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7segsprint.f
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C Seven segment model as used previously to examine the interplay between
C swing leg motion, touchdown conditions and maximum sprinting speed.
C
C Differences from preivous model:
C - Simulated for entire stride
C - Force applied to CoM during virtual second stance
C
C Tom Rottier 2020
C***********************************************************************
PROGRAM MAIN
IMPLICIT DOUBLE PRECISION (A - Z)
INTEGER ILOOP, IPRINT, PRINTINT
INTEGER I,J,NACTP,NROW,FORCE_IDX
LOGICAL STEP1,STEP2,STEP
PARAMETER (NACTP=10)
CHARACTER MESSAGE(99)
EXTERNAL EQNS1
DIMENSION VAR(14)
DIMENSION TT(500),CCHIP(6,500),CCKNEE(6,500),CCHAT(6,500)
DIMENSION HETQP(10),HFTQP(10),KETQP(10),KFTQP(10),AETQP(10)
&,AFTQP(10),HEACTP(NACTP),HFACTP(NACTP),KEACTP(NACTP),KFACTP(NACTP)
&,AEACTP(NACTP),AFACTP(NACTP),METQP(10),MFTQP(10)
DIMENSION FORCE(1000,2)
COMMON/CONSTNTS/ FOOTANG,G,IA,IB,IC,ID,IE,IF,IG,K1,K2,K3,K4,K5,K6,
&K7,K8,L1,L10,L11,L12,L2,L3,L4,L5,L6,L7,L8,L9,MA,MB,MC,MD,ME,MF,MG,
&MTPB,MTPK,POP1XI,POP2XI
COMMON/VARIBLES/ Q1,Q2,Q3,Q4,Q5,Q6,Q7,U1,U2,U3,U4,U5,U6,U7
COMMON/ALGBRAIC/ AANG,AANGVEL,AETOR,AFTOR,ATOR,COP,GRF,HANG,HANGVE
&L,HETOR,HFTOR,HTOR,HZ,KANG,KANGVEL,KECM,KETOR,KFTOR,KTOR,MANG,MANG
&VEL,METOR,MFTOR,MTOR,PECM,PX,PY,RX,RX1,RX2,RY,RY1,RY2,SHANG,SHANGV
&EL,SHTOR,SKANG,SKANGVEL,SKTOR,TE,U8,U9,VRX,VRY,Q1p,Q2p,Q3p,Q4p,Q5p
&,Q6p,Q7p,U1p,U2p,U3p,U4p,U5p,U6p,U7p,AEACT,AECCANG,AECCANGVEL,AESE
&CANG,AESECANGVEL,AFACT,AFCCANG,AFCCANGVEL,AFSECANG,AFSECANGVEL,EA,
&FA,GS,HEACT,HECCANG,HECCANGVEL,HESECANG,HESECANGVEL,HFACT,HFCCANG,
&HFCCANGVEL,HFSECANG,HFSECANGVEL,KEACT,KECCANG,KECCANGVEL,KESECANG,
&KESECANGVEL,KFACT,KFCCANG,KFCCANGVEL,KFSECANG,KFSECANGVEL,MEACT,ME
&CCANG,MECCANGVEL,MESECANG,MESECANGVEL,MFACT,MFCCANG,MFCCANGVEL,MFS
&ECANG,MFSECANGVEL,EAp,FAp,GSp,EApp,FApp,GSpp,DP1X,DP2X,MT,POCMSTAN
&CEX,POCMSTANCEY,POCMSWINGX,POCMSWINGY,POCMX,POCMY,POGOX,POGOY,POP1
&X,POP1Y,POP2X,POP2Y,POP3X,POP3Y,POP4X,POP4Y,POP5X,POP5Y,POP6X,POP6
&Y,POP7X,POP7Y,POP8X,POP8Y,POP9X,POP9Y,PSTANCEX,PSTANCEY,PSWINGX,PS
&WINGY,VOCMSTANCEX,VOCMSTANCEY,VOCMSWINGX,VOCMSWINGY,VOCMX,VOCMY,VO
&P2X,VOP2Y
COMMON/MISCLLNS/ PI,DEGtoRAD,RADtoDEG,Z(435),COEF(7,7),RHS(7)
COMMON/INTEG / TINITIAL,TFINAL,INTEGSTP,ABSERR,RELERR,PRINTINT
COMMON/TQPARAMS/ HETQP,HFTQP,KETQP,KFTQP,AETQP,AFTQP,METQP,MFTQP
COMMON/ACTPARAM/ HEACTP,HFACTP,KEACTP,KFACTP,AEACTP,AFACTP
COMMON/SPLNCOEF/ TT,CCHIP,CCKNEE,CCHAT,NROW
COMMON/OTHER / CMYTD
C** Open input and output files
OPEN(UNIT=20, FILE='7segsprint.in', STATUS='OLD')
OPEN(UNIT=21, FILE='7segsprint.1', STATUS='UNKNOWN')
OPEN(UNIT=22, FILE='7segsprint.2', STATUS='UNKNOWN')
OPEN(UNIT=23, FILE='7segsprint.3', STATUS='UNKNOWN')
OPEN(UNIT=24, FILE='7segsprint.4', STATUS='UNKNOWN')
OPEN(UNIT=25, FILE='7segsprint.5', STATUS='UNKNOWN')
OPEN(UNIT=26, FILE='7segsprint.6', STATUS='UNKNOWN')
OPEN(UNIT=27, FILE='7segsprint.7', STATUS='UNKNOWN')
OPEN(UNIT=28, FILE='7segsprint.8', STATUS='UNKNOWN')
OPEN(UNIT=29, FILE='7segsprint.9', STATUS='UNKNOWN')
OPEN(UNIT=30, FILE='7segsprint.10', STATUS='UNKNOWN')
OPEN(UNIT=31, FILE='7segsprint.11', STATUS='UNKNOWN')
C** Read message from input file
READ(20,7000,END=7100,ERR=7101) (MESSAGE(ILOOP),ILOOP = 1,99)
C** Read values of constants from input file
READ(20,7010,END=7100,ERR=7101) FOOTANG,G,IA,IB,IC,ID,IE,IF,IG,K1,
&K2,K3,K4,K5,K6,K7,K8,L1,L10,L11,L12,L2,L3,L4,L5,L6,L7,L8,L9,MA,MB,
&MC,MD,ME,MF,MG,MTPB,MTPK,POP1XI,POP2XI
C** Read the initial value of each variable from input file
READ(20,7010,END=7100,ERR=7101) Q1,Q2,Q3,Q4,Q5,Q6,Q7,U1,U2,U3,U4,U
&5,U6,U7
C** Read integration parameters from input file
READ(20,7011,END=7100,ERR=7101) TINITIAL,TFINAL,INTEGSTP,PRINTINT,
&ABSERR,RELERR
C** Write heading(s) to output file(s)
! WRITE(*, 6021) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(21,6021) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(22,6022) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(23,6023) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(24,6024) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(25,6025) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(26,6026) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(27,6027) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(28,6028) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(29,6029) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(30,6030) (MESSAGE(ILOOP), ILOOP = 1,99)
WRITE(31,6031) (MESSAGE(ILOOP), ILOOP = 1,99)
C** Read torque parameters
OPEN(UNIT=40, FILE='torque.in', STATUS='OLD')
READ(40, 7200, ERR=7210) HETQP,KETQP,AETQP,HFTQP,KFTQP,AFTQP,METQP
&,MFTQP
CLOSE(UNIT=40)
C** Read activation parameters
OPEN(UNIT=41, FILE='activation.in', STATUS='OLD')
READ(41, 7300, ERR=7310) HEACTP,KEACTP,AEACTP,HFACTP,KFACTP,AFACTP
CLOSE(UNIT=41)
C** Read spline coefficients for angles and HAT CoM location
OPEN(UNIT=42, FILE='angles_coef.csv', STATUS='OLD')
READ(42,*) NROW
READ(42,*) (TT(I), I=1, NROW)
READ(42,*) ((CCHIP(J,I), J=1, 6), I=1, NROW)
READ(42,*) ((CCKNEE(J,I), J=1, 6), I=1, NROW)
CLOSE(UNIT=42)
OPEN(UNIT=43, FILE='HAT_coef.csv', STATUS='OLD')
READ(43,*)
READ(43,*)
READ(43,*) ((CCHAT(J,I), J=1, 6), I=1, NROW)
CLOSE(UNIT=43)
C** Convert to generalised coordinates
CALL INITCOND()
C** Initialize time, print counter, variables array for integrator
T = TINITIAL
IPRINT = 0
VAR(1) = Q1
VAR(2) = Q2
VAR(3) = Q3
VAR(4) = Q4
VAR(5) = Q5
VAR(6) = Q6
VAR(7) = Q7
VAR(8) = U1
VAR(9) = U2
VAR(10) = U3
VAR(11) = U4
VAR(12) = U5
VAR(13) = U6
VAR(14) = U7
C Virtual forces
FORCE_IDX = 1
STEP1 = .TRUE.
STEP2 = .FALSE.
STEP = .TRUE.
VRX = 0.0D0
VRY = 0.0D0
C** Initialise torques for integration
CALL UPDATE(T)
C** Initalize numerical integrator with call to EQNS1 at T=TINITIAL
CALL KUTTA(EQNS1, 14, VAR, T, INTEGSTP, ABSERR, RELERR, 0, *5920)
C** Check exit conditions
5900 IF( TFINAL.GE.TINITIAL .AND. T+.01D0*INTEGSTP.GE.TFINAL) IPRINT=-7
IF( TFINAL.LE.TINITIAL .AND. T+.01D0*INTEGSTP.LE.TFINAL) IPRINT=-7
IF (STEP2 .AND. (Q2 .LE. 0.0D0 .OR. POP2Y .LE. 0.0D0)) IPRINT = -7
C** Print
IF( IPRINT .LE. 0 ) THEN
CALL IO(T)
IF( IPRINT .EQ. -7 ) GOTO 5930
IPRINT = PRINTINT
ENDIF
C Check when second contact occuring
IF ( .NOT. STEP1 .AND. POCMY .LE. CMYTD .AND. .NOT. STEP2) THEN
STEP2 = .TRUE.
FORCE_IDX = 1
ENDIF
C Apply force if second stance phase
IF ( STEP2 .AND. STEP ) THEN
VRX = FORCE(FORCE_IDX,1)
VRY = FORCE(FORCE_IDX,2)
ENDIF
C** Integrate
CALL KUTTA(EQNS1, 14, VAR, T, INTEGSTP, ABSERR, RELERR, 1, *5920)
C Save force if first stance phase
IF ( STEP1 ) THEN
FORCE(FORCE_IDX,1) = RX
FORCE(FORCE_IDX,2) = RY
ENDIF
C** Update torques and forces after integration
CALL UPDATE(T)
C Check if first contact over
IF ( STEP1 .AND. RY .LT. 1.0D-8) STEP1 = .FALSE.
C Check if second contact over
IF ( STEP2 .AND. VRY .LT. 1.0D-8) THEN
STEP2 = .FALSE.
STEP = .FALSE.
