITH VVEC IN MPAC IF VTARGTAG WAS NON-ZERO OR VTARGET

# IN MPAC IF VTARGTAG WAS ZERO

# L+2 BON CONTINUE IF SOLNSW CLEAR SINCE SOLUTION IS ACCEPTABLE

# L+3 SOLNSW

# L+4 LAMABORT

#

# IF A LAMBERT RESULT IS TO BE A FIRST GUESS FOR THE NEXT LAMBERT CALCULATION, COGA MUST BE PRESERVED AND

# GUESSW MUST BE CLEAR FOR EACH SUCCEEDING LAMBERT CALL.

#

# ABORT EXIT MODES -

# IF SOLNSW WAS SET UPON EXITING, EITHER LAMBERT WAS ASKED TO COMPUTE A TRANSFER TOO NEAR 0 OR 360 DEG, OR T

# WAS TOO SMALL TO PRODUCE A REALISTIC TRANSFER BETWEEN R1VEC AND R2VEC. IN EITHER CASE THE FIX MUST BE MADE

# ACCORDING TO THE NEEDS OF THE PARTICULAR USER. THE ABORT EXIT MODE MAY BE CODED AS ...

# LAMABORT DLOAD ABS A MEASURE OF PROXIMITY TO 0 OR

# 1-CSTH 360 DEGREES.

# DSU BMN

# ONEBIT

# CHANGER2 CHANGE R2VEC DIRECTION SLIGHTLY.

# DLOAD DAD

# TDESIRED

# SOMETIME

# STCALL TDESIRED INCREASE TDESIRED

# LAMBERT

#

# OUTPUT -

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

## Page 1268

# --------*--------------* -----------------------

# VVEC * +7 FOR EARTH *DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND REQUIRED TO SATISFY THE BOUNDARY VALUE

# * +5 FOR MOON *PROBLEM.

# VTARGET * +7 FOR EARTH *DP RESULTANT VELOCITY VECTOR AT R2VEC IN METERS/CENTISECOND.

# * +5 FOR MOON *

# SOLNSW * NONE *INTERPRETER SWITCH WHICH IS SET IF THE SUBROUTINE CANNOT SOLVE THE PROBLEM, CLEAR IF THE

# * *SOLUTION EXISTS.

#

# FOR OTHER OUTPUT WHICH MAY BE OF USE, SEE DEBRIS.

#

# DEBRIS -

# PARAMETERS WHICH MAY BE OF USE -

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# SNTH * +1 *DP SIN OF ANGLE BETWEEN R1VEC AND R2VEC

