diff --git a/.github/workflows/makefile.yml b/.github/workflows/makefile.yml index 62e45bf..abfb949 100644 --- a/.github/workflows/makefile.yml +++ b/.github/workflows/makefile.yml @@ -16,5 +16,7 @@ jobs: sudo apt-get install libblas-dev liblapack-dev - name: checkout repo uses: actions/checkout@v3 - - name: build application - run: make + - name: build shooting + run: | + cd shooting + make diff --git a/README.md b/README.md index 4bd79da..dafeee5 100644 --- a/README.md +++ b/README.md @@ -2,3 +2,7 @@ [![CI](https://github.com/djps/homoclinic-orbits/actions/workflows/makefile.yml/badge.svg)](https://github.com/djps/homoclinic-orbits/actions/workflows/makefile.yml) Shooting and continuation of homoclinic orbits as localised solutions of cosserat rods. + +There are two directories: shooting and continutation. + +The continuation software `auto07` must be installed from github: [here](https://github.com/auto-07p/auto-07p) in order to generate bifurcation diagrams. diff --git a/continuation/Makefile b/continuation/Makefile new file mode 100644 index 0000000..923e547 --- /dev/null +++ b/continuation/Makefile @@ -0,0 +1,102 @@ +# +# Makefile +# +PGM = mag +FC = gfortran +FFLAGS = -O +SRC = $(PGM).f +EXE = $(PGM).exe +LIBS = $(AUTO_DIR)/lib/*.o +RM = rm -f +# +all: clean $(EXE) run +# +$(EXE): $(SRC:.f=.o) + $(FC) $(FFLAGS) $(SRC:.f=.o) -o $@ $(LIBS) +# +run: first +# +first: $(EXE) + @echo " " + @echo "Program $(PGM) is started" + @echo " " + @cp $(AUTO_DIR)/include/fcon.h fcon.h + @echo "Starting conversion of $(PGM).dat : " + @echo "(Required files : $(PGM).f, r.$(PGM), $(PGM).dat)" + @f77 $(AUTO_DIR)/src/fcon.f $(PGM).f -o fcon $(AUTO_DIR)/lib/nag.o $(AUTO_DIR)/lib/eispack.o + @cp r.$(PGM) fort.2 + @cp $(PGM).dat fort.3 + @fcon + @mv fort.8 q.dat + @rm fcon* fort.2 fort.3 + @echo " Conversion done : converted file saved as q.dat" + @echo " " + @echo "$(PGM) : first run" + @cp r.$(PGM).1 fort.2 + @cp q.dat fort.3 + @touch fort.3 + @cp $(PGM).dat fort.4 + @$(EXE) + @cp fort.7 p.$(PGM) + @cp fort.8 q.$(PGM) + @cp fort.9 d.$(PGM) + @cp fort.8 t.$(PGM) + @echo " " + @echo " Appended to *.$(PGM)" +# +second: $(EXE) + @echo " " + @echo "$(PGM) : second run" + @cp r.$(PGM).2 fort.2 + @cp t.$(PGM) fort.3 + @$(EXE) + @cp fort.7 p.$(PGM).2 + @cp fort.8 q.$(PGM).2 + @cp fort.9 d.$(PGM).2 + @echo " Appended to *.$(PGM)" + @$(RM) fort.* + @echo " " +# +third: $(EXE) + @echo " " + @echo "$(PGM) : third run " + @cp r.$(PGM).3 fort.2 + @cp t.$(PGM) fort.3 + @$(EXE) + @cp fort.7 p.$(PGM).3 + @cp fort.8 q.$(PGM).3 + @cp fort.9 d.$(PGM).3 + @echo " Appended to *.$(PGM)" + @echo " " +# +fourth: $(EXE) + @echo " " + @echo "$(PGM) : forth run " + @cp r.$(PGM).4 fort.2 + @cp q.$(PGM) fort.3 + @$(EXE) + @cat fort.7 >> p.$(PGM) + @cat fort.8 >> q.$(PGM) + @cat fort.9 >> d.$(PGM) + @echo " Appended to *.$(PGM)" + @echo " " +# +fifth: $(EXE) + @echo " " + @echo "$(PGM) : fifth run : Limit Point Continuation with kappa, rho" + @cp r.$(PGM).5 fort.2 + @cp q.$(PGM) fort.3 + @$(EXE) + @cp fort.7 p.$(PGM).2 + @cp fort.8 q.$(PGM).2 + @cp fort.9 d.$(PGM).2 + @echo " Appended to *.$(PGM)" + @echo " " +# +clean: + @echo "Cleaning $(PGM) ..." + @cp $(SRC) $(EXE) +# @$(RM) *.exe *.o p.* q.* d.* fort.* *~ core + @$(RM) *.exe *.o p.* q.* d.* *~ core + @cp r.$(PGM).1 r.