Essays/Torsion Tensor/TorsionTensor05
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...
... ADDENDUM ...
...
NB. ... script torsiontensorE.ijs ... NB. ... use only k1 ... hkAy=:hycv;hycvdy;hycvdydy;hycvdydydy;Oymg;Oymgdy;Oymgdydy;Oymg;Oymgdy;Oymgdydy;Oymgdydydy hkAx=:hxcv;hxcvdx;hxcvdxdx;hxcvdxdxdx;Oxmg;Oxmgdx;Oxmgdxdx;Oxmg;Oxmgdx;Oxmgdxdx;Oxmgdxdxdx
NB. ... plot (ijs) ...
gXcme =:( 1.5 1.5 0 )"_
gXpAll=:( 0 0 0 )"_
gXqAll=:( _8 0.5 _1 )"_
gXwAll=:( 0 _ _ )"_
yCpts=:5 15 50,(0.1,(1p1-0.1),28),0 2p1 50,:0 20 50"_
load 'plot'
pd (gXT((cy0*cos@cy2);(cy0*sin@cy2);k1)]) (51 51$]) (~:@:((0 2{])"1)#]) yCtotal@yCpts''
pd 'pdf'
pd 'show'
... k1 ...
NB. ... script torsiontensorE.ijs ... R20i=:+/"1@((<0 3)|:])"4@B2k RI0=:hcn+/@((<0 1)|:])@( ])@([smx 0|:])"2 2 R20i RI1=:hcn+/@((<0 1)|:])@(0|:])@([smx ])"2 2 R20i R =:RI1 R20icv=:+/"1@((<0 3)|:])"5@B2kcv R20iI0cv=:hcn ([smx 0|:])"2 3 R20icv R20iI1cv=:hcn(0 2|:])@([smx 1|:])"2 3 R20icv R20iI0dv=:+/"1@((<0 2)|:])"3@R20iI0cv R20iI1dv=:+/"1@((<1 2)|:])"3@R20iI1cv RI0cv=:+/"1@((<0 1)|:])"3@R20iI0cv RI1cv=:+/"1@((<0 1)|:])"3@R20iI1cv Rcv =:RI1cv
NB. ... execute (ijx) ... NB. ... checks ... gXcme =:( 1.5 1.5 0 )"_ gXpAll=:( 0 0 0 )"_ gXqAll=:( _8 0.5 _1 )"_ gXwAll=:( 0 _ _ )"_ yCpts=:5 15 7,(0.1,(1p1-0.1),7),0 2p1 7,:0 20 7"_ (gXT([(RI0-:RI1)hkAx)]) (50 yCrandom yCpts)'' 1 (gXT([(R20iI0dv(((2^_43);2^_42)qteq[;])R20iI1dv)hkAx)]) (50 yCrandom yCpts)'' 1 (gXT([(RI0cv(((2^_44);2^_44)qteq[;])RI1cv)hkAx)]) (10 yCrandom yCpts)'' 1 # RArray=:(gXT([R hkAx)]) yCtotal@yCpts'' 4096 *./ (]<0:) RArray 1
NB. ... script torsiontensorE.ijs ... Edv=:R20iI1dv+-@(0.5*Rcv)
NB. ... script torsiontensorE.ijs ...
S00xL =:00 00;00 01;00 02;00 03"_
S01dxL =:01 00;01 01;01 02;01 03"_
S02d1L =:02 00;02 01;02 02;02 03"_
S03xH =:03 00;03 01;03 02;03 03"_
S04dxH =:04 00;04 01;04 02;04 03"_
S05d1H =:05 00;05 01;05 02;05 03"_
S06ds =:(<06 00)"_
S07count =:07 00;07 01"_
S0700nmbr=:(<07 00)"_
S0701max =:(<07 01)"_
vS00=:''vS00xL `S00xL `]}]
vS01=:''vS01dxL `S01dxL `]}]
vS02=:''vS02d1L `S02d1L `]}]
vS06=:''vS06ds `S06ds `]}]
vS07=:''vS07count`S07count`]}]
vS =:vS07@vS06@vS02@vS01@vS00@(8 4$_"_)
vSgDd2 =:gXT(-@(([([ch2k hkAx)S03xH{])+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]
vSgDxH =:''((S00xL{])+(S02d1L{])*S06ds{])`S03xH`]}]
vSgDdxH =:''((S02d1L{])*S06ds{])`S04dxH`]}]
vSgDd1H =:''((S02d1L{])+vSgDd2*S06ds{])`S05d1H`]}]
vSgDxHtoL =:''(S03xH{]) `S00xL `]}]
vSgDdxHtoL=:''(S04dxH{])`S01dxL`]}]
vSgDd1HtoL=:''(S05d1H{])`S02d1L`]}]
vSgDnmbr =:''(1+S0700nmbr{])`S0700nmbr`]}]
vSgD =:(vSgDnmbr@vSgDd1HtoL@vSgDdxHtoL@vSgDxHtoL@vSgDd1H@vSgDdxH@vSgDxH)`]@.((S0700nmbr{])=S0701max{])^:a:
vSgDplot=:<"1@(0|:])@:(((cx0*cos@cx2),cx0*sin@cx2)@(S00xL{])"2)
NB. ... script torsiontensorE.ijs ... Initds=:%:@((gXT([hcv hkAx)Initx)+/@(+/)@:*(]*/])@Initdx) Initd1=:Initdx%|@Initds
NB. ... plot (ijs) ...