# CSTH * +1 *DP COSINE OF ANGLE

# 1-CSTH * +2 *DP 1-CSTH

# COGA * +5 *DP COTAN OF INITIAL REQUIRED FLIGHT PATH ANGLE MEASURED FROM VERTICAL

# P * +4 *DP RATIO OF SEMILATUS RECTUM TO INITIAL RADIUS

# R1A * +6 *DP RATIO OF INITIAL RADIUS TO SEMIMAJOR AXIS

# R1 (32D)* +29 FOR EARTH*DP INITIAL RADIUS IN METERS

# * +27 FOR MOON *

# UR1 * +1 *DP UNIT VECTOR OF R1VEC

# U2 * +1 *DP UNIT VECTOR OF R2VEC

#

# PARAMETERS OF NO USE

# DP PARAMETERS - EPSILONL, CSTH-RHO, TPREV, TERRLAMB, R2, RTNLAMB (SP), PLUS PUSHLIST REGISTER 0 THROUGH 41D

# ADDITIONAL INTERPRETIVE SWITCHES USED - INFINFLG, 360SW, SLOPESW, ORDERSW

## Page 1269

# PROGRAM DESCRIPTION - TIME-THETA SUBROUTINE DATE - 1 SEPTEMBER 1967

# MOD NO. - 0 LOG SECTION - CONIC SUBROUTINES

# MOD BY KRAUSE ASSEMBLY - COLOSSUS REVISION 88

#

# FUNCTIONAL DESCRIPTION -

# THIS SUBROUTINE, GIVEN AN INITIAL STATE VECTOR AND A DESIRED TRUE-ANOMALY-DIFFERENCE THROUGH WHICH THE

# STATE IS TO BE UPDATED ALONG A CONIC TRAJECTORY, CALCULATES THE CORRESPONDING TIME-OF-FLIGHT AND, IN ADDITION,

# PROVIDES THE OPTION OF COMPUTING THE NEW UPDATED STATE VECTOR. THE RESULTING TRAJECTORY MAY BE A SECTION OF A

# CIRCLE, ELLIPSE, PARABOLA, OR HYPERBOLA WITH RESPECT TO THE EARTH OR THE MOON. THE USE OF THE SUBROUTINE CAN BE

# EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT INTRODUCING ANY CODING CHANGES,

# ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY.

#

# THE RESTRICTIONS ARE -

# 1. THE ANGLE BETWEEN ANY POSITION VECTOR AND ITS VELOCITY VECTOR MUST BE GREATER THAN 1 DEGREE 47.5 MINUTES

# AND LESS THAN 178 DEGREES 12.5 MINUTES.

# 2. THE PARAMETERS IN THE PROBLEM MUST NOT EXCEED THEIR SCALING LIMITS SPECIFIED IN THE GSOP. IF THE LIMITS

# ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS.

#

# THE AGC COMPUTATION TIME IS APPROXIMATELY .292 SECONDS.

#

# REFERENCES -

# R-479, MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP-SECTION 5.5, SGA MEMO 67-8.

#

# INPUT - ERASABLE INITIALIZATION REQUIRED

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# RVEC * +29 FOR EARTH*DP INITIAL POSITION VECTOR IN METERS

# * +27 FOR MOON *

# VVEC * +7 FOR EARTH *DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND

# * +5 FOR MOON *

# SNTH * +1 *DP SINE OF TRUE-ANOMALY-DIFFERENCE THROUGH WHICH THE STATE IS TO BE UPDATED

# CSTH * +1 *DP COSINE OF THE ANGLE

# RVSW * NONE *AN INTERPRETIVE SWITCH TO BE SET IF ONLY TIME IS TO BE AN OUTPUT, CLEAR IF THE NEW STATE

# * *IS TO BE COMPUTED ALSO.

# X1 (38D)* NONE *INDEX REGISTER TO BE SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON,

# * *RESPECTIVELY, IS THE CENTRAL BODY.

#

# SUBROUTINES CALLED -

## Page 1270

# PARAM, GEOM, GETX, DELTIME, NEWSTATE

#

# CALLING SEQUENCE AND NORMAL EXIT MODES -

# IF ONLY TIME IS DESIRED AS OUTPUT -

# L SET CALL MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY.

# L+1 RVSW

# L+2 TIMETHET RETURN WITH PL AT 0 AND T IN MPAC

# L+3 ... CONTINUE

#

# IF THE UPDATE STATE VECTOR IS DESIRED AS WELL -

# L CLEAR CALL MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY.

# L+1 RVSW

# L+2 TIMETHET RETURNS WITH PL AT 6. THE INITIAL POSITION VECTOR IS IN 0D OF THE PUSHLIST AND

# THE INITIAL VELOCITY VECTOR IN MPAC.

# L+3 STOVL NEWVVEC

# L+4 STADR

# L+5 STORE NEWRVEC NEWVVEC AND NEWRVEC ARE SYMBOLIC REPRESENTATIONS OF THE USERS LOCATIONS.

# L+6 ... CONTINUE

#

# ABORT EXIT MODES -

# IF COGAFLAG AND/OR INFINFLG IS SET AT THE EXIT TO TIME-THETA, TIME-THETA WILL TRANSFER TO POODOO WITH

# AN ALARM CODE (ORIGINALLY 00607), AND NOT RETURN TO THE CALLING PROGRAM. (PCR 692 AND 721).

#

# OUTPUT -

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# T(30D) * +28 *DP TRANSFER TIME IN CENTISECONDS

