Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/JupiterL1_01_PQ.dat at {9.3121036058164211587671802449322809734029311713287e-1 ,0 ,5.3237354992487986458035215884716787997905311477546e-2 ,0 ,9.7402826529596892795036599850455505897199976902111e-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]=[-8.4998274883070385488501756395579720863695288021547e-34 ,8.5006634384437819010257330019763135324385599090156e-34 ]
D0[i][3][0]=[5.0774455250869245846577769484208462681029713736617e-1 ,5.0774455250869245846577769484394288740141043652968e-1 ]
D0[i][3][2]=[-1.3583856150002188640221625455109365900378637933222e-30 ,1.3583741251122320349347223823491458154118840768687e-30 ]
dy0=[-6.7188906637382090911181193875993449872970438572111e-33 ,1.5430463537266765123726922727163942742697028250275e-33 ]
Ddy=[2.7162994614331910825374665976011757237992318843394e1 ,2.7162994614332033060343766256500264771001707597229e1 ]
dy=[-5.6806930739239061909421543857475168924806616917048e-35 ,2.4735456304192416072386018296042179179604660944370e-34 ]
r[4]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-1.6020976237090453415315374746807980267372495887363e-32 ,1.6021944204011345777391494669429864443614357336183e-32 ]
D0[i][3][0]=[1.4257053818367066500545957329520062314027463740914e-1 ,1.4257053818367066500545957336607026438073793356834e-1 ]
D0[i][3][2]=[-6.1611275964626823736686308676777550832940747715134e-29 ,6.1611105626322229064876320799963405354823846415800e-29 ]
dy0=[-8.3223639760527216468503498885331529154833527751582e-32 ,1.6216527351130523079632737857264712605295970574325e-32 ]
Ddy=[3.6852302377622079302766444980038260412524569727404e2 ,3.6852302377623393194936682484154262242194683391827e2 ]
dy=[-4.4004109119048495927401077124306837670184194054564e-35 ,2.2583023146760927093853457204877511492995455761461e-34 ]
r[4]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-3.9404565835804433232185900127759302632646701711949e-31 ,3.9406941050931852886717942107469508084135680372093e-31 ]
D0[i][3][0]=[5.0774455250869245846577769345970266142704584697780e-1 ,5.0774455250869245846577769622633334062578221678549e-1 ]
D0[i][3][2]=[-2.5355083377322457623747026091068129818977188873281e-27 ,2.5355036208409630422648346419944426006914440235638e-27 ]
dy0=[-2.0254957924485332066833998472350531770845651543249e-30 ,3.9476239051922637024184532757703205043548110556698e-31 ]
Ddy=[8.9764124628710234250377285306025001772829576399986e3 ,8.9764124628807472968134983166315800970865029966945e3 ]
dy=[-4.3977746360483665905491269357636255631060992340355e-35 ,2.2564647077287900196571103954407360293206288496776e-34 ]
r[4]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-5.2390112942155914788176194913461317745341571494180e-30 ,5.2393255256314435799306491065918396281330868031803e-30 ]
D0[i][3][0]=[-5.1789472319417754570980479223542626419137744066964e-26 ,5.1789585761927170712823460290642509193676957804559e-26 ]
D0[i][3][2]=[-9.7402286623518948023209959496715148420325262920437e-26 ,9.7402214669708318401490958027178292219180164359238e-26 ]
dy0=[-2.6832915830575778663642620876886650475514601100005e-29 ,5.2393255256324202725577146369175304788909555621295e-30 ]
Ddy=[1.1888008757787895494488460792681049604853078374134e5 ,1.1888008757921594063279187375590862429090042905110e5 ]
dy=[-4.4072355870364843527009099212513962482265497632890e-35 ,2.2571413242774907878393202330202323624430261296418e-34 ]
r[4]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
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]=[2.7162994614331971942859216116246352218945216118057e1 ,2.7162994614331971942859216116265669790048810322566e1 ]
D0[i][5][0]=[-1.0924411078559699037362099847826651029469784226998 ,-1.0924411078559699037362099847801960255270233013881 ]
D0[i][3][0]=[5.0774455250869245846577769484208462681029713736617e-1 ,5.0774455250869245846577769484394288740141043652968e-1 ]
DBif[i][5][0]=[-1.0924411078559699037362099847827042908793288367968 ,-1.0924411078559699037362099847801568375946728872911 ]
DBif[i][3][0]=[5.0774455250869245846577769484204946800873917349580e-1 ,5.0774455250869245846577769484397804620296840040005e-1 ]
D[k][3][4]=[2.7162994614331963074438093628540139788839471684548e1 ,2.7162994614331980811280338603971882220154554756075e1 ]
_H(5,0,0)=[2.5368102692628368855003904880534426348039854147989 ,2.5368102693360157090403695016751663396645394415020 ]
_H(5,0,2)=[-2.6653186857039510754879182130358912690407629523271e1 ,-2.6653186856873064017558520706243374226346219819163e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[3.6852302377622736248851563731927083362883965303829e2 ,3.6852302377622736248851563732265439291835287815402e2 ]
D0[i][5][0]=[1.3197668341361791889204201991880988668639328030069 ,1.3197668341361791889204201992291792484163983407123 ]
D0[i][3][0]=[1.4257053818367066500545957329520062314027463740914e-1 ,1.4257053818367066500545957336607026438073793356834e-1 ]
DBif[i][5][0]=[1.3197668341361791889204201991871645138789432623587 ,1.3197668341361791889204201992301136014013878813605 ]
DBif[i][3][0]=[1.4257053818367066500545957329400289125970877041173e-1 ,1.4257053818367066500545957336726799626130380056575e-1 ]
