Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL1_07_PQ.dat at {9.2854470530159509754948120638931212797398642775649e-1 ,0 ,2.9454603159096139829391826962489514694244609154793e-1 ,0 ,8.1797465022555767886535418730543840616986449863482e-2 ,0 }
Validate the existence of a branch of period-1 points:
proveBranchHaloOrbits(this->cr3bpFixPointsSolver.pm,this->cr3bpFixPointsSolver.pm,c,s,this->fp,0,4,2,3,5,&(this->Dfp)): true
############################

y0[i][3]=[-1.0651425952891470846060212455822199628425212971759e-41 ,1.0651425256473365641651149541943495332392853603480e-41 ]
D0[i][3][0]=[-7.2738741894895292588539371613225028173389142137463e1 ,-7.2738741894895292588539371613225028173336997043980e1 ]
D0[i][3][2]=[-1.6436843246411438560673954722370634248790561054409e-37 ,1.6436843265743167041776240003938420317609375070460e-37 ]
dy0=[-1.1026666674819508125951802885930016751737586063561e-39 ,1.1026666558736290823018667525015274255068791726763e-39 ]
Ddy=[-3.5872698767862841241646608149848216865264348217951e2 ,-3.5872698767862841241645487504267310694313566287170e2 ]
dy=[-3.0738324836317953245987777102438065812409472080154e-42 ,3.0738324512720283457819421508645375173079076082282e-42 ]
r[4]=[-9.9999999999999999998718794954586597238790041278445e-26 ,9.9999999999999999998718794954586597238790041278445e-26 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-1.3954733954175512174102009173199457767751977848516e-38 ,1.3954733954103567803271124549473041906634232887891e-38 ]
D0[i][3][0]=[-5.7106685335832028681171633810860851972982462783242 ,-5.7106685335832028681171633810860849985318766766980 ]
D0[i][3][2]=[-5.7126111998653901359143869312486602858907185018075e-34 ,5.7126111998706713389214783350752019688497992148459e-34 ]
dy0=[-1.4040467317992638900095720988620615283528412886478e-38 ,1.4040467317827262335434137506963005402494571250782e-38 ]
Ddy=[-3.9110663451332139166412787113134916114906565786115e1 ,-3.9110663451332139166409496087142549178721559504111e1 ]
dy=[-3.5899333018127080185037039840355886383663664031820e-40 ,3.5899333017704237537871588523670446236448008204848e-40 ]
r[4]=[-9.9999999999999999998718794954586597238790041278445e-26 ,9.9999999999999999998718794954586597238790041278445e-26 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-1.4737988055453777552824878724259509533633113307957e-34 ,1.4737988055454385468709121485186473403467746684800e-34 ]
D0[i][3][0]=[-7.2738741894895292588539371613226403981905223680254e1 ,-7.2738741894895292588539371613223652364820915473804e1 ]
D0[i][3][2]=[-1.1182969294352877404087130476029737711027298320576e-29 ,1.1182969294352784553517482070697620535963950291365e-29 ]
dy0=[-1.4738097257003916644316971768324337041586906093294e-34 ,1.4738097256977447184728106278396262922651552558824e-34 ]
Ddy=[3.3684390840811725634456291819303144672799346037974e3 ,3.3684390840811725634500273905072364513172390624165e3 ]
dy=[-4.3753492015420068300303437360592552284568966545131e-38 ,4.3753492015498649087808121323973797069309069438339e-38 ]
r[4]=[-9.9999999999999999998718794954586597238790041278445e-26 ,9.9999999999999999998718794954586597238790041278445e-26 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-1.2054504342630256461434964730196313634795405077918e-31 ,1.2054504342630256511957884922884711408761447244263e-31 ]
D0[i][3][0]=[-1.6088948746613270804663572729529785865965009005084e-27 ,1.6088948746613270825844982814677781243062067347821e-27 ]
D0[i][3][2]=[-1.8953728074042917488232924798467764641931469105435e-26 ,1.8953728074042917482767150155919082376738973666626e-26 ]
dy0=[-1.2054504342630258519102996113641003110089484935566e-31 ,1.2054504342630256512716034045847059001462304367174e-31 ]
Ddy=[2.9495356905109699214585139750945421825801882374531e2 ,2.9495356905109699214587418427186303538441325001895e2 ]
dy=[-4.0869159106672702817285888927926053479894195928526e-34 ,4.0869159106672709619668272442033200578456474239964e-34 ]
r[4]=[-9.9999999999999999998718794954586597238790041278445e-26 ,9.9999999999999999998718794954586597238790041278445e-26 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