# INFINFLG* NONE *AN INTERPRETIVE SWITCH WHICH IS SET IF THE TRANSFER ANGLE REQUIRES CLOSURE THROUGH

# * *INFINITY (NO SOLUTION), CLEAR IF A PHYSICAL SOLUTION IS POSSIBLE.

# COGAFLAG* NONE *AN INTERPRETIVE SWITCH WHICH IS SET IF RESTRICTION 1 HAS BEEN VIOLATED (NO SOLUTION),

# * *CLEAR IF NOT.

#

# IN ADDITION, IF RVSW IS CLEAR, THE FOLLOWING ARE OUTPUT -

# MPAC - * +7 FOR EARTH *DP TERMINAL VELOCITY VECTOR IN METERS/CENTISEC.

# MPAC +5* +5 FOR MOON *

# 0D - 5D * +29 FOR EARTH*DP TERMINAL POSITION VECTOR IN METERS (PL AT 6D)

# * +27 FOR MOON *

#

# FOR OTHER OUTPUT WHICH MAY BE OF USE, SEE DEBRIS.

## Page 1271

#

# DEBRIS -

# PARAMETERS WHICH MAY BE OF USE -

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# R1 (32D)* +29 FOR EARTH*DP MAGNITUDE OF INITIAL POSITION VECTOR, RVEC, IN METERS