$(PGM) + @echo "Cleaning ... done" diff --git a/continuation/extensibility/Makefile b/continuation/extensibility/Makefile new file mode 100644 index 0000000..18d8b13 --- /dev/null +++ b/continuation/extensibility/Makefile @@ -0,0 +1,164 @@ +# +# Makefile +# +PGM = ext +FC = gfortran +FFLAGS = -O +SRC = $(PGM).f +EXE = $(PGM).exe +LIBS = $(AUTO_DIR)/lib/*.o +RM = rm -f +# +all: clean $(EXE) run +# +$(EXE): $(SRC:.f=.o) + $(FC) $(FFLAGS) $(SRC:.f=.o) -o $@ $(LIBS) +# +run: first second third +# +first: $(EXE) + @echo " " + @echo "Program $(PGM) is started" + @echo " " + @cp $(AUTO_DIR)/include/fcon.h fcon.h + @echo "Starting conversion of $(PGM).dat : " + @echo "(Required files : $(PGM).f, r.$(PGM), $(PGM).dat)" + @f77 $(AUTO_DIR)/src/fcon.f $(PGM).f -o fcon $(AUTO_DIR)/lib/eispack.o + @cp r.$(PGM) fort.2 + @cp $(PGM).dat fort.3 + @fcon + @mv fort.8 q.dat + @rm fcon* fort.2 fort.3 + @echo " Conversion done : converted file saved as q.dat" + @echo " " + @echo "$(PGM) : first run" + @cp r.$(PGM).1 fort.2 + @cp q.dat fort.3 + @touch fort.3 + @cp $(PGM).dat fort.4 + @$(EXE) + @cp fort.7 p.$(PGM).1 + @cp fort.8 q.$(PGM).1 + @cp fort.9 d.$(PGM).1 + @cp q.$(PGM).1 t.$(PGM).1 + @echo " Saved as *.$(PGM)" + @$(RM) fort.* + @echo " Appended to *.$(PGM)" +# +second: $(EXE) + @echo " " + @echo "$(PGM) : second run" + @cp r.$(PGM).2 fort.2 + @cp q.$(PGM).1 fort.3 + @$(EXE) + @cp fort.7 p.$(PGM).2 + @cp fort.8 q.$(PGM).2 + @cp fort.9 d.$(PGM).2 + @cp q.$(PGM).2 t.$(PGM).2 + @echo " Appended to *.$(PGM)" + @$(RM) fort.* +# +third: $(EXE) + @echo " " + @echo "$(PGM) : third run" + @cp r.$(PGM).3 fort.2 + @cp q.$(PGM).2 fort.3 + @$(EXE) + @cp fort.7 p.$(PGM).3 + @cp fort.8 q.$(PGM).3 + @cp fort.9 d.$(PGM).3 + @cp q.$(PGM).3 t.$(PGM).3 + @echo " Appended to *.$(PGM)" + @$(RM) fort.* +# +fourth: $(EXE) + @echo " " + @echo "$(PGM) : fourth run" + @cp r.$(PGM).4 fort.2 + @cp t.$(PGM) fort.3 + @$(EXE) + @cat fort.7 >> p.$(PGM) + @cat fort.8 >> q.$(PGM) + @cat fort.9 >> d.$(PGM) + @cp q.$(PGM) t.$(PGM).1 + @echo " Appended to *.$(PGM)" + @$(RM) fort.* +# +fifth: $(EXE) + @echo " " + @echo "$(PGM) : fifth run" + @cp r.$(PGM).5 fort.2 + @cp t.$(PGM).1 fort.3 + @$(EXE) + @cp fort.7 p.$(PGM).5 + @cp fort.8 q.$(PGM).5 + @cp fort.9 d.$(PGM).5 + @echo " Appended to *.$(PGM)" + @$(RM) fort.* +# +sixth: $(EXE) + @echo " " + @echo "$(PGM) : sixth run" + @cp r.$(PGM).6 fort.2 + @cp t.$(PGM).1 fort.3 + @$(EXE) + @cat fort.7 >> p.$(PGM).5 + @cat fort.8 >> q.$(PGM).5 + @cat fort.9 >> d.$(PGM).5 + @echo " Appended to *.$(PGM)" + @$(RM) fort.* +# +seventh:$(EXE) + @echo " " + @echo "$(PGM) : seventh run" + @cp r.$(PGM).7 fort.2 + @cp t.$(PGM).1 fort.3 + @$(EXE) + @cp fort.7 p.$(PGM).7 + @cp fort.8 q.$(PGM).7 + @cp fort.9 d.$(PGM).7 + @echo " Appended to *.$(PGM)" + @$(RM) fort.* +# +eighth:$(EXE) + @echo " " + @echo "$(PGM) : eighth run" + @cp r.$(PGM).8 fort.2 + @cp t.$(PGM).1 fort.3 + @$(EXE) + @cat fort.7 >> p.$(PGM).7 + @cat fort.8 >> q.$(PGM).7 + @cat fort.9 >> d.$(PGM).7 + @echo " Appended to *.$(PGM)" + @$(RM) fort.* +# +ninth:$(EXE) + @echo " " + @echo "$(PGM) : ninth run" + @cp r.$(PGM).9 fort.2 + @cp t.$(PGM).1 fort.3 + @$(EXE) + @cp fort.7 p.$(PGM).9 + @cp fort.8 q.$(PGM).9 + @cp fort.9 d.$(PGM).9 + @echo " Appended to *.$(PGM)" + @$(RM) fort.* +# +tenth:$(EXE) + @echo " " + @echo "$(PGM) : tenth run" + @cp r.$(PGM).10 fort.2 + @cp t.$(PGM).1 fort.3 + @$(EXE) + @cat fort.7 >> p.