ENDIF
IPRINT = IPRINT - 1
FORCE_IDX = FORCE_IDX + 1
GOTO 5900
C** Print message if numerical integration fails to converge
5920 CALL IO(T)
WRITE(*, 6997)
WRITE(21,6997)
WRITE(22,6997)
WRITE(23,6997)
WRITE(24,6997)
WRITE(25,6997)
WRITE(26,6997)
WRITE(27,6997)
WRITE(28,6997)
WRITE(29,6997)
WRITE(30,6997)
WRITE(31,6997)
C** Inform user of input and output filename(s)
5930 WRITE(*,6999)
6021 FORMAT(1X,'FILE: 7segsprint.1 ',//1X,'*** ',99A1,///,8X,'T',12X,'P
&OP1X',10X,'POP1Y',10X,'POP2X',10X,'POP2Y',10X,'POP3X',10X,'POP3Y',
&10X,'POP4X',10X,'POP4Y',10X,'POP5X',10X,'POP5Y',10X,'POP6X',10X,'P
&OP6Y',10X,'POP7X',10X,'POP7Y',10X,'POP8X',10X,'POP8Y',10X,'POP9X',
&10X,'POP9Y',10X,'POGOX',10X,'POGOY',7X,'POCMSTANCEX',4X,'POCMSTANC
&EY',4X,'POCMSWINGX',5X,'POCMSWINGY',8X,'POCMX',10X,'POCMY',10X,'VO
&CMX',10X,'VOCMY',8X,'PSTANCEX',7X,'PSTANCEY',8X,'PSWINGX',8X,'PSWI
&NGY',6X,'VOCMSTANCEX',4X,'VOCMSTANCEY',4X,'VOCMSWINGX',5X,'VOCMSWI
&NGY',/,7X,'(S)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',
&12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(
&M)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',12
&X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)',12X,'(M)
&',12X,'(M)',11X,'(M/S)',10X,'(M/S)',9X,'(UNITS)',8X,'(UNITS)',8X,'
&(UNITS)',8X,'(UNITS)',9X,'(M/S)',10X,'(M/S)',10X,'(M/S)',10X,'(M/S
&)',/)
6022 FORMAT(1X,'FILE: 7segsprint.2 ',//1X,'*** ',99A1,///,8X,'T',13X,'Q
&1',13X,'Q2',13X,'Q3',13X,'Q4',13X,'Q5',13X,'Q6',13X,'Q7',13X,'U1',
&13X,'U2',13X,'U3',13X,'U4',13X,'U5',13X,'U6',13X,'U7',/,7X,'(S)',1
&2X,'(M)',12X,'(M)',11X,'(DEG)',10X,'(DEG)',10X,'(DEG)',10X,'(DEG)'
&,10X,'(DEG)',10X,'(M/S)',10X,'(M/S)',9X,'(DEG/S)',8X,'(DEG/S)',8X,
&'(DEG/S)',8X,'(DEG/S)',8X,'(DEG/S)',/)
6023 FORMAT(1X,'FILE: 7segsprint.3 ',//1X,'*** ',99A1,///,8X,'T',13X,'R
&X',13X,'RY',13X,'VRX',12X,'VRY',11X,'HTOR',11X,'KTOR',11X,'ATOR',1
&1X,'MTOR',11X,'SHTOR',10X,'SKTOR',/,7X,'(S)',12X,'(N)',12X,'(N)',1
&0X,'(UNITS)',8X,'(UNITS)',9X,'(N/M)',10X,'(N/M)',10X,'(N/M)',10X,'
&(N/M)',10X,'(N/M)',10X,'(N/M)',/)
6024 FORMAT(1X,'FILE: 7segsprint.4 ',//1X,'*** ',99A1,///,8X,'T',13X,'Q
&3',12X,'HANG',11X,'KANG',11X,'AANG',11X,'MANG',11X,'SHANG',10X,'SK
&ANG',11X,'U3',11X,'HANGVEL',8X,'KANGVEL',8X,'AANGVEL',8X,'MANGVEL'
&,7X,'SHANGVEL',7X,'SKANGVEL',/,7X,'(S)',11X,'(DEG)',10X,'(DEG)',10
&X,'(DEG)',10X,'(DEG)',10X,'(DEG)',10X,'(DEG)',10X,'(DEG)',9X,'(DEG
&/S)',8X,'(DEG/S)',8X,'(DEG/S)',8X,'(DEG/S)',8X,'(DEG/S)',8X,'(DEG/
&S)',8X,'(DEG/S)',/)
6025 FORMAT(1X,'FILE: 7segsprint.5 ',//1X,'*** ',99A1,///,8X,'T',12X,'K
&ECM',11X,'PECM',12X,'TE',13X,'HZ',13X,'PX',13X,'PY',/,7X,'(S)',12X
&,'(J)',12X,'(J)',12X,'(J)',8X,'(KG.M^2/S)',6X,'(KG.M/S)',7X,'(KG.M
&/S)',/)
6026 FORMAT(1X,'FILE: 7segsprint.6 ',//1X,'*** ',99A1,///,8X,'T',12X,'H
&EACT',10X,'HFACT',10X,'KEACT',10X,'KFACT',10X,'AEACT',10X,'AFACT',
&10X,'MEACT',10X,'MFACT',/,7X,'(S)',10X,'(UNITS)',8X,'(UNITS)',8X,'
&(UNITS)',8X,'(UNITS)',8X,'(UNITS)',8X,'(UNITS)',8X,'(UNITS)',8X,'(
&UNITS)',/)
6027 FORMAT(1X,'FILE: 7segsprint.7 ',//1X,'*** ',99A1,///,8X,'T',12X,'H
&ETOR',10X,'HEACT',9X,'HECCANG',6X,'HECCANGVEL',6X,'HESECANG',6X,'H
&ESECANGVEL',7X,'HFTOR',10X,'HFACT',9X,'HFCCANG',6X,'HFCCANGVEL',6X
&,'HFSECANG',6X,'HFSECANGVEL',/,7X,'(S)',11X,'(N/M)',9X,'(UNITS)',9
&X,'(DEG)',9X,'(DEG/S)',9X,'(DEG)',9X,'(DEG/S)',9X,'(N/M)',9X,'(UNI
&TS)',9X,'(DEG)',9X,'(DEG/S)',9X,'(DEG)',9X,'(DEG/S)',/)
6028 FORMAT(1X,'FILE: 7segsprint.8 ',//1X,'*** ',99A1,///,8X,'T',12X,'K
&ETOR',10X,'KEACT',9X,'KECCANG',6X,'KECCANGVEL',6X,'KESECANG',6X,'K
&ESECANGVEL',7X,'KFTOR',10X,'KFACT',9X,'KFCCANG',6X,'KFCCANGVEL',6X
&,'KFSECANG',6X,'KFSECANGVEL',/,7X,'(S)',11X,'(N/M)',9X,'(UNITS)',9
&X,'(DEG)',9X,'(DEG/S)',9X,'(DEG)',9X,'(DEG/S)',9X,'(N/M)',9X,'(UNI
&TS)',9X,'(DEG)',9X,'(DEG/S)',9X,'(DEG)',9X,'(DEG/S)',/)
6029 FORMAT(1X,'FILE: 7segsprint.9 ',//1X,'*** ',99A1,///,8X,'T',12X,'A
&ETOR',10X,'AEACT',9X,'AECCANG',6X,'AECCANGVEL',6X,'AESECANG',6X,'A
&ESECANGVEL',7X,'AFTOR',10X,'AFACT',9X,'AFCCANG',6X,'AFCCANGVEL',6X
&,'AFSECANG',6X,'AFSECANGVEL',/,7X,'(S)',11X,'(N/M)',9X,'(UNITS)',9
&X,'(DEG)',9X,'(DEG/S)',9X,'(DEG)',9X,'(DEG/S)',9X,'(N/M)',9X,'(UNI
&TS)',9X,'(DEG)',9X,'(DEG/S)',9X,'(DEG)',9X,'(DEG/S)',/)
6030 FORMAT(1X,'FILE: 7segsprint.10',//1X,'*** ',99A1,///,8X,'T',12X,'M
&ETOR',10X,'MEACT',9X,'MECCANG',6X,'MECCANGVEL',6X,'MESECANG',6X,'M
&ESECANGVEL',7X,'MFTOR',10X,'MFACT',9X,'MFCCANG',6X,'MFCCANGVEL',6X
&,'MFSECANG',6X,'MFSECANGVEL',/,7X,'(S)',11X,'(N/M)',9X,'(UNITS)',9
&X,'(DEG)',9X,'(DEG/S)',9X,'(DEG)',9X,'(DEG/S)',9X,'(N/M)',9X,'(UNI
&TS)',9X,'(DEG)',9X,'(DEG/S)',9X,'(DEG)',9X,'(DEG/S)',/)
6031 FORMAT(1X,'FILE: 7segsprint.11',//1X,'*** ',99A1,///,8X,'T',13X,'R
&X1',12X,'RY1',12X,'RX2',12X,'RY2',12X,'RX',13X,'RY',13X,'GRF',12X,
&'COP',/,7X,'(S)',12X,'(N)',12X,'(N)',12X,'(N)',12X,'(N)',12X,'(N)'
&,12X,'(N)',12X,'(N)',12X,'(M)',/)
6997 FORMAT(/7X,'Error: Numerical integration failed to converge',/)
6999 FORMAT(//1X,'Input is in the file 7segsprint.in',//1X,'Output is i
&n the file(s) 7segsprint.i (i=1, ..., 11)',//1X,'The output quant
&ities and associated files are listed in file 7segsprint.dir',/)
7000 FORMAT(//,99A1,///)
7010 FORMAT( 1000(59X,E30.0,/) )
7011 FORMAT( 3(59X,E30.0,/), 1(59X,I30,/), 2(59X,E30.0,/) )
STOP
7100 WRITE(*,*) 'Premature end of file while reading 7segsprint.in '