# * +27 FOR MOON *

# R1A * +6 *DP RATIO OF R1 TO SEMIMAJOR AXIS (NEG. FOR HYPERBOLIC TRAJECTORIES)

# P * +4 *DP RATIO OF SEMILATUS RECTUM TO R1

# COGA * +5 *DP COTAN OF ANGLE BETWEEN RVEC AND VVEC

# UR1 * +1 *DP UNIT VECTOR OF RVEC

# U2 * +1 *DP UNIT VECTOR OF VVEC

# UN * +1 *DP UNIT VECTOR OF UR1*U2

#

# PARAMETERS OF NO USE -

# SP PARAMETERS - RTNTT, GEOMSGN, RTNPRM, MAGVEC2=R2 (DP), PLUS PUSHLIST LOCATIONS 0-11D, 14D-21D, 24D-39D, 41D

# ADDITIONAL INTERPRETIVE SWITCHES USED - NORMSW, 360SW

## Page 1272

# PROGRAM DESCRIPTION - TIME-RADIUS SUBROUTINE DATE - 11 OCTOBER 1967

# MOD NO. -1 LOG SECTION - CONIC SUBROUTINES

# MOD BY KRAUSE ASSEMBLY - COLOSSUS REVISION 88

#

# FUNCTIONAL DESCRIPTION -

# THIS SUBROUTINE, GIVEN AN INITIAL STATE VECTOR AND A DESIRED RADIUS TO WHICH THE

# STATE IS TO BE UPDATED ALONG A CONIC TRAJECTORY, CALCULATES THE CORRESPONDING TIME-OF-FLIGHT AND, IN ADDITION,

# PROVIDES THE OPTION OF COMPUTING THE NEW UPDATED STATE VECTOR. THE RESULTING TRAJECTORY MAY BE A SECTION OF A

# CIRCLE, ELLIPSE, PARABOLA, OR HYPERBOLA WITH RESPECT TO THE EARTH OR THE MOON. THE USE OF THE SUBROUTINE CAN BE

# EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT INTRODUCING ANY CODING CHANGES,

# ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY.

#

# IF THE DESIRED RADIUS IS BEYOND THE RADIUS OF APOCENTER OF THE CONIC OR BELOW THE RADIUS OF PERICENTER,

# APSESW WILL BE SET AND THE SUBROUTINE WILL RETURN THE APOCENTER OR PERICENTER SOLUTION, RESPECTIVELY.

#

# THE RESTRICTIONS ARE -

# 1. THE ANGLE BETWEEN ANY POSITION VECTOR AND ITS VELOCITY VECTOR MUST BE GREATER THAN 1 DEGREE 47.5 MINUTES

# AND LESS THAN 178 DEGREES 12.5 MINUTES.

# 2. THE PARAMETERS IN THE PROBLEM MUST NOT EXCEED THEIR SCALING LIMITS SPECIFIED IN THE GSOP. IF THE LIMITS

# ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS.

# 3. AN ACCURACY DEGRADATION OCCURS AS THE SENSITIVITIES OF TIME AND UPDATED STATE VECTOR TO CHANGES IN

# RDESIRED INCREASE. THIS WILL OCCUR NEAR EITHER APSIS OF THE CONIC AND WHEN THE CONIC IS NEARLY CIRCULAR. IN

# PARTICULAR, IF THE CONIC IS AN EXACT CIRCLE, THE PROBLEM IS UNDEFINED AND THE SUBROUTINE WILL ABORT.

#

# THE AGC COMPUTATION TIME IS APPROXIMATELY .363 SECONDS

#

# REFERENCES -

# R-479, MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP-SECTION 5.5, SGA MEMO 67-8.

#

# INPUT - ERASABLE INITIALIZATION REQUIRED

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# RVEC * +29 FOR EARTH*DP INITIAL POSITION VECTOR IN METERS

# * +27 FOR MOON *

# VVEC * +7 FOR EARTH *DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND

# * +5 FOR MOON *

# RDESIRED* +29 FOR EARTH*DP TERMINAL RADIAL DISTANCE ON CONIC TRAJECTORY FOR WHICH TRANSFER TIME IS TO BE

# * +27 FOR MOON *COMPUTED.

# SGNRDOT * NONE *SP TAG SET TO +.5 OR -.5 ACCORDING TO WHETHER THE RADIAL VELOCITY AT RDESIRED IS TO BE

# * *POSITIVE OR NEGATIVE, RESPECTIVELY. THIS TAG REDUCES THE DOUBLE-VALUED PROBLEM TO A

## Page 1273

# * *SINGLE-VALUED PROBLEM.

# X1 (38D)* NONE *INDEX REGISTER TO BE SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON,

# * *RESPECTIVELY, IS THE CENTRAL BODY.

# RVSW * NONE *AN INTERPRETIVE SWITCH TO BE SET IF ONLY TIME IS TO BE AN OUTPUT, CLEAR IF THE NEW STATE

# * *IS TO BE COMPUTED ALSO.

#

# SUBROUTINES CALLED -

# PARAM, GEOM, GETX, DELTIME, NEWSTATE

#

# CALLING SEQUENCE AND NORMAL EXIT MODES -

# IF ONLY TIME IS DESIRED AS OUTPUT -

# L SET CALL MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY.

# L+1 RVSW

# L+2 TIMERAD RETURN WITH PL AT 0 AND T IN MPAC

# L+3 ... CONTINUE

#

# IF THE UPDATE STATE VECTOR IS DESIRED AS WELL -

# L CLEAR CALL MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY.

# L+1 RVSW

# L+2 TIMERAD RETURNS WITH PL AT 6. THE INITIAL POSITION VECTOR IS IN 0D OF THE PUSHLIST AND

# THE INITIAL VELOCITY VECTOR IN MPAC.

# L+3 STOVL NEWVVEC

# L+4 STADR

# L+5 STORE NEWRVEC NEWVVEC AND NEWRVEC ARE SYMBOLIC REPRESENTATIONS OF THE USERS LOCATIONS.

# L+6 ... CONTINUE

#

# ABORT EXIT MODES -

# IF SOLNSW AND/OR COGAFLAG AND/OR INFINFLG IS SET AT THE EXIT TO TIME-RADIUS, TIME-RADIUS WILL TRANSFER

# TO POODOO WITH AN ALARM CODE (ORIGINALLY 00607), AND NOT RETURN TO THE CALLING PROGRAM. (PCR 692 & 721)

#

# OUTPUT -

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# T (30D) * +28 *DP TRANSFER TIME IN CENTISECONDS