vSgDd2M=:[([(hcn smx"2 1 Edv)hkAx)S03xH{]
load 'plot'
NB. ... mass only (blue) ...
gXcme =:( 1.5 1.5 0 )"_
gXpAll=:( 0 0 0 )"_
gXqAll=:( 0 0 0 )"_
gXwAll=:( 0 _ _ )"_
Initx =: 7 , 0.5p1 , 1p1 , 0 "_
Initdx=: 0 , 0 , _0.01 , 0.1008115"_
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:|@Initds
vS07count =:0,628"_
pd vSgDplot pdDa=:vSgD@vS''
NB. ... increase mass (red) ...
gXcme =:( 1.5 1.8 0 )"_
gXpAll=:( 0 0 0 )"_
gXqAll=:( 0 0 0 )"_
gXwAll=:( 0 _ _ )"_
Initx =: 7 , 0.5p1 , 1p1 , 0 "_
Initdx=: 0 , 0 , _0.01 , 0.1008115"_
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:|@Initds
vS07count =:0,150"_
pd vSgDplot pdDb=:vSgD@vS''
NB. ... increase (negative) potential (green) ...
gXcme =:( 1.5 1.5 0 )"_
gXpAll=:( 0 0 0 )"_
gXqAll=:( _18.4638663 0.5 _1 )"_
gXwAll=:( 0 _ _ )"_
Initx =: 7 , 0.5p1 , 1p1 , 0 "_
Initdx=: 0 , 0 , _0.01 , 0.1008115"_
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:|@Initds
vS07count =:0,200"_
pd vSgDplot pdDc=:vSgD@vS''
NB. ... increase mass and (negative) potential (purple overwrites blue) ...
gXcme =:( 1.5 1.8 0 )"_
gXpAll=:( 0 0 0 )"_
gXqAll=:( _18.4638663 0.5 _1 )"_
gXwAll=:( 0 _ _ )"_
Initx =: 7 , 0.5p1 , 1p1 , 0 "_
Initdx=: 0 , 0 , _0.01 , 0.1008115"_
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:|@Initds
vS07count =:0,628"_
pd vSgDplot pdDd=:vSgD@vS''
pd 'pdf'
pd 'show'
... geodesics ...
NB. ... execute (ijx) ...
(S00xL{]) {: pdDa
7.00008 1.5708 _3.13837 63.3095
(S00xL{]) {: pdDd
7 1.5708 _3.13841 63.3096
NB. ... plot (ijs) ...
vSgDd2M=:[([-@(hcn smx"2 1 Edv)hkAx)S03xH{]
load 'plot'
NB. ... (negative) potential (blue) ...
gXcme =:( 1.5 0 0 )"_
gXpAll=:( 0 0 0 )"_
gXqAll=:( _020.62867905 0.5 _1 )"_
gXwAll=:( 0 _ _ )"_
Initx =: 7 , 0.5p1 , 1p1 , 0 "_
Initdx=: (0 , 0 , _0.02 , 0.1200"_)%2:
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:|@Initds
vS07count =:(0,314"_)*2:
pd vSgDplot pdDe=:vSgD@vS''
NB. ... increase (negative) potential (red overwrites blue) ...
gXcme =:( 1.5 0 0 )"_
gXpAll=:( 0 0 0 )"_
gXqAll=:( _100.75958575 0.5 _1 )"_
gXwAll=:( 0 _ _ )"_
Initx =: 7 , 0.5p1 , 1p1 , 0 "_
Initdx=: (0 , 0 , _0.02 , 0.0934"_)%2:
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:|@Initds
vS07count =:(0,314"_)*2:
pd vSgDplot pdDf=:vSgD@vS''
pd 'pdf'
pd 'show'
... geodesics ...
NB. ... execute (ijx) ...
(S00xL{]) {: pdDe
7.00009 1.5708 _3.13839 37.68
(S00xL{]) {: pdDf
7.00001 1.5708 _3.13841 29.3276
NB. ... time difference (blue - red) ...
(cx3 (S00xL{]) {: pdDe)-(cx3 (S00xL{]) {: pdDf)
8.3524
NB. ... execute (ijx) ... NB. ... for this potential ... gXcme =:( 1.5 0 0 )"_ gXpAll=:( 0 0 0 )"_ gXqAll=:( _8 0.5 _1 )"_ gXwAll=:( 0 _ _ )"_ yCpts=:5 15 7,(0.1,(1p1-0.1),7),0 2p1 7,:0 20 7"_ *./^:2"2 (0=]) ((2^_44)qtsz]) (gXT([+/"1@((<0 1)|:])"4@B2k hkAx)]) (50 yCrandom yCpts)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 *./^:3"3 (0=]) ((2^_44)qtsz]) (gXT([+/"1@((<0 1)|:])"5@B2kcv hkAx)]) (50 yCrandom yCpts)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Download: File:LTT0500C.txt
Download: File:LTT0501C.txt
Download: File:LTT0502C.txt
Download: File:LTT0503C.txt
Download: File:LTT0504C.txt
Download: File:LTT0505D.txt
Download: File:LTT0506C.txt
Download MoinMoin source: File:TorsionTensor05.ijs
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Contributed by Tom Allen