7101 WRITE(*,*) 'Error while reading file 7segsprint.in'
STOP
7200 FORMAT(//, 8(///, 10(8X, F7.2, /)))
7210 WRITE(*,*) 'Error reading torque parameters'
STOP
7300 FORMAT(//, 6(///, 10(5X, G30.10, /)))
7310 WRITE(*,*) 'Error reading activation parameters'
STOP
END PROGRAM MAIN
C**********************************************************************
SUBROUTINE EQNS1(T, VAR, VARp, BOUNDARY)
IMPLICIT DOUBLE PRECISION (A - Z)
INTEGER BOUNDARY,NROW
DIMENSION VAR(*), VARp(*)
DIMENSION TT(500),CCHIP(6,500),CCKNEE(6,500),CCHAT(6,500)
COMMON/CONSTNTS/ FOOTANG,G,IA,IB,IC,ID,IE,IF,IG,K1,K2,K3,K4,K5,K6,
&K7,K8,L1,L10,L11,L12,L2,L3,L4,L5,L6,L7,L8,L9,MA,MB,MC,MD,ME,MF,MG,
&MTPB,MTPK,POP1XI,POP2XI
COMMON/VARIBLES/ Q1,Q2,Q3,Q4,Q5,Q6,Q7,U1,U2,U3,U4,U5,U6,U7
COMMON/ALGBRAIC/ AANG,AANGVEL,AETOR,AFTOR,ATOR,COP,GRF,HANG,HANGVE
&L,HETOR,HFTOR,HTOR,HZ,KANG,KANGVEL,KECM,KETOR,KFTOR,KTOR,MANG,MANG
&VEL,METOR,MFTOR,MTOR,PECM,PX,PY,RX,RX1,RX2,RY,RY1,RY2,SHANG,SHANGV
&EL,SHTOR,SKANG,SKANGVEL,SKTOR,TE,U8,U9,VRX,VRY,Q1p,Q2p,Q3p,Q4p,Q5p
&,Q6p,Q7p,U1p,U2p,U3p,U4p,U5p,U6p,U7p,AEACT,AECCANG,AECCANGVEL,AESE
&CANG,AESECANGVEL,AFACT,AFCCANG,AFCCANGVEL,AFSECANG,AFSECANGVEL,EA,
&FA,GS,HEACT,HECCANG,HECCANGVEL,HESECANG,HESECANGVEL,HFACT,HFCCANG,
&HFCCANGVEL,HFSECANG,HFSECANGVEL,KEACT,KECCANG,KECCANGVEL,KESECANG,
&KESECANGVEL,KFACT,KFCCANG,KFCCANGVEL,KFSECANG,KFSECANGVEL,MEACT,ME
&CCANG,MECCANGVEL,MESECANG,MESECANGVEL,MFACT,MFCCANG,MFCCANGVEL,MFS
&ECANG,MFSECANGVEL,EAp,FAp,GSp,EApp,FApp,GSpp,DP1X,DP2X,MT,POCMSTAN
&CEX,POCMSTANCEY,POCMSWINGX,POCMSWINGY,POCMX,POCMY,POGOX,POGOY,POP1
&X,POP1Y,POP2X,POP2Y,POP3X,POP3Y,POP4X,POP4Y,POP5X,POP5Y,POP6X,POP6
&Y,POP7X,POP7Y,POP8X,POP8Y,POP9X,POP9Y,PSTANCEX,PSTANCEY,PSWINGX,PS
&WINGY,VOCMSTANCEX,VOCMSTANCEY,VOCMSWINGX,VOCMSWINGY,VOCMX,VOCMY,VO
&P2X,VOP2Y
COMMON/MISCLLNS/ PI,DEGtoRAD,RADtoDEG,Z(435),COEF(7,7),RHS(7)
COMMON/SPLNCOEF/ TT,CCHIP,CCKNEE,CCHAT,NROW
C** Update variables after integration step
Q1 = VAR(1)
Q2 = VAR(2)
Q3 = VAR(3)
Q4 = VAR(4)
Q5 = VAR(5)
Q6 = VAR(6)
Q7 = VAR(7)
U1 = VAR(8)
U2 = VAR(9)
U3 = VAR(10)
U4 = VAR(11)
U5 = VAR(12)
U6 = VAR(13)
U7 = VAR(14)
Q1p = U1
Q2p = U2
Q3p = U3
Q4p = U4
Q5p = U5
Q6p = U6
Q7p = U7
C** Specified variables
CALL EVALSPLINE2(T,NROW,TT,CCHAT,GS,GSp,GSpp)
CALL EVALSPLINE2(T,NROW,TT,CCHIP,EA,EAp,EApp)
CALL EVALSPLINE2(T,NROW,TT,CCKNEE,FA,FAp,FApp)
EA = EA *DEGtoRAD
EAp = EAp *DEGtoRAD
EApp = EApp*DEGtoRAD
FA = FA *DEGtoRAD
FAp = FAp *DEGtoRAD
FApp = FApp*DEGtoRAD
C** Intermediate variables
Z(3) = COS(Q4)
Z(5) = COS(Q5)
Z(4) = SIN(Q4)
Z(6) = SIN(Q5)
Z(18) = Z(3)*Z(5) - Z(4)*Z(6)
Z(1) = COS(Q3)
Z(7) = COS(Q6)
Z(10) = SIN(Q7)
Z(8) = SIN(Q6)
Z(9) = COS(Q7)
Z(22) = -Z(7)*Z(10) - Z(8)*Z(9)
Z(2) = SIN(Q3)
Z(21) = Z(7)*Z(9) - Z(8)*Z(10)
Z(25) = Z(1)*Z(22) + Z(2)*Z(21)
Z(19) = -Z(3)*Z(6) - Z(4)*Z(5)
Z(23) = Z(7)*Z(10) + Z(8)*Z(9)
Z(27) = Z(1)*Z(21) + Z(2)*Z(23)
Z(29) = Z(18)*Z(25) + Z(19)*Z(27)
Z(20) = Z(3)*Z(6) + Z(4)*Z(5)
Z(31) = Z(18)*Z(27) + Z(20)*Z(25)
Z(24) = Z(1)*Z(21) - Z(2)*Z(22)
Z(26) = Z(1)*Z(23) - Z(2)*Z(21)
Z(28) = Z(18)*Z(24) + Z(19)*Z(26)
Z(30) = Z(18)*Z(26) + Z(20)*Z(24)
C** Calculate forces
POP2X = Q1 - L2*Z(28)
VOP2X = U1 - L2*Z(30)*(U3-U4-U5-U6-U7)
POP2Y = Q2 - L2*Z(29)
VOP2Y = U2 - L2*Z(31)*(U3-U4-U5-U6-U7)
IF (Q2 .LT. 0.0D0) THEN
DP1X = Q1 - POP1XI
RY1 = -K3*(Q2) - K4*ABS(Q2)*U2
RX1 = (-K1*DP1X - K2*U1)*RY1
ELSE
RX1 = 0.0D0
RY1 = 0.0D0
ENDIF
IF (POP2Y .LT. 0.0D0) THEN
DP2X = POP2X - POP2XI
RY2 = -K7*(POP2Y) - K8*ABS(POP2Y)*VOP2Y
RX2 = (-K5*DP2X - K6*VOP2X)*RY2
ELSE
RX2 = 0.0D0
RY2 = 0.0D0
ENDIF
C Total force
RX = RX1 + RX2
RY = RY1 + RY2
Z(32) = Z(15)*Z(3) - Z(16)*Z(4)
Z(33) = Z(15)*Z(4) + Z(16)*Z(3)
Z(34) = -Z(15)*Z(4) - Z(16)*Z(3)
Z(35) = Z(28)*Z(32) + Z(30)*Z(33)
Z(36) = Z(29)*Z(32) + Z(31)*Z(33)
Z(37) = Z(28)*Z(34) + Z(30)*Z(32)
Z(38) = Z(29)*Z(34) + Z(31)*Z(32)
Z(39) = Z(3)*Z(28) + Z(4)*Z(30)
Z(40) = Z(3)*Z(29) + Z(4)*Z(31)
Z(41) = Z(3)*Z(30) - Z(4)*Z(28)
Z(42) = Z(3)*Z(31) - Z(4)*Z(29)
Z(43) = Z(7)*Z(24) + Z(8)*Z(26)
Z(44) = Z(7)*Z(25) + Z(8)*Z(27)
Z(45) = Z(7)*Z(26) - Z(8)*Z(24)
Z(46) = Z(7)*Z(27) - Z(8)*Z(25)
Z(77) = Z(1)*Z(30) + Z(2)*Z(31)
Z(78) = Z(1)*Z(29) - Z(2)*Z(28)
Z(79) = Z(1)*Z(31) - Z(2)*Z(30)
Z(82) = Z(1)*Z(41) + Z(2)*Z(42)
Z(83) = Z(1)*Z(40) - Z(2)*Z(39)
Z(84) = Z(1)*Z(42) - Z(2)*Z(41)
Z(106) = L1*(U3-U4-U5-U6-U7)
Z(107) = (U3-U4-U5-U6-U7)*Z(106)
Z(108) = L2*(U3-U4-U5-U6-U7)
Z(109) = (U3-U4-U5-U6-U7)*Z(108)
Z(110) = L4*(U3-U5-U6-U7)
Z(111) = L3*(U3-U5-U6-U7)
Z(112) = (U3-U5-U6-U7)*Z(110)
Z(113) = (U3-U5-U6-U7)*Z(111)
Z(116) = L6*(U3-U5-U6-U7)
Z(117) = (U3-U5-U6-U7)*Z(116)
Z(118) = L7*(U3-U6-U7)
Z(119) = (U3-U6-U7)*Z(118)
Z(120) = L8*(U3-U6-U7)
Z(121) = (U3-U6-U7)*Z(120)
Z(122) = L9*(U3-U7)
Z(123) = (U3-U7)*Z(122)
Z(124) = L10*(U3-U7)
Z(125) = (U3-U7)*Z(124)
Z(157) = Z(7)*Z(18) + Z(8)*Z(19)
Z(158) = Z(7)*Z(19) - Z(8)*Z(18)
Z(159) = Z(7)*Z(20) + Z(8)*Z(18)
Z(160) = Z(7)*Z(18) - Z(8)*Z(20)
Z(162) = Z(3)*Z(158) + Z(4)*Z(160)
Z(163) = Z(3)*Z(159) - Z(4)*Z(157)
Z(164) = Z(3)*Z(160) - Z(4)*Z(158)
Z(303) = RX1 + RX2 + VRX
Z(305) = Z(304) + RY1 + RY2 + VRY
Z(314) = MTOR + Z(306)*Z(31) + Z(308)*Z(31) + Z(309)*Z(31) + Z(310
&)*Z(31) + Z(311)*Z(31) + Z(312)*Z(31) + Z(313)*Z(31) + L2*(RX2*Z(3
&0)+RY2*Z(31)) + Z(54)*(VRX*Z(30)+VRY*Z(31))
Z(336) = Z(335)*Z(30)
Z(337) = Z(273)*Z(30) + MC*(L2*Z(30)-L6*Z(41)) + MD*(L2*Z(30)-L6*Z