# INFINFLG* NONE *AN INTERPRETIVE SWITCH WHICH IS SET IF RDESIRED AND SGNRDOT REQUIRE CLOSURE THROUGH

# * *INFINITY (NO SOLUTION), CLEAR IF A PHYSICAL SOLUTION IS POSSIBLE.

# COGAFLAG* NONE *AN INTERPRETIVE SWITCH WHICH IS SET IF RESTRICTION 1 HAS BEEN VIOLATED (NO SOLUTION),

# * *CLEAR IF NOT.

# APSESW * NONE *AN INTERPRETIVE SWITCH WHICH IS SET IF RDESIRED WAS GREATER THAN RADIUS OF APOCENTER OR

## Page 1274

# * *LESS THAN RADIUS OF PERICENTER. THE APOCENTER OR PERICENTER SOLUTION, RESPECTIVELY,

# * *WILL THEN BE RETURNED. THE SWITCH IS CLEAR IF RDESIRED WAS BETWEEN PERICENTER AND

# * *APOCENTER.

# SOLNSW * NONE *AN INTERPRETIVE SWITCH WHICH IS SET IF THE CONIC IS SO CLOSE TO A CIRCLE THAT THE TERMIN

# *POINT IS AMBIGUOUS, VIOLATING RESTRICTION 3. IF ECCENTRICITY IS GREATER THAN 2-TO-THE-

# *MINUS-18, THE SWITCH IS CLEAR.

#

# IN ADDITION, IF RVSW IS CLEAR, THE FOLLOWING ARE OUTPUT -

# MPAC - * +7 FOR EARTH *DP TERMINAL VELOCITY VECTOR IN METERS/CENTISEC.

# MPAC +5* +5 FOR MOON *

# 0D - 5D * +29 FOR EARTH*DP TERMINAL POSITION VECTOR IN METERS (PL AT 6D)

# * +27 FOR MOON *

#

# FOR OTHER OUTPUT WHICH MAY BE OF USE, SEE DEBRIS.

#

# DEBRIS -

# PARAMETERS WHICH MAY BE OF USE -

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# R1 (32D)* +29 FOR EARTH*DP MAGNITUDE OF INITIAL POSITION VECTOR, RVEC, IN METERS