$(PGM).9 + @cat fort.8 >> q.$(PGM).9 + @cat fort.9 >> d.$(PGM).9 + @echo " Appended to *.$(PGM)" + @$(RM) fort.* +# +clean: + @echo "Cleaning $(PGM) ..." + @cp $(SRC) $(EXE) + @$(RM) *.exe *.o p.* q.* d.* fort.* *~ core + @cp r.$(PGM).1 r.$(PGM) + @echo "Cleaning ... done" diff --git a/continuation/extensibility/ext.dat b/continuation/extensibility/ext.dat new file mode 100644 index 0000000..849f250 --- /dev/null +++ b/continuation/extensibility/ext.dat @@ -0,0 +1,1001 @@ + 0.0000000000E+00 -0.5582901121E-05 -0.2246498147E-05 0.1000000000E+01 -0.3603375013E-05 0.8945108541E-06 0.1000000000E+01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1000000000E+01 0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 + 0.1000000000E-02 -0.5720102818E-05 -0.2106952362E-05 0.1000000000E+01 -0.3621541529E-05 0.1013870884E-05 0.1000000000E+01 -0.6425918468E-07 0.1696549263E-07 0.2371271540E-01 0.9997188140E+00 0.6102468437E-09 0.2522263329E-08 0.3912964804E-01 + 0.2000000000E-02 -0.5854829217E-05 -0.1961543840E-05 0.1000000000E+01 -0.3636351498E-05 0.1135267666E-05 0.1000000000E+01 -0.1288264558E-06 0.3605510058E-07 0.4741209543E-01 0.9988754143E+00 0.2390938441E-08 0.1014670128E-07 0.7825929609E-01 + 0.3000000000E-02 -0.5986873373E-05 -0.1810273645E-05 0.1000000000E+01 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-0.6908443476E+00 0.1000000000E+01 -0.3845936338E+00 0.4187201101E+00 -0.6266477888E+00 0.5329856987E+00 -0.2274529361E+00 -0.1984495397E+01 0.3702762995E+02 + 0.1000000000E+01 0.9710051208E-09 -0.9354671769E+00 0.3534135836E+00 0.4441625303E-09 -0.6911909177E+00 0.1000000000E+01 -0.3821351359E+00 0.4210266602E+00 -0.6091340602E+00 0.5528697731E+00 -0.1932093732E+00 -0.1988274302E+01 0.3704064753E+02 diff --git a/continuation/extensibility/ext.f b/continuation/extensibility/ext.f new file mode 100644 index 0000000..4d9a524 --- /dev/null +++ b/continuation/extensibility/ext.f @@ -0,0 +1,303 @@ +C---------------------------------------------------------------------- +C---------------------------------------------------------------------- +C ext : Non-Dimensional Formulation of a Cosserat rod under +C uniform dimensionless load parameter from a given homoclinic +C solution using Euler Parameters. +C---------------------------------------------------------------------- +C---------------------------------------------------------------------- +C + SUBROUTINE FUNC(NDIM,U,ICP,PAR,IJAC,F,DFDU,DFDP) +C ---------- ---- +C + IMPLICIT DOUBLE PRECISION (A-H,O-Z) + DIMENSION U(NDIM),PAR(*),F(NDIM) +C + F1 = U(1) + F2 = U(2) + F3 = U(3) +C + XM1 = U(4) + XM2 = U(5) + XM3 = U(6) +C + Q1 = U(7) + Q2 = U(8) + Q3 = U(9) + Q4 = U(10) +C + X = U(11) + Y = U(12) + Z = U(13) +C + xnu = PAR(1) + xrho = PAR(2) + xm = PAR(3) + xgamma = PAR(4) + xsigma = PAR(5) + xepsilon = PAR(6) + xT = PAR(7) + xD = PAR(8) + xR = PAR(9) +C + F(1) = (1.d0+xnu)*F2*XM3 - F3*XM2 + F(2) = (1.d0+xrho)*F3*XM1 - (1.d0+xnu)*F1*XM3 + F(3) = F1*XM2 - (1.d0+xrho)*F2*XM1 +C + F(4) = xnu*XM2*XM3 + F2*(1.d0+xepsilon*F3)/(xm**2.d0) + F(5) = (xrho-xnu)*XM1*XM3 - F1*(1.d0+xepsilon*F3)/(xm**2.d0) + F(6) =-xrho*XM1*XM2 +C + F(7) = 0.5*(+(1.d0+xrho)*XM1*Q4-XM2*Q3+(1.d0+xnu)*XM3*Q2) + F(8) = 0.5*(+(1.d0+xrho)*XM1*Q3+XM2*Q4-(1.d0+xnu)*XM3*Q1) + F(9) = 0.5*(-(1.d0+xrho)*XM1*Q2+XM2*Q1+(1.d0+xnu)*XM3*Q4) + F(10) = 