&(41)) + ME*(L2*Z(30)-L6*Z(41)) + MF*(L2*Z(30)-L6*Z(41)) + MG*(L2*Z
&(30)-L6*Z(41)) + 0.5D0*MB*(2*L2*Z(30)-L3*Z(37)-L4*Z(41))
Z(338) = Z(273)*Z(30) + MC*(L2*Z(30)-L6*Z(41)-L7*Z(26)) + MD*(L2*Z
&(30)-L6*Z(41)-L8*Z(26)) + ME*(L2*Z(30)-L6*Z(41)-L8*Z(26)) + MF*(L2
&*Z(30)-L6*Z(41)-L8*Z(26)) + MG*(L2*Z(30)-L6*Z(41)-L8*Z(26)) + 0.5D
&0*MB*(2*L2*Z(30)-L3*Z(37)-L4*Z(41))
Z(339) = Z(273)*Z(30) + MC*(L2*Z(30)-L6*Z(41)-L7*Z(26)) + 0.5D0*MB
&*(2*L2*Z(30)-L3*Z(37)-L4*Z(41)) + MD*(L2*Z(30)-L6*Z(41)-L8*Z(26)-L
&9*Z(45)) + ME*(L2*Z(30)-L10*Z(45)-L6*Z(41)-L8*Z(26)) + MF*(L2*Z(30
&)-L10*Z(45)-L6*Z(41)-L8*Z(26)) + MG*(L2*Z(30)-L10*Z(45)-L6*Z(41)-L
&8*Z(26))
Z(342) = Z(335)*Z(31)
Z(343) = Z(273)*Z(31) + MC*(L2*Z(31)-L6*Z(42)) + MD*(L2*Z(31)-L6*Z
&(42)) + ME*(L2*Z(31)-L6*Z(42)) + MF*(L2*Z(31)-L6*Z(42)) + MG*(L2*Z
&(31)-L6*Z(42)) + 0.5D0*MB*(2*L2*Z(31)-L3*Z(38)-L4*Z(42))
Z(344) = Z(273)*Z(31) + MC*(L2*Z(31)-L6*Z(42)-L7*Z(27)) + MD*(L2*Z
&(31)-L6*Z(42)-L8*Z(27)) + ME*(L2*Z(31)-L6*Z(42)-L8*Z(27)) + MF*(L2
&*Z(31)-L6*Z(42)-L8*Z(27)) + MG*(L2*Z(31)-L6*Z(42)-L8*Z(27)) + 0.5D
&0*MB*(2*L2*Z(31)-L3*Z(38)-L4*Z(42))
Z(345) = Z(273)*Z(31) + MC*(L2*Z(31)-L6*Z(42)-L7*Z(27)) + 0.5D0*MB
&*(2*L2*Z(31)-L3*Z(38)-L4*Z(42)) + MD*(L2*Z(31)-L6*Z(42)-L8*Z(27)-L
&9*Z(46)) + ME*(L2*Z(31)-L10*Z(46)-L6*Z(42)-L8*Z(27)) + MF*(L2*Z(31
&)-L10*Z(46)-L6*Z(42)-L8*Z(27)) + MG*(L2*Z(31)-L10*Z(46)-L6*Z(42)-L
&8*Z(27))
Z(390) = Z(389) + Z(277)*(L2-L6*Z(3)) + Z(280)*(L2-L6*Z(3)) + Z(28
&4)*(L2-L6*Z(3)) + Z(290)*(L2-L6*Z(3)) + Z(297)*(L2-L6*Z(3)) + 0.5D
&0*Z(274)*(2*L2-L3*Z(32)-L4*Z(3))
Z(391) = Z(389) + Z(277)*(L2-L6*Z(3)-L7*Z(18)) + Z(280)*(L2-L6*Z(3
&)-L8*Z(18)) + Z(284)*(L2-L6*Z(3)-L8*Z(18)) + Z(290)*(L2-L6*Z(3)-L8
&*Z(18)) + Z(297)*(L2-L6*Z(3)-L8*Z(18)) + 0.5D0*Z(274)*(2*L2-L3*Z(3
&2)-L4*Z(3))
Z(392) = Z(389) + Z(277)*(L2-L6*Z(3)-L7*Z(18)) + 0.5D0*Z(274)*(2*L
&2-L3*Z(32)-L4*Z(3)) + Z(280)*(L2-L6*Z(3)-L8*Z(18)-L9*Z(160)) + Z(2
&84)*(L2-L10*Z(160)-L6*Z(3)-L8*Z(18)) + Z(290)*(L2-L10*Z(160)-L6*Z(
&3)-L8*Z(18)) + Z(297)*(L2-L10*Z(160)-L6*Z(3)-L8*Z(18))
Z(396) = Z(394) + MC*(Z(395)-2*Z(351)*Z(3)) + MD*(Z(395)-2*Z(351)*
&Z(3)) + ME*(Z(395)-2*Z(351)*Z(3)) + MF*(Z(395)-2*Z(351)*Z(3)) + MG
&*(Z(395)-2*Z(351)*Z(3)) + 0.25D0*MB*(Z(348)-4*Z(349)*Z(32)-4*Z(350
&)*Z(3))
Z(397) = Z(394) + 0.25D0*MB*(Z(348)-4*Z(349)*Z(32)-4*Z(350)*Z(3))
&- MC*(Z(352)*Z(18)+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(356)*Z(5)) - MD*(
&Z(357)*Z(18)+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(361)*Z(5)) - ME*(Z(357)
&*Z(18)+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(361)*Z(5)) - MF*(Z(357)*Z(18)
&+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(361)*Z(5)) - MG*(Z(357)*Z(18)+2*Z(3
&51)*Z(3)-Z(353)-Z(354)-Z(361)*Z(5))
Z(398) = Z(394) + 0.25D0*MB*(Z(348)-4*Z(349)*Z(32)-4*Z(350)*Z(3))
&- MC*(Z(352)*Z(18)+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(356)*Z(5)) - MD*(
&Z(357)*Z(18)+Z(358)*Z(160)+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(361)*Z(5)
&-Z(362)*Z(164)) - ME*(Z(357)*Z(18)+Z(364)*Z(160)+2*Z(351)*Z(3)-Z(3
&53)-Z(354)-Z(361)*Z(5)-Z(368)*Z(164)) - MF*(Z(357)*Z(18)+Z(364)*Z(
&160)+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(361)*Z(5)-Z(368)*Z(164)) - MG*(
&Z(357)*Z(18)+Z(364)*Z(160)+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(361)*Z(5)
&-Z(368)*Z(164))
Z(401) = Z(400) + 0.25D0*MB*(Z(348)-4*Z(349)*Z(32)-4*Z(350)*Z(3))
&- MC*(2*Z(351)*Z(3)+2*Z(352)*Z(18)-Z(353)-Z(354)-Z(355)-2*Z(356)*Z
&(5)) - MD*(2*Z(351)*Z(3)+2*Z(357)*Z(18)-Z(353)-Z(354)-Z(359)-2*Z(3
&61)*Z(5)) - ME*(2*Z(351)*Z(3)+2*Z(357)*Z(18)-Z(353)-Z(354)-Z(359)-
&2*Z(361)*Z(5)) - MF*(2*Z(351)*Z(3)+2*Z(357)*Z(18)-Z(353)-Z(354)-Z(
&359)-2*Z(361)*Z(5)) - MG*(2*Z(351)*Z(3)+2*Z(357)*Z(18)-Z(353)-Z(35
&4)-Z(359)-2*Z(361)*Z(5))
Z(402) = Z(400) + 0.25D0*MB*(Z(348)-4*Z(349)*Z(32)-4*Z(350)*Z(3))
&- MC*(2*Z(351)*Z(3)+2*Z(352)*Z(18)-Z(353)-Z(354)-Z(355)-2*Z(356)*Z
&(5)) - MD*(Z(358)*Z(160)+2*Z(351)*Z(3)+2*Z(357)*Z(18)-Z(353)-Z(354
&)-Z(359)-2*Z(361)*Z(5)-Z(362)*Z(164)-Z(363)*Z(7)) - ME*(Z(364)*Z(1
&60)+2*Z(351)*Z(3)+2*Z(357)*Z(18)-Z(353)-Z(354)-Z(359)-2*Z(361)*Z(5
&)-Z(368)*Z(164)-Z(369)*Z(7)) - MF*(Z(364)*Z(160)+2*Z(351)*Z(3)+2*Z
&(357)*Z(18)-Z(353)-Z(354)-Z(359)-2*Z(361)*Z(5)-Z(368)*Z(164)-Z(369
&)*Z(7)) - MG*(Z(364)*Z(160)+2*Z(351)*Z(3)+2*Z(357)*Z(18)-Z(353)-Z(
&354)-Z(359)-2*Z(361)*Z(5)-Z(368)*Z(164)-Z(369)*Z(7))
Z(405) = Z(404) + 0.25D0*MB*(Z(348)-4*Z(349)*Z(32)-4*Z(350)*Z(3))
&- MC*(2*Z(351)*Z(3)+2*Z(352)*Z(18)-Z(353)-Z(354)-Z(355)-2*Z(356)*Z
&(5)) - MD*(2*Z(351)*Z(3)+2*Z(357)*Z(18)+2*Z(358)*Z(160)-Z(353)-Z(3
&54)-Z(359)-Z(360)-2*Z(361)*Z(5)-2*Z(362)*Z(164)-2*Z(363)*Z(7)) - M
&E*(2*Z(351)*Z(3)+2*Z(357)*Z(18)+2*Z(364)*Z(160)-Z(353)-Z(354)-Z(35
&9)-Z(366)-2*Z(361)*Z(5)-2*Z(368)*Z(164)-2*Z(369)*Z(7)) - MF*(2*Z(3
&51)*Z(3)+2*Z(357)*Z(18)+2*Z(364)*Z(160)-Z(353)-Z(354)-Z(359)-Z(366
&)-2*Z(361)*Z(5)-2*Z(368)*Z(164)-2*Z(369)*Z(7)) - MG*(2*Z(351)*Z(3)
&+2*Z(357)*Z(18)+2*Z(364)*Z(160)-Z(353)-Z(354)-Z(359)-Z(366)-2*Z(36
&1)*Z(5)-2*Z(368)*Z(164)-2*Z(369)*Z(7))
Z(11) = COS(EA)
Z(12) = SIN(EA)
Z(13) = COS(FA)
Z(14) = SIN(FA)
Z(47) = Z(11)*Z(1) + Z(12)*Z(2)
Z(48) = Z(11)*Z(2) - Z(12)*Z(1)
Z(49) = Z(12)*Z(1) - Z(11)*Z(2)
Z(50) = -Z(13)*Z(47) - Z(14)*Z(49)
Z(51) = -Z(13)*Z(48) - Z(14)*Z(47)
Z(52) = Z(14)*Z(47) - Z(13)*Z(49)
Z(53) = Z(14)*Z(48) - Z(13)*Z(47)
Z(60) = MG*GS/MT