# * +27 FOR MOON *

# R1A * +6 *DP RATIO OF R1 TO SEMIMAJOR AXIS (NEG. FOR HYPERBOLIC TRAJECTORIES)

# P * +4 *DP RATIO OF SEMILATUS RECTUM TO R1

# COGA * +5 *DP COTAN OF ANGLE BETWEEN RVEC AND VVEC

# UR1 * +1 *DP UNIT VECTOR OF RVEC

# U2 * +1 *DP UNIT VECTOR OF VVEC

# UN * +1 *DP UNIT VECTOR OF UR1*U2

# CSTH * +1 *DP COSINE OF TRUE ANOMALY DIFFERENCE BETWEEN RVEC AND RDESIRED.

# SNTH * +1 *DP SINE OF TRUE ANOMALY DIFFERENCE.

#

# PARAMETERS OF NO USE -

# SP PARAMETERS - RTNTT, GEOMSGN, RTNPRM, MAGVEC2=R2 (DP), PLUS PUSHLIST LOCATIONS 0-11D, 14D-21D, 24D-39D, 41D

# ADDITIONAL INTERPRETIVE SWITCHES USED - NORMSW, 360SW

#

## Page 1275

# PROGRAM DESCRIPTION - APSIDES SUBROUTINE DATE - 1 SEPTEMBER 1967

# MOD NO. - 0 LOG SECTION - CONIC SUBROUTINES

# MOD BY KRAUSE ASSEMBLY - COLOSSUS REVISION 88

#

# FUNCTIONAL DESCRIPTION -

# THIS SUBROUTINE, GIVEN AN INITIAL STATE VECTOR CALCULATES THE RADIUS OF PERICENTER AND OF APOCENTER AND THE

# ECCENTRICITY OF THE RESULTING CONIC TRAJECTORY, WHICH MAY BE A STRAIGHT LINE,

# CIRCLE, ELLIPSE, PARABOLA, OR HYPERBOLA WITH RESPECT TO THE EARTH OR THE MOON. THE USE OF THE SUBROUTINE CAN BE

# EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT INTRODUCING ANY CODING CHANGES,

# ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY.

#

# THE RESTRICTIONS ARE -

# 1. IF APOCENTER IS BEYOND THE SCALING OF POSITION, THE SCALE FACTOR LIMIT (536,870,910 METERS WITH RESPECT

# TO THE EARTH OR 134,217,727.5 METERS WITH RESPECT TO THE MOON) WILL BE RETURNED.

# 2. THE PARAMETERS IN THE PROBLEM MUST NOT EXCEED THEIR SCALING LIMITS SPECIFIED IN THE GSOP. IF THE LIMITS

# ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS.

#

# THE AGC COMPUTATION TIME IS APPROXIMATELY .103 SECONDS.

#

# REFERENCES -

# MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP-SECTION 5.5

#

# INPUT - ERASABLE INITIALIZATION REQUIRED

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# RVEC * +29 FOR EARTH*DP INITIAL POSITION VECTOR IN METERS

# * +27 FOR MOON *

# VVEC * +7 FOR EARTH *DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND

# * +5 FOR MOON *

# X1 (38D)* NONE *INDEX REGISTER TO BE SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON,

# * *RESPECTIVELY, IS THE CENTRAL BODY.

#

# SUBROUTINES CALLED -

# PARAM, GEOM

#

# CALLING SEQUENCE AND NORMAL EXIT MODES -

## Page 1276

# IF ONLY TIME IS DESIRED AS OUTPUT -

# L CALL MUST BE IN INTERPRETIVE MODE BUT OVFIND ARBITRARY.

# L+1 APSIDES RETURNS WITH PL AT 0, RADIUS OF APOCENTER IN MPAC AND RADIUS OF PERICENTER IN 0D

# L+2 STODL APOAPSE

# L+3 0D

# L+4 STORE PERIAPSE APOAPSE AND PERIAPSE ARE SYMBOLIC REPRESENTATIONS OF THE USERS LOCATIONS

# L+5 ... CONTINUE

#

# OUTPUT -

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# MPAC * +29 FOR EARTH*DP RADIUS OF APOCENTER IN METERS

# * +27 FOR MOON *

# 0D-1D * +29 FOR EARTH*DP RADIUS OF PERICENTER IN METERS

# * +27 FOR MOON *

# ECC * +3 *DP ECCENTRICITY OF CONIC TRAJECTORY.

#

# FOR OTHER OUTPUT WHICH MAY BE OF USE, SEE DEBRIS.

#

# DEBRIS -

# PARAMETERS WHICH MAY BE OF USE -

# * SCALE FACTOR *

# VARIABLE*IN POWERS OF 2* DESCRIPTION AND REMARKS

# --------*--------------* -----------------------

# R1 (32D)* +29 FOR EARTH*DP MAGNITUDE OF INITIAL POSITION VECTOR, RVEC, IN METERS

# * +27 FOR MOON *

# R1A * +6 *DP RATIO OF R1 TO SEMIMAJOR AXIS (NEG. FOR HYPERBOLIC TRAJECTORIES)

# P * +4 *DP RATIO OF SEMILATUS RECTUM TO R1

# COGA * +5 *DP COTAN OF ANGLE BETWEEN RVEC AND VVEC

# UR1 * +1 *DP UNIT VECTOR OF RVEC

# U2 * +1 *DP UNIT VECTOR OF VVEC

# UN * +1 *DP UNIT VECTOR OF UR1*U2

# MAGVEC2 * +7 FOR EARTH *DP MAGNITUDE OF VVEC

# * +5 FOR MOON *

#

# PARAMETERS OF NO USE -

# SP PARAMETERS - RTNAPSE, GEOMSGN, RTNPRM, PLUS PUSHLIST LOCATIONS 0-5, 10D-11D, 14D-21D, 31D-38D.

# ADDITIONAL INTERPRETIVE SWITCHES USED - NORMSW

SETLOC CONICS

## Page 1277

BANK

COUNT 12/CONIC

EBANK= UR1

KEPLERN SETPD BOV

0

+1

VLOAD*

MUTABLE,1

STOVL 14D

RRECT

UNIT SSP

ITERCTR

20D

STODL URRECT

36D

STOVL R1

RRECT

DOT SL1R

VRECT

DMP SL1R

1/ROOTMU # 1/ROOTMU (-17 OR -14)

STOVL KEPC1 # C1=R.V/ROOTMU (+17 OR +16)

VRECT

VSQ DMPR

1/MU # 1/MU (-34 OR -28)

DMP SL3

R1

DSU ROUND

D1/64

STORE KEPC2 # C2=RV.V/MU -1 (+6)

BDSU SR1R

D1/64

DDV

R1

STORE ALPHA # ALPHA=(1-C2)/R1 (-22 OR -20)

BPL DLOAD # MAXIMUM X DEPENDS ON TYPE OF CONIC

1REV

-50SC # -50SC (+12)

DDV BOV

ALPHA

STOREMAX

SQRT GOTO

STOREMAX

## Page 1278

1REV SQRT BDDV

2PISC # 2PISC (+6)

BOV

STOREMAX

STOREMAX STORE XMAX

DMP PDDL

1/ROOTMU

ALPHA

NORM PDDL

X1

SL* DDV

0 -6,1

BOV BMN

MODDONE

MODDONE # MPAC=PERIOD

PERIODCH PDDL ABS # 0D=PERIOD

TAU.