Intersection of two enclosures of dy(x,z) along fixed point curve:
intersection(r[4],fp[4],fp[4]): true
############################

DBif[i][3][4]=[-3.5872698767862841241646047827059353278517187789053e2 ,-3.5872698767862841241646047827056174281060726716068e2 ]
D0[i][5][0]=[1.9002596207515587772493225205474897268047495770525 ,1.9002596207515587772493225205474897273224653402120 ]
D0[i][3][0]=[-7.2738741894895292588539371613225028173389142137463e1 ,-7.2738741894895292588539371613225028173336997043980e1 ]
DBif[i][5][0]=[1.9002596207515587772493225205455176338799474121217 ,1.9002596207515587772493225205494618202472675051428 ]
DBif[i][3][0]=[-7.2738741894895292588539371613235775672056578985283e1 ,-7.2738741894895292588539371613214280674669560196160e1 ]
D[k][3][4]=[-3.5872698767862841241646219226093860146216666700501e2 ,-3.5872698767862841241645876428021667413361247804620e2 ]
_H(5,0,0)=[1.2185270867191590213427035104246118893892763871403e2 ,1.2185270867191598618098590081187577969302590682949e2 ]
_H(5,0,2)=[7.4110102555230146631313935873410576081285231242589e1 ,7.4110102555231239285312876197395682720451032501778e1 ]
Dg!=0.: true
############################

Check principal period of new branch:
!intersection(-g/Dg,r[2],tmp): true
############################

DBif[i][3][4]=[-3.9110663451332139166411141600144560698740547740521e1 ,-3.9110663451332139166411141600132904594887577549706e1 ]
D0[i][5][0]=[2.3582332735222095653385610761677448310226069472673e1 ,2.3582332735222095653385610761677448584746486395811e1 ]
D0[i][3][0]=[-5.7106685335832028681171633810860851972982462783242 ,-5.7106685335832028681171633810860849985318766766980 ]
DBif[i][5][0]=[2.3582332735222095653385610761675174413072037454715e1 ,2.3582332735222095653385610761679722481900518413768e1 ]
DBif[i][3][0]=[-5.7106685335832028681171633810867438955815155550041 ,-5.7106685335832028681171633810854263002486074000182 ]
D[k][3][4]=[-3.9110663451332139166411361102528817805063445637755e1 ,-3.9110663451332139166410922097748647488564679652472e1 ]
_H(5,0,0)=[5.9050251629258900015488078667736182176322483015535e1 ,5.9050251629367570772001311893942372801670275272139e1 ]
_H(5,0,2)=[1.4950974678305271650162442331950347389504088682307e2 ,1.4950974678407375426992792247866295544997343602616e2 ]
Dg!=0.: true
############################

Check principal period of new branch:
!intersection(-g/Dg,r[2],tmp): true
############################

DBif[i][3][4]=[3.3684390840811725634478282862098588804170489946738e3 ,3.3684390840811725634478282862276920381801246715401e3 ]
D0[i][5][0]=[1.9002596207515587772493225205403699760739061345876 ,1.9002596207515587772493225205546094780533087816094 ]
D0[i][3][0]=[-7.2738741894895292588539371613226403981905223680254e1 ,-7.2738741894895292588539371613223652364820915473804e1 ]
DBif[i][5][0]=[1.9002596207515587772493225205395668121472117351582 ,1.9002596207515587772493225205554126419800031810388 ]
DBif[i][3][0]=[-7.2738741894895292588539371613235717739616468369631e1 ,-7.2738741894895292588539371613214338607109670784427e1 ]
D[k][3][4]=[3.3684390840811725634478074749442614487956208977657e3 ,3.3684390840811725634478490974932894698015527684481e3 ]
_H(5,0,0)=[-5.7679987298508791701885480137336735613484189408322e1 ,-5.7679983081794815962691884921921340938228601984131e1 ]
_H(5,0,2)=[-5.4645053759891964408522637178118256988983606381235e2 ,-5.4645047711857128413738984046958242699635368684547e2 ]
Dg!=0.: true
############################

Check principal period of new branch:
!intersection(-g/Dg,r[2],tmp): true
############################