Z(86) = U8 - EAp
Z(88) = FApp - EApp
Z(97) = Z(17)*EAp
Z(98) = L10*EAp
Z(99) = L12*(EAp-FAp)
Z(126) = Z(17)*U3 + Z(17)*U8 - Z(97)
Z(127) = Z(17)*EApp
Z(128) = Z(126)*(U3+Z(86))
Z(129) = L10*U3 + L10*U8 - Z(98)
Z(130) = L10*EApp
Z(131) = Z(129)*(U3+Z(86))
Z(132) = L12*U3 + L12*U8 + L12*U9 - Z(99)
Z(133) = L12*(EApp-FApp)
Z(134) = FAp + U9
Z(135) = Z(132)*(U3+Z(86)+Z(134))
Z(139) = GS*U3
Z(140) = GSp*U3
Z(141) = GSpp - U3*Z(139)
Z(142) = GSp*U3 + Z(140)
Z(152) = MTOR - ATOR
Z(153) = ATOR + KTOR
Z(154) = -HTOR - KTOR
Z(165) = Z(28)*Z(47) + Z(29)*Z(48)
Z(166) = Z(28)*Z(49) + Z(29)*Z(47)
Z(167) = Z(30)*Z(47) + Z(31)*Z(48)
Z(168) = Z(30)*Z(49) + Z(31)*Z(47)
Z(169) = Z(3)*Z(165) + Z(4)*Z(167)
Z(170) = Z(3)*Z(166) + Z(4)*Z(168)
Z(171) = Z(3)*Z(167) - Z(4)*Z(165)
Z(172) = Z(3)*Z(168) - Z(4)*Z(166)
Z(173) = Z(5)*Z(169) + Z(6)*Z(171)
Z(174) = Z(5)*Z(170) + Z(6)*Z(172)
Z(175) = Z(5)*Z(171) - Z(6)*Z(169)
Z(176) = Z(5)*Z(172) - Z(6)*Z(170)
Z(178) = Z(7)*Z(174) + Z(8)*Z(176)
Z(179) = Z(7)*Z(175) - Z(8)*Z(173)
Z(180) = Z(7)*Z(176) - Z(8)*Z(174)
Z(181) = Z(28)*Z(50) + Z(29)*Z(51)
Z(182) = Z(28)*Z(52) + Z(29)*Z(53)
Z(183) = Z(30)*Z(50) + Z(31)*Z(51)
Z(184) = Z(30)*Z(52) + Z(31)*Z(53)
Z(185) = Z(3)*Z(181) + Z(4)*Z(183)
Z(186) = Z(3)*Z(182) + Z(4)*Z(184)
Z(187) = Z(3)*Z(183) - Z(4)*Z(181)
Z(188) = Z(3)*Z(184) - Z(4)*Z(182)
Z(189) = Z(5)*Z(185) + Z(6)*Z(187)
Z(190) = Z(5)*Z(186) + Z(6)*Z(188)
Z(191) = Z(5)*Z(187) - Z(6)*Z(185)
Z(192) = Z(5)*Z(188) - Z(6)*Z(186)
Z(194) = Z(7)*Z(190) + Z(8)*Z(192)
Z(195) = Z(7)*Z(191) - Z(8)*Z(189)
Z(196) = Z(7)*Z(192) - Z(8)*Z(190)
Z(315) = MTOR + Z(306)*Z(31) + Z(54)*VRX*Z(30) + Z(54)*VRY*Z(31) +
& L2*(RX2*Z(30)+RY2*Z(31)) + Z(147)*(L2*Z(31)-L6*Z(42)) + Z(148)*(L
&2*Z(31)-L6*Z(42)) + Z(149)*(L2*Z(31)-L6*Z(42)) + Z(150)*(L2*Z(31)-
&L6*Z(42)) + Z(151)*(L2*Z(31)-L6*Z(42)) + 0.5D0*Z(146)*(2*L2*Z(31)-
&L3*Z(38)-L4*Z(42)) - Z(152) - 0.5D0*Z(55)*VRX*Z(41) - 0.5D0*Z(55)*
&VRY*Z(42) - 0.5D0*Z(61)*VRX*Z(37) - 0.5D0*Z(61)*VRY*Z(38)
Z(316) = MTOR + Z(306)*Z(31) + Z(54)*VRX*Z(30) + Z(54)*VRY*Z(31) +
& L2*(RX2*Z(30)+RY2*Z(31)) + Z(147)*(L2*Z(31)-L6*Z(42)-L7*Z(27)) +
&Z(148)*(L2*Z(31)-L6*Z(42)-L8*Z(27)) + Z(149)*(L2*Z(31)-L6*Z(42)-L8
&*Z(27)) + Z(150)*(L2*Z(31)-L6*Z(42)-L8*Z(27)) + Z(151)*(L2*Z(31)-L
&6*Z(42)-L8*Z(27)) + 0.5D0*Z(146)*(2*L2*Z(31)-L3*Z(38)-L4*Z(42)) -
&Z(152) - Z(153) - Z(56)*VRX*Z(26) - Z(56)*VRY*Z(27) - 0.5D0*Z(55)*
&VRX*Z(41) - 0.5D0*Z(55)*VRY*Z(42) - 0.5D0*Z(61)*VRX*Z(37) - 0.5D0*
&Z(61)*VRY*Z(38)
Z(317) = MTOR + Z(306)*Z(31) + Z(54)*VRX*Z(30) + Z(54)*VRY*Z(31) +
& L2*(RX2*Z(30)+RY2*Z(31)) + Z(147)*(L2*Z(31)-L6*Z(42)-L7*Z(27)) +
&0.5D0*Z(146)*(2*L2*Z(31)-L3*Z(38)-L4*Z(42)) + Z(148)*(L2*Z(31)-L6*
&Z(42)-L8*Z(27)-L9*Z(46)) + Z(149)*(L2*Z(31)-L10*Z(46)-L6*Z(42)-L8*
&Z(27)) + Z(150)*(L2*Z(31)-L10*Z(46)-L6*Z(42)-L8*Z(27)) + Z(151)*(L
&2*Z(31)-L10*Z(46)-L6*Z(42)-L8*Z(27)) - Z(152) - Z(153) - Z(154) -
&Z(56)*VRX*Z(26) - Z(56)*VRY*Z(27) - Z(57)*VRX*Z(45) - Z(57)*VRY*Z(
&46) - 0.5D0*Z(55)*VRX*Z(41) - 0.5D0*Z(55)*VRY*Z(42) - 0.5D0*Z(61)*
&VRX*Z(37) - 0.5D0*Z(61)*VRY*Z(38)
Z(331) = IE*EApp
Z(333) = IF*Z(88)
Z(334) = MG*(L10*Z(45)+L6*Z(41)+L8*Z(26)-L2*Z(30)-GS*Z(2)) - Z(273
&)*Z(30) - MC*(L2*Z(30)-L6*Z(41)-L7*Z(26)) - 0.5D0*MB*(2*L2*Z(30)-L
&3*Z(37)-L4*Z(41)) - MD*(L2*Z(30)-L6*Z(41)-L8*Z(26)-L9*Z(45)) - ME*
&(L2*Z(30)-L10*Z(45)-L6*Z(41)-L8*Z(26)-Z(17)*Z(49)) - MF*(L2*Z(30)-
&L10*Z(45)-L10*Z(49)-L12*Z(52)-L6*Z(41)-L8*Z(26))
Z(340) = MA*Z(28)*Z(107) + MC*(Z(28)*Z(109)-Z(24)*Z(119)-Z(39)*Z(1
&17)) + 0.5D0*MB*(2*Z(28)*Z(109)-Z(35)*Z(113)-Z(39)*Z(112)) + MD*(Z
&(28)*Z(109)-Z(24)*Z(121)-Z(39)*Z(117)-Z(43)*Z(123)) + MG*(Z(1)*Z(1
&41)+Z(28)*Z(109)-Z(2)*Z(142)-Z(24)*Z(121)-Z(39)*Z(117)-Z(43)*Z(125
&)) + ME*(Z(28)*Z(109)-Z(127)*Z(49)-Z(24)*Z(121)-Z(39)*Z(117)-Z(43)
&*Z(125)-Z(47)*Z(128)) + MF*(Z(28)*Z(109)-Z(130)*Z(49)-Z(133)*Z(52)
&-Z(24)*Z(121)-Z(39)*Z(117)-Z(43)*Z(125)-Z(47)*Z(131)-Z(50)*Z(135))
Z(341) = -Z(273)*Z(31) - MC*(L2*Z(31)-L6*Z(42)-L7*Z(27)) - 0.5D0*M
&B*(2*L2*Z(31)-L3*Z(38)-L4*Z(42)) - MD*(L2*Z(31)-L6*Z(42)-L8*Z(27)-
&L9*Z(46)) - ME*(L2*Z(31)-L10*Z(46)-L6*Z(42)-L8*Z(27)-Z(17)*Z(47))
&- MG*(L2*Z(31)-L10*Z(46)-L6*Z(42)-L8*Z(27)-GS*Z(1)) - MF*(L2*Z(31)
&-L10*Z(46)-L10*Z(47)-L12*Z(53)-L6*Z(42)-L8*Z(27))
Z(346) = MA*Z(29)*Z(107) + MC*(Z(29)*Z(109)-Z(25)*Z(119)-Z(40)*Z(1
&17)) + 0.5D0*MB*(2*Z(29)*Z(109)-Z(36)*Z(113)-Z(40)*Z(112)) + MD*(Z
&(29)*Z(109)-Z(25)*Z(121)-Z(40)*Z(117)-Z(44)*Z(123)) + MG*(Z(1)*Z(1
&42)+Z(2)*Z(141)+Z(29)*Z(109)-Z(25)*Z(121)-Z(40)*Z(117)-Z(44)*Z(125
&)) + ME*(Z(29)*Z(109)-Z(127)*Z(47)-Z(25)*Z(121)-Z(40)*Z(117)-Z(44)
&*Z(125)-Z(48)*Z(128)) + MF*(Z(29)*Z(109)-Z(130)*Z(47)-Z(133)*Z(53)
&-Z(25)*Z(121)-Z(40)*Z(117)-Z(44)*Z(125)-Z(48)*Z(131)-Z(51)*Z(135))
Z(378) = Z(347) + 0.25D0*MB*(Z(348)-4*Z(349)*Z(32)-4*Z(350)*Z(3))
&- MC*(2*Z(351)*Z(3)+2*Z(352)*Z(18)-Z(353)-Z(354)-Z(355)-2*Z(356)*Z
&(5)) - MD*(2*Z(351)*Z(3)+2*Z(357)*Z(18)+2*Z(358)*Z(160)-Z(353)-Z(3
&54)-Z(359)-Z(360)-2*Z(361)*Z(5)-2*Z(362)*Z(164)-2*Z(363)*Z(7)) - M
&E*(2*Z(351)*Z(3)+2*Z(357)*Z(18)+2*Z(364)*Z(160)+2*Z(365)*Z(168)-Z(
&353)-Z(354)-Z(359)-Z(366)-Z(367)-2*Z(361)*Z(5)-2*Z(368)*Z(164)-2*Z
&(369)*Z(7)-2*Z(370)*Z(180)-2*Z(371)*Z(172)-2*Z(372)*Z(176)) - MG*(
&2*Z(351)*Z(3)+2*Z(357)*Z(18)+2*Z(364)*Z(160)+2*L2*GS*Z(79)-Z(353)-
&Z(354)-Z(359)-Z(366)-GS**2-2*Z(361)*Z(5)-2*Z(368)*Z(164)-2*Z(369)*