DSU BMN

0D

MODDONE

SIGN

TAU.

STODL TAU.

GOTO

PERIODCH

MODDONE SETPD DLOAD

0

XKEPNEW

STORE X

SIGN BZE

TAU.

BADX

BMN ABS

BADX

DSU BPL

XMAX

BADX

STORBNDS DLOAD BPL

TAU.

STOREMIN

DLOAD DCOMP

XMAX

STODL XMIN

KEPZERO

STCALL XMAX

DXCOMP

STOREMIN DLOAD

KEPZERO

STORE XMIN

DXCOMP DLOAD DMPR

## Page 1279

TAU.

BEE22

ABS

STODL EPSILONT

XPREV

XDIFF BDSU

X

STORE DELX

KEPLOOP DLOAD DSQ

X # X=XKEP

NORM PUSH # 0D=XSQ (+34 OR +32 -N1) PL AT 2

X1

DMP SRR*

ALPHA

0 -6,1

STCALL XI # XI=ALPHA XSQ (+6)

DELTIME

BOV BDSU

TIMEOVFL # UNLIKELY

TAU.

STORE DELT # DELT=DELINDEP

ABS BDSU

EPSILONT

BPL DLOAD

KEPCONVG

T

DSU NORM

TC

X1

PDDL NORM

DELX

X2

XSU,1 DMP

X2

DELT

SLR* DDV

1,1

SR1 PUSH # 0D=TRIAL DELX PL AT 2

BPL DLOAD

POSDELX

X

STORE XMAX # MOVE MAX BOUND IN

BDSU DSU # PL AT 0

XMIN

BOV BPL

NDXCHNGE

NDXCHNGE

DLOAD GOTO

## Page 1280

0D

NEWDELX

NDXCHNGE DLOAD DSU

XMIN

X

DMPR GOTO # TO FORCE MPAC +2 TO ZERO

DP9/10

NEWDELX

POSDELX DLOAD

X

STORE XMIN # MOVE MIN BOUND IN

BDSU DSU # PL AT 0

XMAX

BOV BMN

PDXCHNGE

PDXCHNGE

DLOAD

0D

NEWDELX STORE DELX

BZE DAD

KEPCONVG

X

STODL X

T

STORE TC

BRNCHCTR RTB BHIZ

CHECKCTR

KEPCONVG

GOTO

KEPLOOP # ITERATE

PDXCHNGE DLOAD DSU

XMAX

X

DMPR GOTO # TO FORCE MPAC +2 TO ZERO

DP9/10

NEWDELX

BADX DLOAD SR1

XMAX

SIGN

TAU.

STCALL X

STORBNDS

## Page 1281

TIMEOVFL DLOAD BMN # X WAS TOO BIG

X

NEGTOVFL

STORE XMAX

CMNTOVFL DLOAD SR1

DELX

STORE DELX

BZE BDSU

KEPRTN

X

STODL X

TC

STCALL T

BRNCHCTR

NEGTOVFL STCALL XMIN

CMNTOVFL

KEPCONVG DLOAD SR4R

R1

DSU VXSC

XSQC(XI)

URRECT

VSL1 PDDL # 0D=(R1-XSQC(XI))URRECT (+33 OR +31)

X

DSQ NORM

X1

DMPR DMPR

1/ROOTMU

X

DMP SRR*

S(XI)

0 -7,1

BDSU

T

SL1 VXSC

VRECT

VSL1 VAD # PL AT 0

VSL4

STORE RCV # RCV (+29 OR +27)

ABVAL NORM

X2

STODL RCNORM

XI

DMPR DSU

S(XI)