0.5*(-(1.d0+xrho)*XM1*Q1-XM2*Q2-(1.d0+xnu)*XM3*Q3) +C + F(11) = (1.d0+xepsilon*F3)*2.d0*(Q1*Q3 + Q2*Q4) +C + F(12) = (1.d0+xepsilon*F3)*2.d0*(Q2*Q3 - Q1*Q4) +C + F(13) = (1.d0+xepsilon*F3)*(Q3**2.d0+Q4**2.d0-Q1**2.d0-Q2**2.d0) +C + do i = 1,NDIM + F(i) = xT*F(i) + end do +C + RETURN + END +C + SUBROUTINE STPNT(NDIM,U,PAR,S) +C ---------- ---- +C + IMPLICIT DOUBLE PRECISION (A-H,O-Z) + DIMENSION U(NDIM),PAR(*) +C + open(unit=1,file='parameters.dat') + read(1,*) (PAR(i), i=1,9) + close(1) +C + + RETURN + END +C + SUBROUTINE BCND(NDIM,PAR,ICP,NBC,U0,U1,FB,IJAC,DBC) +C ---------- ---- +C + IMPLICIT DOUBLE PRECISION (A-H,O-Z) + PARAMETER (n=6) + DIMENSION PAR(*),ICP(*),U0(NDIM),U1(NDIM),FB(NBC) + DIMENSION z(n,n),vr(n,n),vi(n,n),vrdum(n,n),vidum(n,n) + DIMENSION wrdum(n),widum(n),wr(n),wi(n),fv1(n),iv1(n) + DIMENSION xnorm(n), V(n,n), c(n,n), a(n,n), xI(4), xI1(4) +C + xnu = PAR(1) + xrho = PAR(2) + xm = PAR(3) + xgamma = PAR(4) + xsigma = PAR(5) + xepsilon = PAR(6) + xT = PAR(7) + xD = PAR(8) + xR = PAR(9) +C + matz = 1 + zero = 0.00000001 + pi = 4.d0*datan(1.d0) + do i = 1,n + wrdum(i) = 0.d0 + widum(i) = 0.d0 + xnorm(i) = 0.d0 + do j = 1,n + c(i,j) = 0.d0 + a(i,j) = 0.d0 + vr(i,j) = 0.d0 + vi(i,j) = 0.d0 + vrdum(i,j) = 0.d0 + vidum(i,j) = 0.d0 + end do + end do +C + c(1,2) = (1.d0+xnu) + c(1,5) =-1.d0 + c(2,1) =-(1.d0+xnu) + c(2,4) = (1.d0+xrho) + c(4,2) = (1.d0+xepsilon)/(xm**2.d0) + c(4,5) = xnu + c(5,1) =-(1.d0+xepsilon)/(xm**2.d0) + c(5,4) = xrho - xnu +C + do i = 1,n + do j = 1,n + a(i,j) = c(j,i) + end do + end do +C + call rg(n,n,a,wr,wi,matz,z,iv1,fv1,ierr) + if ( ierr.ne.0 ) then + print*, "failure in eigenvalue, eigenvector solver" + end if +C +C Convert output z into matrices of real and imaginary parts of eigenvectors. +C + iflag = 0 + do i = 1,n + if ( wi(i+iflag).eq.0.d0 ) then + do j = 1,n + vr(j,i+iflag) = z(j,i+iflag) + vi(j,i+iflag) = 0.d0 + end do + else if ( abs(wi(i+iflag)).eq.abs(wi(i+iflag+1)) ) then + do j = 1,n + vr(j,i+iflag) = z(j,i+iflag) + vr(j,i+iflag+1) = z(j,i+iflag) + vi(j,i+iflag) = z(j,i+iflag+1) + vi(j,i+iflag+1) =-z(j,i+iflag+1) + end do + iflag = 1 + iflag + end if + if ( i+iflag.eq.n ) goto 18 + end do +C +C Normalize vectors +C +18 do i = 1,n + do j = 1,n + xnorm(i) = xnorm(i) + vr(j,i)**2.d0 + vi(j,i)**2.d0 + end do + end do + do i = 1,n + do j = 1,n + vr(j,i) = vr(j,i)/dsqrt(xnorm(i)) + vi(j,i) = vi(j,i)/dsqrt(xnorm(i)) + end do + end do +C +C Order the eigenvectors/values according to the size of the real part of the +C eigenvalue. +C + do i = 1,n-1 + do j = i+1,n + if ( wr(i).gt.wr(j) ) then + wrdum(i) = wr(i) + widum(i) = wi(i) + wr(i) = wr(j) + wi(i) = wi(j) + wr(j) = wrdum(i) + wi(j) = widum(i) + do k = 1,n + vrdum(k,i) = vr(k,i) + vidum(k,i) = vi(k,i) + vr(k,i) = vr(k,j) + vi(k,i) = vi(k,j) + vr(k,j) = vrdum(k,i) + vi(k,j) = vidum(k,i) + end do + end if + end do + end do +C +C Use real and imaginary parts of complex eigenvectors +C + do i = 1,n-1 + jflag = 0 + do j = 1,n + if ( abs(vr(j,i)-vr(j,i+1)).lt.zero ) then + jflag = jflag + 1 + if ( jflag.eq.n ) then + do k = 1,n + vr(k,i+1) = vi(k,i) + end do + end if + end if + end do + end do +C +C Let V contain the stable as well as the unstable 6D eigenvectors +C + do i = 1,n + do j = 1,n + V(i,j) = 0.d0 + end do + end do + do i = 1,n + do j = 1,n + V(i,j) = vr(j,i) + end do + end do +C +C Code the