&Z(7)-2*L10*GS*Z(9)-2*L6*GS*Z(84)-2*L8*GS*Z(21)) - MF*(2*Z(373)*Z(1
&3)+2*Z(351)*Z(3)+2*Z(357)*Z(18)+2*Z(364)*Z(160)+2*Z(364)*Z(168)+2*
&Z(374)*Z(184)-2*Z(366)-Z(353)-Z(354)-Z(359)-Z(375)-2*Z(361)*Z(5)-2
&*Z(366)*Z(180)-2*Z(368)*Z(164)-2*Z(368)*Z(172)-2*Z(369)*Z(7)-2*Z(3
&69)*Z(176)-2*Z(373)*Z(196)-2*Z(376)*Z(188)-2*Z(377)*Z(192))
Z(380) = Z(379) - Z(277)*(L2-L6*Z(3)-L7*Z(18)) - 0.5D0*Z(274)*(2*L
&2-L3*Z(32)-L4*Z(3)) - Z(280)*(L2-L6*Z(3)-L8*Z(18)-L9*Z(160)) - Z(2
&84)*(L2-L10*Z(160)-L6*Z(3)-L8*Z(18)-Z(17)*Z(168)) - Z(297)*(L2-L10
&*Z(160)-L6*Z(3)-L8*Z(18)-GS*Z(79)) - Z(290)*(L2-L10*Z(160)-L10*Z(1
&68)-L12*Z(184)-L6*Z(3)-L8*Z(18))
Z(382) = MC*(Z(352)*Z(18)+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(356)*Z(5))
& + MD*(Z(357)*Z(18)+Z(358)*Z(160)+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(36
&1)*Z(5)-Z(362)*Z(164)) + ME*(Z(357)*Z(18)+Z(364)*Z(160)+Z(365)*Z(1
&68)+2*Z(351)*Z(3)-Z(353)-Z(354)-Z(361)*Z(5)-Z(368)*Z(164)-Z(371)*Z
&(172)) + MG*(Z(357)*Z(18)+Z(364)*Z(160)+2*Z(351)*Z(3)+L2*GS*Z(79)-
&Z(353)-Z(354)-Z(361)*Z(5)-Z(368)*Z(164)-L6*GS*Z(84)) + MF*(Z(357)*
&Z(18)+Z(364)*Z(160)+Z(364)*Z(168)+Z(374)*Z(184)+2*Z(351)*Z(3)-Z(35
&3)-Z(354)-Z(361)*Z(5)-Z(368)*Z(164)-Z(368)*Z(172)-Z(376)*Z(188)) -
& IA - IB - Z(381) - 0.25D0*MB*(Z(348)-4*Z(349)*Z(32)-4*Z(350)*Z(3)
&)
Z(383) = MC*(2*Z(351)*Z(3)+2*Z(352)*Z(18)-Z(353)-Z(354)-Z(355)-2*Z
&(356)*Z(5)) + MD*(Z(358)*Z(160)+2*Z(351)*Z(3)+2*Z(357)*Z(18)-Z(353
&)-Z(354)-Z(359)-2*Z(361)*Z(5)-Z(362)*Z(164)-Z(363)*Z(7)) + ME*(Z(3
&64)*Z(160)+Z(365)*Z(168)+2*Z(351)*Z(3)+2*Z(357)*Z(18)-Z(353)-Z(354
&)-Z(359)-2*Z(361)*Z(5)-Z(368)*Z(164)-Z(369)*Z(7)-Z(371)*Z(172)-Z(3
&72)*Z(176)) + MG*(Z(364)*Z(160)+2*Z(351)*Z(3)+2*Z(357)*Z(18)+L2*GS
&*Z(79)-Z(353)-Z(354)-Z(359)-2*Z(361)*Z(5)-Z(368)*Z(164)-Z(369)*Z(7
&)-L6*GS*Z(84)-L8*GS*Z(21)) + MF*(Z(364)*Z(160)+Z(364)*Z(168)+Z(374
&)*Z(184)+2*Z(351)*Z(3)+2*Z(357)*Z(18)-Z(353)-Z(354)-Z(359)-2*Z(361
&)*Z(5)-Z(368)*Z(164)-Z(368)*Z(172)-Z(369)*Z(7)-Z(369)*Z(176)-Z(376
&)*Z(188)-Z(377)*Z(192)) - IA - IB - IC - Z(381) - 0.25D0*MB*(Z(348
&)-4*Z(349)*Z(32)-4*Z(350)*Z(3))
Z(384) = MC*(2*Z(351)*Z(3)+2*Z(352)*Z(18)-Z(353)-Z(354)-Z(355)-2*Z
&(356)*Z(5)) + MD*(2*Z(351)*Z(3)+2*Z(357)*Z(18)+2*Z(358)*Z(160)-Z(3
&53)-Z(354)-Z(359)-Z(360)-2*Z(361)*Z(5)-2*Z(362)*Z(164)-2*Z(363)*Z(
&7)) + ME*(Z(365)*Z(168)+2*Z(351)*Z(3)+2*Z(357)*Z(18)+2*Z(364)*Z(16
&0)-Z(353)-Z(354)-Z(359)-Z(366)-2*Z(361)*Z(5)-2*Z(368)*Z(164)-2*Z(3
&69)*Z(7)-Z(370)*Z(180)-Z(371)*Z(172)-Z(372)*Z(176)) + MG*(2*Z(351)
&*Z(3)+2*Z(357)*Z(18)+2*Z(364)*Z(160)+L2*GS*Z(79)-Z(353)-Z(354)-Z(3
&59)-Z(366)-2*Z(361)*Z(5)-2*Z(368)*Z(164)-2*Z(369)*Z(7)-L10*GS*Z(9)
&-L6*GS*Z(84)-L8*GS*Z(21)) + MF*(Z(364)*Z(168)+Z(374)*Z(184)+2*Z(35
&1)*Z(3)+2*Z(357)*Z(18)+2*Z(364)*Z(160)-Z(353)-Z(354)-Z(359)-Z(366)
&-2*Z(361)*Z(5)-2*Z(368)*Z(164)-2*Z(369)*Z(7)-Z(366)*Z(180)-Z(368)*
&Z(172)-Z(369)*Z(176)-Z(373)*Z(196)-Z(376)*Z(188)-Z(377)*Z(192)) -
&IA - IB - IC - ID - Z(381) - 0.25D0*MB*(Z(348)-4*Z(349)*Z(32)-4*Z(
&350)*Z(3))
Z(387) = Z(333) + 0.25D0*MB*(Z(385)*Z(112)+2*L2*Z(4)*Z(112)+2*L2*Z
&(33)*Z(113)+2*L3*Z(34)*Z(109)-Z(386)*Z(113)-2*L4*Z(4)*Z(109)) + MD
&*(L2*Z(4)*Z(117)+L2*Z(20)*Z(121)+L2*Z(159)*Z(123)+L8*Z(6)*Z(117)+L
&8*Z(19)*Z(109)+L9*Z(8)*Z(121)+L9*Z(158)*Z(109)-L6*Z(4)*Z(109)-L6*Z
&(6)*Z(121)-L6*Z(163)*Z(123)-L8*Z(8)*Z(123)-L9*Z(162)*Z(117)) + MG*
&(GS*Z(142)+L10*Z(8)*Z(121)+L10*Z(9)*Z(142)+L10*Z(10)*Z(141)+L10*Z(
&158)*Z(109)+L2*Z(4)*Z(117)+L2*Z(20)*Z(121)+L2*Z(159)*Z(125)+L6*Z(8
&2)*Z(141)+L6*Z(84)*Z(142)+L8*Z(6)*Z(117)+L8*Z(19)*Z(109)+L8*Z(21)*
&Z(142)+L8*Z(23)*Z(141)+GS*Z(10)*Z(125)+GS*Z(78)*Z(109)-L10*Z(162)*
&Z(117)-L2*Z(77)*Z(141)-L2*Z(79)*Z(142)-L6*Z(4)*Z(109)-L6*Z(6)*Z(12
&1)-L6*Z(163)*Z(125)-L8*Z(8)*Z(125)-GS*Z(22)*Z(121)-GS*Z(83)*Z(117)
&) + ME*(L2*Z(127)*Z(168)+L10*Z(8)*Z(121)+L10*Z(158)*Z(109)+L2*Z(4)
&*Z(117)+L2*Z(20)*Z(121)+L2*Z(159)*Z(125)+L2*Z(167)*Z(128)+L8*Z(6)*
&Z(117)+L8*Z(19)*Z(109)+Z(17)*Z(166)*Z(109)-Z(17)*Z(127)-L10*Z(127)
&*Z(180)-L6*Z(127)*Z(172)-L8*Z(127)*Z(176)-L10*Z(162)*Z(117)-L10*Z(
&179)*Z(128)-L6*Z(4)*Z(109)-L6*Z(6)*Z(121)-L6*Z(163)*Z(125)-L6*Z(17
&1)*Z(128)-L8*Z(8)*Z(125)-L8*Z(175)*Z(128)-Z(17)*Z(170)*Z(117)-Z(17
&)*Z(174)*Z(121)-Z(17)*Z(178)*Z(125)) + MF*(L10*Z(13)*Z(133)+L12*Z(
&13)*Z(130)+L2*Z(130)*Z(168)+L2*Z(133)*Z(184)+L10*Z(14)*Z(135)+L10*
&Z(8)*Z(121)+L10*Z(158)*Z(109)+L10*Z(166)*Z(109)+L12*Z(182)*Z(109)+
&L2*Z(4)*Z(117)+L2*Z(20)*Z(121)+L2*Z(159)*Z(125)+L2*Z(167)*Z(131)+L
&2*Z(183)*Z(135)+L8*Z(6)*Z(117)+L8*Z(19)*Z(109)-L10*Z(130)-L12*Z(13
&3)-L10*Z(130)*Z(180)-L10*Z(133)*Z(196)-L6*Z(130)*Z(172)-L6*Z(133)*
&Z(188)-L8*Z(130)*Z(176)-L8*Z(133)*Z(192)-L10*Z(162)*Z(117)-L10*Z(1
&70)*Z(117)-L10*Z(174)*Z(121)-L10*Z(178)*Z(125)-L10*Z(179)*Z(131)-L
&10*Z(195)*Z(135)-L12*Z(14)*Z(131)-L12*Z(186)*Z(117)-L12*Z(190)*Z(1
&21)-L12*Z(194)*Z(125)-L6*Z(4)*Z(109)-L6*Z(6)*Z(121)-L6*Z(163)*Z(12
&5)-L6*Z(171)*Z(131)-L6*Z(187)*Z(135)-L8*Z(8)*Z(125)-L8*Z(175)*Z(13
&1)-L8*Z(191)*Z(135)) - Z(331) - MC*(L6*Z(4)*Z(109)+L6*Z(6)*Z(119)-
&L2*Z(4)*Z(117)-L2*Z(20)*Z(119)-L7*Z(6)*Z(117)-L7*Z(19)*Z(109))
Z(393) = L2*(2*MG*(Z(77)*Z(141)+Z(79)*Z(142)-Z(4)*Z(117)-Z(20)*Z(1
&21)-Z(159)*Z(125))-2*MC*(Z(4)*Z(117)+Z(20)*Z(119))-MB*(Z(4)*Z(112)
&+Z(33)*Z(113))-2*MD*(Z(4)*Z(117)+Z(20)*Z(121)+Z(159)*Z(123))-2*ME*
&(Z(127)*Z(168)+Z(4)*Z(117)+Z(20)*Z(121)+Z(159)*Z(125)+Z(167)*Z(128