D[k][3][4]=[3.6852302377622713794122840740663636532589901299955e2 ,3.6852302377622758703580286723528886122129351819276e2 ]
_H(5,0,0)=[-1.0349112543818436687137712183937909313140640570926 ,-1.0349112454100612774135486483002092482450281729520 ]
_H(5,0,2)=[-5.9204405506327500215652840651070831379961426984232e-1 ,-5.9204402729563026712409266923761610819023152175915e-1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[8.9764124628758853609256134222101393797703423230315e3 ,8.9764124628758853609256134250239408945991183136617e3 ]
D0[i][5][0]=[-1.0924411078559699037362099874980290031303827040931 ,-1.0924411078559699037362099820648316866052375178576 ]
D0[i][3][0]=[5.0774455250869245846577769345970266142704584697780e-1 ,5.0774455250869245846577769622633334062578221678549e-1 ]
DBif[i][5][0]=[-1.0924411078559699037362099875003622375446525530539 ,-1.0924411078559699037362099820624984521909676688968 ]
DBif[i][3][0]=[5.0774455250869245846577769344585695614951243963704e-1 ,5.0774455250869245846577769624017904590331562412624e-1 ]
D[k][3][4]=[8.9764124628758777068324851465801714391972831010829e3 ,8.9764124628758930150187417006539088351721775356102e3 ]
_H(5,0,0)=[1.5867096272135329322534745136543848560806067744764 ,1.5867108575093611957836348639546075779675609934987 ]
_H(5,0,2)=[7.0415854628487428208526676682206447825862921425891e1 ,7.0415858569114791714950615915641627635695046073047e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[1.1888008757854744778883824058145475501334627749398e5 ,1.1888008757854744778883824110126436532608493529847e5 ]
D0[i][5][0]=[-3.0235296584610581244776398187293713705633708464821e-26 ,3.0235232646180687513303021162013251053384276265390e-26 ]
D0[i][3][0]=[-5.1789472319417754570980479223542626419137744066964e-26 ,5.1789585761927170712823460290642509193676957804559e-26 ]
DBif[i][5][0]=[-3.0483472856358866291725629006090016963102589193139e-26 ,3.0483408917928972560252251980809554310853156993708e-26 ]
DBif[i][3][0]=[-5.2020073622994789026503053984551807416035612103771e-26 ,5.2020187065504205168346035051651690190574825841367e-26 ]
D[k][3][4]=[1.1888008757854731058014501769725970349519507915897e5 ,1.1888008757854758499753146398545941684423613363348e5 ]
_H(5,0,0)=[-6.5201416767514867120412126848362905470853723175391e-5 ,6.5201416767775064375002066705169958176134323000882e-5 ]
_H(5,0,2)=[-1.1874675201798788782847953475152307199687535489464e2 ,-1.1874633776010503097793090445626593469392894828018e2 ]
g=[-6.0525671218722108755413657441593309413853911771622e-26 ,6.0525673249542064952479718375630305866644363137852e-26 ]
Dg=[-1.1874675201798788782848574796455085110294646677910e2 ,-1.1874633776010503097792469124323815558627452339888e2 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-5.0970558217128273547915549245044194991620654537944e-28 ,5.0970559927345190131726667010260837866501455808526e-28 ]
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={[-9.5292607673057561824551464213046694466717270526016e-17 ,9.5292607673057586107965465589112044321695680465202e-17 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-3.6617737505265308742114315167690187523682185230132e-17 ,3.6617737505265314615120760380648333945586810525207e-17 ],[0 ,0 ]}
DH[2]=[-3.8791454493492138602305553913856738721391218578926e-1 ,-3.8791454493492138602305552749637690056564369727397e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-3.8791454493492139091162784997704719821264493000573e-1 ,-3.8791454493492138113448321665789787363000838816412e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[1.1888008757854744778883823358785094872981758196170e5 ,1.1888008757854744778883824809486793695298920763686e5 ]
_H(5,0,0)=[-2.5484665420321635585846906476248696694369453411054e-13 ,2.5484671283771569355541973753377647781577293243246e-13 ]
_H(5,0,2)=[-1.1874654488904704854011381171992291739492763401661e2 ,-1.1874654488904587201210300633349390095993936852033e2 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-2.1461395313972241980177356480816687015564977438910e-15 ,2.1461400251757959660108298673549655250875412863407e-15 ],[0 ,0 ],[-1.2635589612845757176166857650642938336890445190295e-15 ,1.2635592520011531440594295067234594399985939401546e-15 ],[0 ,0 ]}
DH*T2=[-1.0012076922928687182453278821250976917352529647187e-15 ,1.0012074619374871764953395171859951247818799952740e-15 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[1.0908912231821958865294714790556676887197889144899e1 ,1.0972299125502855628498053770921419120988109557903e1 ],[0 ,0 ],[1.1053789896703423372048639640005801959886303261504 ,1.1053789896703429711436556221217186670590444924093 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[-6.5196826760514568476463063385689282585052962471343 ,-6.4950939780343542402297305344096170534303177970780 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [3.0197999277408856967604296245434539100233582861334 ,3.0197999277408856967604296258380668677289819879949 ]
dat/JupiterL1_01_PQ.dat at {9.3121036058164211587671802449322809734029311713287e-1 ,0 ,5.3237354992487986458035215884716787997905311477546e-2 ,0 ,9.7402826529596892795036599850455505897199976902111e-2 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 11:29:39 2018
elapsed time: 0hours 53minutes 43seconds