boundary conditions +C + do i = 1,NBC + FB(i) = 0.d0 + end do +C +C Two Projection conditions +C + do i = 1,2 + do j = 1,n + FB(i) = FB(i) + U0(j)*V(i,j) + end do + end do +C +C Integral fixing conditions +C + FB(3) = U0(3) - 1.d0 + FB(4) = U0(6) - 1.d0 +C +C Two end point conditions in the symmetry plane, corresponding to specific +C reversibility +C + FB(5) = U1(1) + FB(6) = U1(4) +C +C The Postprocessed Euler parameters +C + FB(7) = U0(7) + FB(8) = U0(8) + FB(9) = U0(9) + FB(10) = U0(10) - 1.d0 +C +C The Centreline Equation +C + FB(11) = U0(11) + FB(12) = U0(12) + FB(13) = U0(13) +C +C Two additional parameters in order to free parameters containing the end +C displacements: the end-shortening and the end rotation. +C + short = 2.d0*( xT*(1.d0+xepsilon) - U1(13) ) + FB(14) = xD - short +C + D11 = U1(7)**2.d0 - U1(8)**2.d0 - U1(9)**2.d0 + U1(10)**2.d0 + D12 = 2.d0*( U1(7)*U1(8) + U1(9)*U1(10) ) + twopi = 2.d0*pi + if ( D11.lt.-1.d0 ) D11 = -1.d0 + if ( D11.gt.+1.d0 ) D11 = +1.d0 + xxnorm = DSQRT( D11**2.d0 + D12**2.d0) + D1_11 = D11/xxnorm + D1_12 = D12/xxnorm + if ( D1_12.gt.0.d0 ) then + rot = ( dacos(D1_11) - (1.d0 + xnu)*xT )/twopi + nsign = +1 + else + rot = ( twopi - dacos(D1_11) - (1.d0 + xnu)*xT )/twopi + nsign = -1 + end if + rotate = rot - DINT(rot) + if ( rotate.lt.0.d0 ) rotate = rotate + 1.d0 + FB(15) = xR - 2.d0*rotate +C + RETURN + END +C + SUBROUTINE ICND + RETURN + END +C + SUBROUTINE FOPT + RETURN + END +C + SUBROUTINE PVLS + RETURN + END \ No newline at end of file diff --git a/continuation/extensibility/parameters.dat b/continuation/extensibility/parameters.dat new file mode 100644 index 0000000..7886d7d --- /dev/null +++ b/continuation/extensibility/parameters.dat @@ -0,0 +1,14 @@ + 0.33333333333333E+00 0.00000000000000E+00 0.17000000000000E+01 0.00000000000000E+00 0.00000000000000E+00 0.10000000000000E+00 0.35572407313312E+02 0.41780010342088E+01 0.37179971830428E+00 0.12095786586622E+01 1 + + xnu = 0.333333333333E+00 + xrho = 0.000000000000E+00 + xm = 0.170000000000E+01 + xgamma = 0.000000000000E+00 + xsigma = 0.000000000000E+00 + xepsilon = 0.100000000000E+00 + xT = 0.355724073133E+02 + xD = 0.417800103421E+01 + xR = 0.371799718304E+00 + R = 1 + epsilon = 0.100000000000E-04 + delta = 0.590062112268E+01 diff --git a/continuation/mag.dat b/continuation/mag.dat new file mode 100644 index 0000000..74a7a4f --- /dev/null +++ b/continuation/mag.dat @@ -0,0 +1,2001 @@ + 0.0000000000E+00 0.6528217926E-07 0.8188257390E-05 0.1000000000E+01 0.2521869756E-05 0.4117996981E-05 0.1000000000E+01 -0.4897755025E-05 0.1016781233E-04 0.1000000000E+01 0.0000000000E+00 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-0.8859178433E+00 0.4638353157E+00 0.1037602443E-01 -0.6112743492E+00 0.1000000000E+01 0.1862495288E-01 -0.8940647834E+00 0.4475503037E+00 0.4060385397E+00 -0.3337007390E+00 0.5537479908E+00 -0.6458635179E+00 0.3223929717E+00 -0.1791418838E+01 0.3911481501E+02 + 0.1000000000E+01 0.1073040298E-07 -0.8861194525E+00 0.4638145757E+00 0.6505259435E-08 -0.6113741992E+00 0.1000000000E+01 0.1085447555E-07 -0.8942694526E+00 0.4475289334E+00 0.4048812743E+00 -0.3351199564E+00 0.5424590589E+00 -0.6553654995E+00 0.3403093519E+00 -0.1788139241E+01 0.3912393040E+02 diff --git a/continuation/mag.f b/continuation/mag.f new file mode 100644 index 0000000..64c50e0 --- /dev/null +++ b/continuation/mag.f @@ -0,0 +1,395 @@ +C---------------------------------------------------------------------- +C---------------------------------------------------------------------- +C mag : Non-Dimensional Formulation of a Cosserat rod under +C uniform dimensionless load parameter in a magnetic field +C from a given homoclinic solution using Euler Parameters. +C---------------------------------------------------------------------- +C---------------------------------------------------------------------- +C + SUBROUTINE FUNC(NDIM,U,ICP,PAR,IJAC,F,DFDU,DFDP) +C ---------- ---- +C + IMPLICIT DOUBLE PRECISION (A-H,O-Z) + DIMENSION U(NDIM),PAR(*),F(NDIM) +C + F1 = U(1) + F2 = U(2) + F3 = U(3) +C + XM1 = U(4) + XM2 = U(5) + XM3 = U(6) +C + E31 = U(7) + E32 = U(8) + E33 = U(9) +C + Q1 = U(10) + Q2 = U(11) + Q3 = U(12) + Q4 = U(13) +C + X = U(14) + Y = U(15) + Z = U(16) +C + xnu = PAR(1) + xrho = PAR(2) + xm = PAR(3) + xlambda = PAR(4) + xepsilon = PAR(5) + xT = PAR(6) + xD = PAR(7) + xR = PAR(8) +C +C The Governing equations +C +C i) Force Balance +C + F(1) = (1.d0+xnu)*F2*XM3 - F3*XM2 + + & xlambda*xlambda*(1.d0+xepsilon*F3)*E32 + F(2) = (1.d0+xrho)*F3*XM1 - (1.d0+xnu)*F1*XM3 - + & xlambda*(1.d0+xepsilon*F3)*E31 + F(3) = F1*XM2 - (1.d0+xrho)*F2*XM1 +C +C ii) Moment Balance +C + F(4) = xnu*XM2*XM3 + F2/(xm**2.d0) + F(5) = (1.d0+xrho)*XM1*XM3 - (1.d0+xnu)*XM1*XM3 - F1/(xm**2.d0) + F(6) = -xrho*XM1*XM2 +C +C iii) Magnetic field +C + F(7) = (1.d0+xnu)*E32*XM3 - E33*XM2 + F(8) = (1.d0+xrho)*E33*XM1 - (1.d0+xnu)*E31*XM3 + F(9) = E31*XM2 - (1.d0+xrho)*E32*XM1 +C +C iv) EulerParameter +C + F(7) = (1.d0/2.d0)*( +(1.d0+xrho)*XM1*Q4 - XM2*Q3 + + & (1.d0+xnu)*XM3*Q2 ) + F(8) = (1.d0/2.d0)*( +(1.d0+xrho)*XM1*Q3 + XM2*Q4 - + & (1.d0+xnu)*XM3*Q1 ) + F(9) = (1.d0/2.d0)*( -(1.d0+xrho)*XM1*Q2 + XM2*Q1 + + & (1.d0+xnu)*XM3*Q4 ) + F(10) = (1.d0/2.d0)*( -(1.d0+xrho)*XM1*Q1 - XM2*Q2 - + & (1.d0+xnu)*XM3*Q3 ) +C +C v) Centre line equations +C + F(11) = 2.d0*(Q1*Q3 + Q2*Q4) + F(12) = 2.d0*(Q2*Q3 - Q1*Q4) + F(13) = Q3**2.d0 + Q4**2.d0 - Q1**2.d0 - Q2**2.d0 +C +C vi) Realign the solution to the initial data +C + do i = 1,NDIM + F(i) = xT*F(i) + end do +C + RETURN + END +C + SUBROUTINE STPNT(NDIM,U,PAR,S) +C ---------- ---- +C + IMPLICIT DOUBLE PRECISION (A-H,O-Z) + DIMENSION U(NDIM),PAR(*) +C +C Load initial values +C + open(unit=1,file='parameters.dat') + read(1,'(8e20.12)') (PAR(i), i=1,8) + close(1) +C + RETURN + END +C + SUBROUTINE BCND(NDIM,PAR,ICP,NBC,U0,U1,FB,IJAC,DBC) +C ---------- ---- +C + IMPLICIT DOUBLE PRECISION (A-H,O-Z) + PARAMETER (n=9, nrdens=9, lrpar=8, lipar=8) + PARAMETER (lwork=11*n+8*nrdens+20, liwork=nrdens+20) + DIMENSION PAR(*),ICP(*),U0(NDIM),U1(NDIM),FB(NBC) + DIMENSION y(n),work(lwork),iwork(liwork) + DIMENSION rpar(lrpar),ipar(lipar) + DIMENSION z(n,n),vr(n,n),vi(n,n),vrdum(n,n),vidum(n,n) + DIMENSION wrdum(n),widum(n),wr(n),wi(n),fv1(n) + DIMENSION V(n,n), xProjection(n,n) + DIMENSION xnorm(n) + DIMENSION static(n),v1(n),v2(n),vecdum(n) + INTEGER, DIMENSION(n) :: iv1 +C +C define constants +C + matz = 1 !not zero as only eigenvalues then + zero = 0.00000001 + ierr = 0 + pi = 4.d0*datan(1.d0) +C +C clear vectors +C + do i = 1,n + do j = 1,n + vr(i,j) = 0.d0 + vi(i,j) = 0.d0 + vrdum(i,j) = 0.d0 + vidum(i,j) = 0.d0 + xProjection(i,j) = 0.d0 + z(i,j) = 0.d0 + V(i,j) = 0.d0 + end do + fv1(i) = 0.d0 + iv1(i) = 0 + wr(i) = 0.d0 + wi(i) = 0.d0 + xnorm(i) = 0.d0 + wrdum(i) = 0.d0 + widum(i) = 0.d0 + static(i) = 0.d0 + end do +C +C load parameters +C + xnu = PAR(1) + xrho = PAR(2) + xm = PAR(3) + xlambda = PAR(4) + xepsilon = PAR(5) + xT = PAR(6) + xD = PAR(7) + xR = PAR(8) +C +C Create Projection matrix - linearise about the trivial solution +C + y1 = 0.d0 + y2 = 0.d0 + y3 = 1.d0 +C + y4 = 0.d0 + y5 = 0.d0 + y6 = 1.d0 +C + y7 = 0.d0 + y8 = 0.d0 + y9 = 1.d0 +C + vrdum(1,2) = (1.d0+xnu)*y6 + vrdum(1,3) =-y5 + vrdum(1,5) =-1.d0*y3 + vrdum(1,6) = (1.d0+xnu)*y2 + vrdum(1,8) = xlambda*(1.d0+xepsilon) +C + vrdum(2,1) = -(1.d0+xnu)*y6 + vrdum(2,3) = +(1.d0+xrho)*y4 + vrdum(2,4) = +(1.d0+xrho)*y3 + vrdum(2,6) = -(1.d0+xnu)*y1 + vrdum(2,7) = -xlambda*(1.d0+xepsilon) +C + vrdum(3,1) = y5 + vrdum(3,2) =-(1.d0+xrho)*y4 + vrdum(3,4) =-(1.d0+xrho)*y2 + vrdum(3,5) = y1 +C + vrdum(4,2) = 1.d0/xm**2.d0 + vrdum(4,5) = xnu*y6 + vrdum(4,6) = xnu*y5 +C + vrdum(5,1) =-1.d0/xm**2.d0 + vrdum(5,4) = (xrho - xnu)*y6 + vrdum(5,6) = (xrho - xnu)*y4 +C + vrdum(6,4) = -xrho*y5 + vrdum(6,5) = -xrho*y4 +C + vrdum(7,5) = (1.d0+xnu) + vrdum(7,8) =-1.d0 +C + vrdum(8,4) = (1.d0+xrho) + vrdum(8,7) = -(1.d0+xnu) +C +C Take transpose of linearised matrix +C + do i = 1,n + do j= 1,n + xProjection(j,i) = vrdum(i,j) + end do + end do +C +C Find eigenvalues and eigenvectors of transpose of linearised matrix +C + call rg(n,n,xProjection,wr,wi,matz,z,iv1,fv1,ierr) + if ( ierr.ne.0 ) then + print*, "failure in eigenvalue, eigenvector solver" + end if + write(99,*) ( wr(i), i = 1,9 ) + write(99,*) ( wi(i), i = 1,9 ) +C +C Create matrices vr, vi from output matrix z +C + iflag = 0 + do i = 1,n + if ( wi(i+iflag).eq.0.d0 ) then + do j = 1,n + vr(j,i+iflag) = z(j,i+iflag) + vi(j,i+iflag) = 0.d0 + end do + else if ( abs(wi(i+iflag)).eq.abs(wi(i+1+iflag)) ) then + do j = 1,n + vr(j,i+iflag) = z(j,i+iflag) + vr(j,i+1+iflag) = z(j,i+iflag) + vi(j,i+iflag) = z(j,i+1+iflag) + vi(j,i+1+iflag) =-z(j,i+1+iflag) + end do + iflag = 1+iflag + end if + if ( i+iflag.eq.n ) goto 10 + end do +C +C Normalize vectors +C +10 do i = 1,n + do j = 1,n + xnorm(i) = xnorm(i) + vr(j,i)**2.d0 + vi(j,i)**2.d0 + end do + end do + do i = 1,n + do j = 1,n + vr(j,i) = vr(j,i)/dsqrt(xnorm(i)) + vi(j,i) = vi(j,i)/dsqrt(xnorm(i)) + end do + end do +C +C Order the eigenvectors/values according to the size of the real part of the eigenvalue. +C + do i = 1,n-1 + do j = i+1,n + if ( wr(i).gt.wr(j) ) then + wrdum(i) = wr(i) + widum(i) = wi(i) + wr(i) = wr(j) + wi(i) = wi(j) + wr(j) = wrdum(i) + wi(j) = widum(i) + do k = 1,n + vrdum(k,i) = vr(k,i) + vidum(k,i) = vi(k,i) + vr(k,i) = vr(k,j) + vi(k,i) = vi(k,j) + vr(k,j) = vrdum(k,i) + vi(k,j) = vidum(k,i) + end do + end if + end do + end do +C +C Use real and imaginary parts of complex eigenvectors +C + do i = 1,n-1 + jflag = 0 + do j = 1,n + if ( abs(vr(j,i)-vr(j,i+1)).lt.zero ) then + jflag = jflag + 1 + if ( jflag.eq.n ) then + do k = 1,n + vr(k,i+1) = vi(k,i) + end do + end if + end if + end do + end do +C +C Let V contain the stable as well as the unstable 9D eigenvectors +C + do i = 1,n + do j = 1,n + V(i,j) = vr(j,i) + end do + end do +C +C define trivial solution +C + static(3) = 1.d0 + static(6) = 1.d0 + static(9) = 1.d0 +C +C Code the boundary conditions +C + do i = 1,NBC + FB(i) = 0.d0 + end do +C +C Four Projection conditions +C + do i = 1,7 + do j = 1,n + FB(i) = FB(i) + ( U0(j) - static(j) )*V(i,j) + end do + end do +C +C symmetric section + FB(8) = U1(1) + FB(9) = U1(4) + FB(10) = U1(7) +! C +! C casimirs +! FB(5) = U0(3)-1.d0 +! FB(6) = U0(6)-1.d0 +! FB(7) = U0(9)-1.d0 +C +C euler parameters + FB(11) = U0(10) + FB(12) = U0(11) + FB(13) = U0(12) + FB(14) = U0(13)-1.d0 +C +C centreline + FB(15) = U0(14) + FB(16) = U0(15) + FB(17) = U0(16) +C +! write(99,*) FB +! C +! C Two additional parameters in order to free parameters containing the end displacements: the end-shortening and the end rotation. +! C +! short = xT - U1(16) +! FB(18) = xD - short +! C +! D11 = U1(10)**2.d0 - U1(11)**2.d0 - U1(12)**2.d0 + U1(13)**2.d0 +! D12 = 2.d0*( U1(10)*U1(11) + U1(12)*U1(13) ) +! twopi = 2.d0*pi +! if ( D12.lt.-1.d0 ) D12 = -1.d0 +! if ( D12.gt.+1.d0 ) D12 = +1.d0 +! xxnorm = DSQRT( D11**2.d0 + D12**2.d0) +! D1_11 = D11/xxnorm +! D1_12 = D12/xxnorm +! if ( D1_12.gt.0.d0 ) then +! rot = ( dasin(D1_12) - (1.d0 + xnu)*xT )/twopi +! nsign = +1 +! else +! rot = ( twopi - dasin(D1_12) - (1.d0 + xnu)*xT )/twopi +! nsign = -1 +! end if +! rotate = rot - DINT(rot) +! if ( rotate.lt.0.d0 ) rotate = rotate + 1.d0 +! FB(19) = xR - rotate +C +C +100 format(9e15.6) +C + RETURN + END +C + SUBROUTINE ICND + RETURN + END +C + SUBROUTINE FOPT + RETURN + END +C + SUBROUTINE PVLS + RETURN + END +C \ No newline at end of file diff --git a/continuation/parameters.dat b/continuation/parameters.dat new file mode 100644 index 0000000..82f7e76 --- /dev/null +++ b/continuation/parameters.dat @@ -0,0 +1,12 @@ + 0.333333333333E+00 0.000000000000E+00 0.170000000000E+01 0.100000000000E-01 0.100000000000E-01 0.405475691275E+02 0.182911441836E+01 0.175455031153E+00 + + xnu = 0.333333333333E+00 + xrho = 0.000000000000E+00 + xm = 0.170000000000E+01 + xlambda = 0.100000000000E-01 + xepsilon = 0.100000000000E-01 + xT = 0.405475691275E+02 + xdelta = 0.694526697277E+00 + xtheta = 0.157104750823E+01 + xD = 0.182911441836E+01 + xR = 0.175455031153E+00 diff --git a/continuation/r.mag b/continuation/r.mag new file mode 100644 index 0000000..7d30d2e --- /dev/null +++ b/continuation/r.mag @@ -0,0 +1,10 @@ +16 4 1 0 NDIM,IPS,IRS,ILP +4 4 6 7 8 NICP,(ICP(I),I=1,NICP) +100 4 3 2 1 0 19 0 NTST,NCOL,IAD,ISP,ISW,IPLT,NBC,NINT +5000 -100.0 500.0 -100.0 500.0 NMX,RL0,RL1,A0,A1 +10 10 2 8 5 3 0 NPR,MXBF,IID,ITMX,ITNW,NWTN,JAC +1.e-10 1.e-10 1.e-8 EPSL,EPSU,EPSS +-0.01 0.000000000000001 0.05 1 DS,DSMIN,DSMAX,IADS +0 NTHL,(/,I,THL(I)),I=1,NTHL) +0 NTHU,(/,I,THU(I)),I=1,NTHU) +0 NUZR,(/,I,PAR(I)),I=1,NUZR) \ No newline at end of file diff --git a/Makefile b/shooting/Makefile similarity index 100% rename from Makefile rename to shooting/Makefile diff --git a/dop853.f b/shooting/dop853.f similarity index 100% rename from dop853.f rename to shooting/dop853.f diff --git a/monodromy.f b/shooting/monodromy.f similarity index 100% rename from monodromy.f rename to shooting/monodromy.f diff --git a/newton.f b/shooting/newton.f similarity index 100% rename from newton.f rename to shooting/newton.f diff --git a/postprocess.f b/shooting/postprocess.f similarity index 100% rename from postprocess.f rename to shooting/postprocess.f diff --git a/shooting.f b/shooting/shooting.f similarity index 100% rename from shooting.f rename to shooting/shooting.f