&))-2*MF*(Z(130)*Z(168)+Z(133)*Z(184)+Z(4)*Z(117)+Z(20)*Z(121)+Z(15
&9)*Z(125)+Z(167)*Z(131)+Z(183)*Z(135)))
Z(399) = -MC*(L2*Z(4)*Z(117)+L2*Z(20)*Z(119)-L6*Z(4)*Z(109)-L6*Z(6
&)*Z(119)) - MD*(L2*Z(4)*Z(117)+L2*Z(20)*Z(121)+L2*Z(159)*Z(123)-L6
&*Z(4)*Z(109)-L6*Z(6)*Z(121)-L6*Z(163)*Z(123)) - 0.25D0*MB*(Z(385)*
&Z(112)+2*L2*Z(4)*Z(112)+2*L2*Z(33)*Z(113)+2*L3*Z(34)*Z(109)-Z(386)
&*Z(113)-2*L4*Z(4)*Z(109)) - ME*(L2*Z(127)*Z(168)+L2*Z(4)*Z(117)+L2
&*Z(20)*Z(121)+L2*Z(159)*Z(125)+L2*Z(167)*Z(128)-L6*Z(127)*Z(172)-L
&6*Z(4)*Z(109)-L6*Z(6)*Z(121)-L6*Z(163)*Z(125)-L6*Z(171)*Z(128)) -
&MG*(L2*Z(4)*Z(117)+L2*Z(20)*Z(121)+L2*Z(159)*Z(125)+L6*Z(82)*Z(141
&)+L6*Z(84)*Z(142)-L2*Z(77)*Z(141)-L2*Z(79)*Z(142)-L6*Z(4)*Z(109)-L
&6*Z(6)*Z(121)-L6*Z(163)*Z(125)) - MF*(L2*Z(130)*Z(168)+L2*Z(133)*Z
&(184)+L2*Z(4)*Z(117)+L2*Z(20)*Z(121)+L2*Z(159)*Z(125)+L2*Z(167)*Z(
&131)+L2*Z(183)*Z(135)-L6*Z(130)*Z(172)-L6*Z(133)*Z(188)-L6*Z(4)*Z(
&109)-L6*Z(6)*Z(121)-L6*Z(163)*Z(125)-L6*Z(171)*Z(131)-L6*Z(187)*Z(
&135))
Z(403) = MC*(L6*Z(4)*Z(109)+L6*Z(6)*Z(119)-L2*Z(4)*Z(117)-L2*Z(20)
&*Z(119)-L7*Z(6)*Z(117)-L7*Z(19)*Z(109)) + MD*(L6*Z(4)*Z(109)+L6*Z(
&6)*Z(121)+L6*Z(163)*Z(123)+L8*Z(8)*Z(123)-L2*Z(4)*Z(117)-L2*Z(20)*
&Z(121)-L2*Z(159)*Z(123)-L8*Z(6)*Z(117)-L8*Z(19)*Z(109)) + MG*(L2*Z
&(77)*Z(141)+L2*Z(79)*Z(142)+L6*Z(4)*Z(109)+L6*Z(6)*Z(121)+L6*Z(163
&)*Z(125)+L8*Z(8)*Z(125)-L2*Z(4)*Z(117)-L2*Z(20)*Z(121)-L2*Z(159)*Z
&(125)-L6*Z(82)*Z(141)-L6*Z(84)*Z(142)-L8*Z(6)*Z(117)-L8*Z(19)*Z(10
&9)-L8*Z(21)*Z(142)-L8*Z(23)*Z(141)) - 0.25D0*MB*(Z(385)*Z(112)+2*L
&2*Z(4)*Z(112)+2*L2*Z(33)*Z(113)+2*L3*Z(34)*Z(109)-Z(386)*Z(113)-2*
&L4*Z(4)*Z(109)) - ME*(L2*Z(127)*Z(168)+L2*Z(4)*Z(117)+L2*Z(20)*Z(1
&21)+L2*Z(159)*Z(125)+L2*Z(167)*Z(128)+L8*Z(6)*Z(117)+L8*Z(19)*Z(10
&9)-L6*Z(127)*Z(172)-L8*Z(127)*Z(176)-L6*Z(4)*Z(109)-L6*Z(6)*Z(121)
&-L6*Z(163)*Z(125)-L6*Z(171)*Z(128)-L8*Z(8)*Z(125)-L8*Z(175)*Z(128)
&) - MF*(L2*Z(130)*Z(168)+L2*Z(133)*Z(184)+L2*Z(4)*Z(117)+L2*Z(20)*
&Z(121)+L2*Z(159)*Z(125)+L2*Z(167)*Z(131)+L2*Z(183)*Z(135)+L8*Z(6)*
&Z(117)+L8*Z(19)*Z(109)-L6*Z(130)*Z(172)-L6*Z(133)*Z(188)-L8*Z(130)
&*Z(176)-L8*Z(133)*Z(192)-L6*Z(4)*Z(109)-L6*Z(6)*Z(121)-L6*Z(163)*Z
&(125)-L6*Z(171)*Z(131)-L6*Z(187)*Z(135)-L8*Z(8)*Z(125)-L8*Z(175)*Z
&(131)-L8*Z(191)*Z(135))
Z(406) = MC*(L6*Z(4)*Z(109)+L6*Z(6)*Z(119)-L2*Z(4)*Z(117)-L2*Z(20)
&*Z(119)-L7*Z(6)*Z(117)-L7*Z(19)*Z(109)) + MG*(L10*Z(162)*Z(117)+L2
&*Z(77)*Z(141)+L2*Z(79)*Z(142)+L6*Z(4)*Z(109)+L6*Z(6)*Z(121)+L6*Z(1
&63)*Z(125)+L8*Z(8)*Z(125)-L10*Z(8)*Z(121)-L10*Z(9)*Z(142)-L10*Z(10
&)*Z(141)-L10*Z(158)*Z(109)-L2*Z(4)*Z(117)-L2*Z(20)*Z(121)-L2*Z(159
&)*Z(125)-L6*Z(82)*Z(141)-L6*Z(84)*Z(142)-L8*Z(6)*Z(117)-L8*Z(19)*Z
&(109)-L8*Z(21)*Z(142)-L8*Z(23)*Z(141)) - 0.25D0*MB*(Z(385)*Z(112)+
&2*L2*Z(4)*Z(112)+2*L2*Z(33)*Z(113)+2*L3*Z(34)*Z(109)-Z(386)*Z(113)
&-2*L4*Z(4)*Z(109)) - MD*(L2*Z(4)*Z(117)+L2*Z(20)*Z(121)+L2*Z(159)*
&Z(123)+L8*Z(6)*Z(117)+L8*Z(19)*Z(109)+L9*Z(8)*Z(121)+L9*Z(158)*Z(1
&09)-L6*Z(4)*Z(109)-L6*Z(6)*Z(121)-L6*Z(163)*Z(123)-L8*Z(8)*Z(123)-
&L9*Z(162)*Z(117)) - ME*(L2*Z(127)*Z(168)+L10*Z(8)*Z(121)+L10*Z(158
&)*Z(109)+L2*Z(4)*Z(117)+L2*Z(20)*Z(121)+L2*Z(159)*Z(125)+L2*Z(167)
&*Z(128)+L8*Z(6)*Z(117)+L8*Z(19)*Z(109)-L10*Z(127)*Z(180)-L6*Z(127)
&*Z(172)-L8*Z(127)*Z(176)-L10*Z(162)*Z(117)-L10*Z(179)*Z(128)-L6*Z(
&4)*Z(109)-L6*Z(6)*Z(121)-L6*Z(163)*Z(125)-L6*Z(171)*Z(128)-L8*Z(8)
&*Z(125)-L8*Z(175)*Z(128)) - MF*(L2*Z(130)*Z(168)+L2*Z(133)*Z(184)+
&L10*Z(8)*Z(121)+L10*Z(158)*Z(109)+L2*Z(4)*Z(117)+L2*Z(20)*Z(121)+L
&2*Z(159)*Z(125)+L2*Z(167)*Z(131)+L2*Z(183)*Z(135)+L8*Z(6)*Z(117)+L
&8*Z(19)*Z(109)-L10*Z(130)*Z(180)-L10*Z(133)*Z(196)-L6*Z(130)*Z(172
&)-L6*Z(133)*Z(188)-L8*Z(130)*Z(176)-L8*Z(133)*Z(192)-L10*Z(162)*Z(
&117)-L10*Z(179)*Z(131)-L10*Z(195)*Z(135)-L6*Z(4)*Z(109)-L6*Z(6)*Z(
&121)-L6*Z(163)*Z(125)-L6*Z(171)*Z(131)-L6*Z(187)*Z(135)-L8*Z(8)*Z(
&125)-L8*Z(175)*Z(131)-L8*Z(191)*Z(135))
Z(425) = Z(303) - Z(340)
Z(426) = Z(305) - Z(346)
Z(428) = Z(314) - 0.5D0*Z(393)
Z(429) = Z(315) - Z(399)
Z(430) = Z(316) - Z(403)
Z(431) = Z(317) - Z(406)
Z(435) = HTOR + Z(152) + Z(153) + Z(154) + Z(56)*VRX*Z(26) + Z(56)
&*VRY*Z(27) + Z(57)*VRX*Z(45) + Z(57)*VRY*Z(46) + Z(58)*VRX*Z(49) +
& Z(58)*VRY*Z(47) + Z(59)*VRX*Z(52) + Z(59)*VRY*Z(53) + Z(60)*VRY*Z
&(1) + 0.5D0*Z(55)*VRX*Z(41) + 0.5D0*Z(55)*VRY*Z(42) + 0.5D0*Z(61)*
&VRX*Z(37) + 0.5D0*Z(61)*VRY*Z(38) - MTOR - Z(306)*Z(31) - Z(54)*VR
&X*Z(30) - Z(54)*VRY*Z(31) - Z(60)*VRX*Z(2) - L2*(RX2*Z(30)+RY2*Z(3
&1)) - Z(147)*(L2*Z(31)-L6*Z(42)-L7*Z(27)) - 0.5D0*Z(146)*(2*L2*Z(3
&1)-L3*Z(38)-L4*Z(42)) - Z(148)*(L2*Z(31)-L6*Z(42)-L8*Z(27)-L9*Z(46
&)) - Z(149)*(L2*Z(31)-L10*Z(46)-L6*Z(42)-L8*Z(27)-Z(17)*Z(47)) - Z
&(151)*(L2*Z(31)-L10*Z(46)-L6*Z(42)-L8*Z(27)-GS*Z(1)) - Z(150)*(L2*
&Z(31)-L10*Z(46)-L10*Z(47)-L12*Z(53)-L6*Z(42)-L8*Z(27)) - Z(387)
COEF(1,1) = -MT
COEF(1,2) = 0
COEF(1,3) = -Z(334)
COEF(1,4) = -Z(336)
COEF(1,5) = -Z(337)
COEF(1,6) = -Z(338)
COEF(1,7) = -Z(339)
COEF(2,1) = 0
COEF(2,2) = -MT
COEF(2,3) = -Z(341)
COEF(2,4) = -Z(342)
COEF(2,5) = -Z(343)
COEF(2,6) = -Z(344)
COEF(2,7) = -Z(345)
COEF(3,1) = -Z(334)
COEF(3,2) = -Z(341)
COEF(3,3) = -Z(378)
COEF(3,4) = -Z(380)
COEF(3,5) = -Z(382)
COEF(3,6) = -Z(383)
COEF(3,7) = -Z(384)
COEF(4,1) = -Z(336)
COEF(4,2) = -Z(342)
COEF(4,3) = -Z(380)
COEF(4,4) = -Z(388)
COEF(4,5) = -Z(390)
COEF(4,6) = -Z(391)
COEF(4,7) = -Z(392)
