Essays/Torsion Tensor/TorsionTensor05
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... ADDENDUM ...
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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$]) (~:@:((0 2{])"1)#]) yCtotal@yCpts'' pd 'pdf' pd 'show'
NB. ... script torsiontensorE.ijs ... R20i=:+/"1@((<0 3)|:])"4@B2k RI0=:hcn+/@((<0 1)|:])@( ])@([smx 0|:])"2 2 R20i RI1=:hcn+/@((<0 1)|:])@(0|:])@([smx ])"2 2 R20i R =:RI1 R20icv=:+/"1@((<0 3)|:])"5@B2kcv R20iI0cv=:hcn ([smx 0|:])"2 3 R20icv R20iI1cv=:hcn(0 2|:])@([smx 1|:])"2 3 R20icv R20iI0dv=:+/"1@((<0 2)|:])"3@R20iI0cv R20iI1dv=:+/"1@((<1 2)|:])"3@R20iI1cv RI0cv=:+/"1@((<0 1)|:])"3@R20iI0cv RI1cv=:+/"1@((<0 1)|:])"3@R20iI1cv Rcv =:RI1cv
NB. ... execute (ijx) ... NB. ... checks ... gXcme =:( 1.5 1.5 0 )"_ gXpAll=:( 0 0 0 )"_ gXqAll=:( _8 0.5 _1 )"_ gXwAll=:( 0 _ _ )"_ yCpts=:5 15 7,(0.1,(1p1-0.1),7),0 2p1 7,:0 20 7"_ (gXT([(RI0-:RI1)hkAx)]) (50 yCrandom yCpts)'' 1 (gXT([(R20iI0dv(((2^_43);2^_42)qteq[;])R20iI1dv)hkAx)]) (50 yCrandom yCpts)'' 1 (gXT([(RI0cv(((2^_44);2^_44)qteq[;])RI1cv)hkAx)]) (10 yCrandom yCpts)'' 1 # RArray=:(gXT([R hkAx)]) yCtotal@yCpts'' 4096 *./ (]<0:) RArray 1
NB. ... script torsiontensorE.ijs ... Edv=:R20iI1dv+-@(0.5*Rcv)
NB. ... script torsiontensorE.ijs ... S00xL =:00 00;00 01;00 02;00 03"_ S01dxL =:01 00;01 01;01 02;01 03"_ S02d1L =:02 00;02 01;02 02;02 03"_ S03xH =:03 00;03 01;03 02;03 03"_ S04dxH =:04 00;04 01;04 02;04 03"_ S05d1H =:05 00;05 01;05 02;05 03"_ S06ds =:(<06 00)"_ S07count =:07 00;07 01"_ S0700nmbr=:(<07 00)"_ S0701max =:(<07 01)"_ vS00=:''vS00xL `S00xL `]}] vS01=:''vS01dxL `S01dxL `]}] vS02=:''vS02d1L `S02d1L `]}] vS06=:''vS06ds `S06ds `]}] vS07=:''vS07count`S07count`]}] vS =:vS07@vS06@vS02@vS01@vS00@(8 4$_"_) 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'
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'
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
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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