DBif[i][3][4]=[2.9495356905109699214586279084717190553703710899625e2 ,2.9495356905109699214586279093414534810539496476801e2 ]
D0[i][5][0]=[-2.2189325302349382287767156067162537091541612077132e-27 ,2.2189325302349382196052348037770772913208396393125e-27 ]
D0[i][3][0]=[-1.6088948746613270804663572729529785865965009005084e-27 ,1.6088948746613270825844982814677781243062067347821e-27 ]
DBif[i][5][0]=[-2.2227766226535053902125069458563556895036248723715e-27 ,2.2227766226535053810410261429171792716703033039707e-27 ]
DBif[i][3][0]=[-1.6107099050426559222526141592448123268868002127790e-27 ,1.6107099050426559243707551677596118645965060470527e-27 ]
D[k][3][4]=[2.9495356905109699214586143846161200543286242653811e2 ,2.9495356905109699214586414331970524820956964722614e2 ]
_H(5,0,0)=[-1.4015932000685657865130089195839444679744874273016e-3 ,1.4015932000710558104184348810712607296782120749112e-3 ]
_H(5,0,2)=[-1.1250415056793053647668810345432647483804212719932e3 ,-1.1249795991002624642779608472349827352822556854336e3 ]
g=[-8.7944195467281529331260073086477664485140527095458e-27 ,8.7944195467281529326065816996240534512707870466752e-27 ]
Dg=[-1.1250415056793053647668810345467256988776045442063e3 ,-1.1249795991002624642779608472315217847850724132204e3 ]
r[2]=[-3.9999999999999999999487517981834638895516016511378e-25 ,3.9999999999999999999487517981834638895516016511378e-25 ]
Dg!=0.: true
############################

-g/Dg=[-7.8174035811509509745558122653814885829135723737495e-30 ,7.8174035811509509740940922400235711281861126560388e-30 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

Check intersection of two enclosures of hessian at bif point:intersection(H1,H[3],H[3]): true
############################

Check intersection of two enclosures of derivative at bif point:intersection(D1,D[3],D[3]): true
############################

T1={[-2.4692974373789872001097764849302727227648892113306e-24 ,2.4692974373789872001097336707351796540950886020154e-24 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-4.6852357796573885066511451102149535384811074128238e-25 ,4.6852357796573885066512398522193785838109726647520e-25 ],[0 ,0 ]}
DH[2]=[-8.5275674453929457116142932559048537321272179224459e-1 ,-8.5275674453929457116142932543551778330944627771785e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-8.5275674453929457116142944029278742551402969037989e-1 ,-8.5275674453929457116142921073321573100813837958486e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[2.9495356905109699214586279082074242602053485220973e2 ,2.9495356905109699214586279096057482762189722155297e2 ]
_H(5,0,0)=[-1.7252900494483717789260184784793915484438317725683e-11 ,1.7252900494483717416741769435565045050176808633928e-11 ]
_H(5,0,2)=[-1.1250105523897870325555993421072448180317236667631e3 ,-1.1250105523897828534952905975714681606123674088956e3 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.5335767702653600082480779544065111032911239220765e-14 ,1.5335767702653599751356405147830766272512632337945e-14 ],[0 ,0 ],[-4.7726595100355186672028306689286242126782283036602e-16 ,4.7726595100355185641532849853963782970727991359934e-16 ],[0 ,0 ]}
DH*T2=[-1.3194521920338070264329939676662546366919355983130e-14 ,1.3194521920338070549221306124094123062729037222567e-14 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[-8.7836005188798737354122676562919801013561451394362 ,-8.2663573393182533450380656889721115787423587655401 ],[0 ,0 ],[-1.6921529033582331025299081813143081272648785350790 ,-1.6921529033581895670296906428590920715585753595510 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[7.7593433323706767567877624471701422198878520754213 ,8.2004259423088950790042656238526157608870462309927 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [2.9406839227669313847339696284706040456298209039317 ,2.9406839227669313847339696284959951520184706297717 ]
dat/MoonL1_07_PQ.dat at {9.2854470530159509754948120638931212797398642775649e-1 ,0 ,2.9454603159096139829391826962489514694244609154793e-1 ,0 ,8.1797465022555767886535418730543840616986449863482e-2 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Fri Nov 30 02:25:56 2018
elapsed time: 15hours 50minutes 0seconds