D1/128

DMP SL1R

ROOTMU

DMP SLR*

## Page 1282

X

0 -3,2

DDV VXSC

RCNORM

URRECT

VSL1 PDDL # 0D=URRECT(XI S(XI)-1)X ROOTMU/RCV (+15

XSQC(XI) # OR +13) PL AT 6

SLR* DDV

0 -4,2

RCNORM

BDSU VXSC

D1/256

VRECT

VAD VSL8

STADR # PL AT 0

STODL VCV # VCV (+7 OR +5)

T

STODL TC

X

STCALL XPREV

KEPRTN

## Page 1283

DELTIME EXIT # MPAC=XI (+6), 0D=XSQ (+34 OR +32 -N1)

TC POLY

DEC 8

2DEC .083333334

2DEC -.266666684

2DEC .406349155

2DEC -.361198675

2DEC .210153242

2DEC -.086221951

2DEC .026268812

2DEC -.006163316

2DEC .001177342

2DEC -.000199055

TC INTPRET

STODL S(XI)

XI

EXIT

TC POLY

DEC 8

2DEC .031250001

2DEC -.166666719

2DEC .355555413

2DEC -.406347410

2DEC .288962094

2DEC -.140117894

2DEC .049247387

2DEC -.013081923

2DEC .002806389

2DEC -.000529414

TC INTPRET

## Page 1284

DMP SRR* # PL AT 0

0D

0 -5,1

STORE XSQC(XI) # XSQC(XI) (+33 OR +31)

DMP SL1

KEPC1

RTB PDDL # XCH WITH PL. 0D=C1 XSQ C(XI) (+49 OR +46

TPMODE # PL AT 0,3

DMP SRR*

S(XI)

0 -5,1

DMP SL1

KEPC2

RTB PDDL # 3D=C2 XSQ S(XI) (+35 OR +33) PL AT 6

TPMODE

R1

SR TAD # PL AT 3

6

NORM DMP # TO PRESERVE SIGNIF.

X1

X

SR* TAD # X(C2 XSQ S(XI) +R1) (+49 OR +46) PL AT 0

0 -3,1

SL4R DMPR

1/ROOTMU

STORE T

RVQ

## Page 1285

ITERATOR BONCLR DLOAD

SLOPESW

FIRSTIME

DEP

DSU NORM

DEPREV

X1

PDDL NORM

DELINDEP

X2

XSU,1 DMP

X2

DELDEP

SLR* DDV # PL UP 2

1,1

SR1 BOFF

ORDERSW

SGNCHECK

ABS SIGN # IN CASE 2ND DERIV. CHANGED SIGN, MUST

DELDEP # DISREGARD IT TO FIND MIN.

SGNCHECK PUSH BPL # TRIAL DELINDEP PL DOWN 2

POSDEL

DLOAD BON

INDEP

ORDERSW

MINCHECK

STORE MAX # IF NOT 2ND ORDER, CAN MOVE MAX BOUND IN.

MINCHECK BDSU DSU

MIN

BOV BPL

MODNGDEL

MODNGDEL

GOTO

DELOK

MODNGDEL DLOAD DSU # TRIAL DELINDEP WOULD EXCEED MIN BOUND

MIN

INDEP

DMP GOTO

DP9/10

NEWDEL

FIRSTIME DLOAD DMP

MIN

TWEEKIT # DLOAD TWEEKIT(40D) SENSITIVE TO CHANGE.

PDDL DMP # S2(41D) SHOULDNT CONTAIN HI ORDER ONES

## Page 1286

MAX

TWEEKIT

DSU

SIGN GOTO

DELDEP

SGNCHECK

POSDEL DLOAD BON

INDEP

ORDERSW

MAXCHECK

STORE MIN # IF NOT 2ND ORDER, CAN MOVE MIN BOUND IN.

MAXCHECK BDSU DSU

MAX

BOV BMN

MODPSDEL

MODPSDEL

DELOK DLOAD

0D

NEWDEL STORE DELINDEP

RVQ

MODPSDEL DLOAD DSU

MAX

INDEP

DMP GOTO

DP9/10

NEWDEL

CHECKCTR CS ONE

INDEX FIXLOC

AD ITERCTR

INDEX FIXLOC

TS ITERCTR