COEF(5,1) = -Z(337)
COEF(5,2) = -Z(343)
COEF(5,3) = -Z(382)
COEF(5,4) = -Z(390)
COEF(5,5) = -Z(396)
COEF(5,6) = -Z(397)
COEF(5,7) = -Z(398)
COEF(6,1) = -Z(338)
COEF(6,2) = -Z(344)
COEF(6,3) = -Z(383)
COEF(6,4) = -Z(391)
COEF(6,5) = -Z(397)
COEF(6,6) = -Z(401)
COEF(6,7) = -Z(402)
COEF(7,1) = -Z(339)
COEF(7,2) = -Z(345)
COEF(7,3) = -Z(384)
COEF(7,4) = -Z(392)
COEF(7,5) = -Z(398)
COEF(7,6) = -Z(402)
COEF(7,7) = -Z(405)
RHS(1) = -Z(425)
RHS(2) = -Z(426)
RHS(3) = -Z(435)
RHS(4) = -Z(428)
RHS(5) = -Z(429)
RHS(6) = -Z(430)
RHS(7) = -Z(431)
CALL SOLVE(7,COEF,RHS,VARp)
C** Update variables after uncoupling equations
U1p = VARp(1)
U2p = VARp(2)
U3p = VARp(3)
U4p = VARp(4)
U5p = VARp(5)
U6p = VARp(6)
U7p = VARp(7)
C** Update derivative array prior to integration step
VARp(1) = Q1p
VARp(2) = Q2p
VARp(3) = Q3p
VARp(4) = Q4p
VARp(5) = Q5p
VARp(6) = Q6p
VARp(7) = Q7p
VARp(8) = U1p
VARp(9) = U2p
VARp(10) = U3p
VARp(11) = U4p
VARp(12) = U5p
VARp(13) = U6p
VARp(14) = U7p
RETURN
END
C**********************************************************************
SUBROUTINE IO(T)
IMPLICIT DOUBLE PRECISION (A - Z)
INTEGER ILOOP,NACTP
PARAMETER (NACTP=10)
DIMENSION HEACTP(NACTP),HFACTP(NACTP),KEACTP(NACTP),KFACTP(
&NACTP),AEACTP(NACTP),AFACTP(NACTP)
COMMON/CONSTNTS/ FOOTANG,G,IA,IB,IC,ID,IE,IF,IG,K1,K2,K3,K4,K5,K6,
&K7,K8,L1,L10,L11,L12,L2,L3,L4,L5,L6,L7,L8,L9,MA,MB,MC,MD,ME,MF,MG,
&MTPB,MTPK,POP1XI,POP2XI
COMMON/VARIBLES/ Q1,Q2,Q3,Q4,Q5,Q6,Q7,U1,U2,U3,U4,U5,U6,U7
COMMON/ALGBRAIC/ AANG,AANGVEL,AETOR,AFTOR,ATOR,COP,GRF,HANG,HANGVE
&L,HETOR,HFTOR,HTOR,HZ,KANG,KANGVEL,KECM,KETOR,KFTOR,KTOR,MANG,MANG
&VEL,METOR,MFTOR,MTOR,PECM,PX,PY,RX,RX1,RX2,RY,RY1,RY2,SHANG,SHANGV
&EL,SHTOR,SKANG,SKANGVEL,SKTOR,TE,U8,U9,VRX,VRY,Q1p,Q2p,Q3p,Q4p,Q5p
&,Q6p,Q7p,U1p,U2p,U3p,U4p,U5p,U6p,U7p,AEACT,AECCANG,AECCANGVEL,AESE
&CANG,AESECANGVEL,AFACT,AFCCANG,AFCCANGVEL,AFSECANG,AFSECANGVEL,EA,
&FA,GS,HEACT,HECCANG,HECCANGVEL,HESECANG,HESECANGVEL,HFACT,HFCCANG,
&HFCCANGVEL,HFSECANG,HFSECANGVEL,KEACT,KECCANG,KECCANGVEL,KESECANG,
&KESECANGVEL,KFACT,KFCCANG,KFCCANGVEL,KFSECANG,KFSECANGVEL,MEACT,ME
&CCANG,MECCANGVEL,MESECANG,MESECANGVEL,MFACT,MFCCANG,MFCCANGVEL,MFS
&ECANG,MFSECANGVEL,EAp,FAp,GSp,EApp,FApp,GSpp,DP1X,DP2X,MT,POCMSTAN
&CEX,POCMSTANCEY,POCMSWINGX,POCMSWINGY,POCMX,POCMY,POGOX,POGOY,POP1
&X,POP1Y,POP2X,POP2Y,POP3X,POP3Y,POP4X,POP4Y,POP5X,POP5Y,POP6X,POP6
&Y,POP7X,POP7Y,POP8X,POP8Y,POP9X,POP9Y,PSTANCEX,PSTANCEY,PSWINGX,PS
&WINGY,VOCMSTANCEX,VOCMSTANCEY,VOCMSWINGX,VOCMSWINGY,VOCMX,VOCMY,VO
&P2X,VOP2Y
COMMON/MISCLLNS/ PI,DEGtoRAD,RADtoDEG,Z(435),COEF(7,7),RHS(7)
COMMON/ACTPARAM/ HEACTP,HFACTP,KEACTP,KFACTP,AEACTP,AFACTP
C** Evaluate output quantities
RX = RX1 + RX2
RY = RY1 + RY2
GRF = SQRT(RX**2+RY**2)
IF (GRF .GT. 0.0D0) THEN
COP = (Q1*RY1+RY2*POP2X)/GRF
ELSE
COP = 0.0D0
ENDIF
KECM = 0.5D0*IG*U3**2 + 0.5D0*ID*(U3-U7)**2 + 0.5D0*IC*(U3-U6-U7)*
&*2 + 0.5D0*IE*(EAp-U3-U8)**2 + 0.5D0*IB*(U3-U5-U6-U7)**2 + 0.5D0*I
&A*(U3-U4-U5-U6-U7)**2 + 0.5D0*IF*(EAp-FAp-U3-U8-U9)**2 + 0.5D0*MC*
&(U1**2+U2**2+L7**2*(U3-U6-U7)**2+2*L7*Z(26)*U1*(U3-U6-U7)+2*L7*Z(2
&7)*U2*(U3-U6-U7)+L6**2*(U3-U5-U6-U7)**2+2*L6*Z(41)*U1*(U3-U5-U6-U7
&)+2*L6*Z(42)*U2*(U3-U5-U6-U7)+L2**2*(U3-U4-U5-U6-U7)**2+2*L6*L7*Z(
&5)*(U3-U6-U7)*(U3-U5-U6-U7)-2*L2*Z(30)*U1*(U3-U4-U5-U6-U7)-2*L2*Z(
&31)*U2*(U3-U4-U5-U6-U7)-2*L2*L7*Z(18)*(U3-U6-U7)*(U3-U4-U5-U6-U7)-
&2*L2*L6*Z(3)*(U3-U5-U6-U7)*(U3-U4-U5-U6-U7)) + 0.125D0*MB*(4*U1**2
&+4*U2**2+L3**2*(U3-U5-U6-U7)**2+L4**2*(U3-U5-U6-U7)**2+4*L3*Z(37)*
&U1*(U3-U5-U6-U7)+4*L3*Z(38)*U2*(U3-U5-U6-U7)+4*L4*Z(41)*U1*(U3-U5-
&U6-U7)+4*L4*Z(42)*U2*(U3-U5-U6-U7)+2*L3*L4*Z(15)*(U3-U5-U6-U7)**2+
&4*L2**2*(U3-U4-U5-U6-U7)**2-8*L2*Z(30)*U1*(U3-U4-U5-U6-U7)-8*L2*Z(
&31)*U2*(U3-U4-U5-U6-U7)-4*L2*L3*Z(32)*(U3-U5-U6-U7)*(U3-U4-U5-U6-U
&7)-4*L2*L4*Z(3)*(U3-U5-U6-U7)*(U3-U4-U5-U6-U7)) + 0.5D0*MD*(U1**2+
&U2**2+L9**2*(U3-U7)**2+2*L9*Z(45)*U1*(U3-U7)+2*L9*Z(46)*U2*(U3-U7)
&+L8**2*(U3-U6-U7)**2+2*L8*Z(26)*U1*(U3-U6-U7)+2*L8*Z(27)*U2*(U3-U6
&-U7)+L6**2*(U3-U5-U6-U7)**2+2*L6*Z(41)*U1*(U3-U5-U6-U7)+2*L6*Z(42)
&*U2*(U3-U5-U6-U7)+L2**2*(U3-U4-U5-U6-U7)**2+2*L8*L9*Z(7)*(U3-U7)*(
&U3-U6-U7)+2*L6*L9*Z(164)*(U3-U7)*(U3-U5-U6-U7)+2*L6*L8*Z(5)*(U3-U6
&-U7)*(U3-U5-U6-U7)-2*L2*Z(30)*U1*(U3-U4-U5-U6-U7)-2*L2*Z(31)*U2*(U
&3-U4-U5-U6-U7)-2*L2*L9*Z(160)*(U3-U7)*(U3-U4-U5-U6-U7)-2*L2*L8*Z(1
&8)*(U3-U6-U7)*(U3-U4-U5-U6-U7)-2*L2*L6*Z(3)*(U3-U5-U6-U7)*(U3-U4-U
&5-U6-U7)) + 0.5D0*ME*(U1**2+U2**2+L10**2*(U3-U7)**2+2*L10*Z(45)*U1
&*(U3-U7)+2*L10*Z(46)*U2*(U3-U7)+(Z(97)-Z(17)*U3-Z(17)*U8)**2+L8**2
&*(U3-U6-U7)**2+2*L8*Z(26)*U1*(U3-U6-U7)+2*L8*Z(27)*U2*(U3-U6-U7)+L
&6**2*(U3-U5-U6-U7)**2+2*L6*Z(41)*U1*(U3-U5-U6-U7)+2*L6*Z(42)*U2*(U
&3-U5-U6-U7)+L2**2*(U3-U4-U5-U6-U7)**2+2*L10*L8*Z(7)*(U3-U7)*(U3-U6
&-U7)+2*L10*L6*Z(164)*(U3-U7)*(U3-U5-U6-U7)+2*L6*L8*Z(5)*(U3-U6-U7)
&*(U3-U5-U6-U7)+2*L2*Z(168)*(Z(97)-Z(17)*U3-Z(17)*U8)*(U3-U4-U5-U6-
&U7)-2*Z(47)*U2*(Z(97)-Z(17)*U3-Z(17)*U8)-2*Z(49)*U1*(Z(97)-Z(17)*U
&3-Z(17)*U8)-2*L2*Z(30)*U1*(U3-U4-U5-U6-U7)-2*L2*Z(31)*U2*(U3-U4-U5
&-U6-U7)-2*L10*Z(180)*(U3-U7)*(Z(97)-Z(17)*U3-Z(17)*U8)-2*L8*Z(176)
&*(U3-U6-U7)*(Z(97)-Z(17)*U3-Z(17)*U8)-2*L10*L2*Z(160)*(U3-U7)*(U3-
&U4-U5-U6-U7)-2*L6*Z(172)*(Z(97)-Z(17)*U3-Z(17)*U8)*(U3-U5-U6-U7)-2
&*L2*L8*Z(18)*(U3-U6-U7)*(U3-U4-U5-U6-U7)-2*L2*L6*Z(3)*(U3-U5-U6-U7
&)*(U3-U4-U5-U6-U7)) + 0.5D0*MG*(GSp**2+U1**2+U2**2+2*GSp*Z(1)*U1+2