Essays/Torsion Tensor/TorsionTensor03
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NB. ... script torsiontensor.ijs ... Phicn=:hcn smx"2 1 Phicv Phicndxt1=:hcn (( [)smx 0|:])"2 2 Phicvdx Phicndxt2=:hcndx((1|:[)smx ])"3 1 Phicv Phicndx =:Phicndxt1+Phicndxt2 Phicndxdxt1=:hcn (( [)smx 0|:])"2 3 Phicvdxdx Phicndxdxt2=:hcndx (1|:])@((1|:[)smx 0|:])"3 2 Phicvdx Phicndxdxt3=:hcndx ((1|:[)smx 0|:])"3 2 Phicvdx Phicndxdxt4=:hcndxdx ((1|:[)smx ])"4 1 Phicv Phicndxdx =:Phicndxdxt1+Phicndxdxt2+Phicndxdxt3+Phicndxdxt4
NB. ... execute (ijx) ... gXcme =:( 1.5 0.45 0.754 )"_ gXpAll=:( 6 _1.4 1.7 )"_ gXqAll=:( 1 1 _1 )"_ gXwAll=:( 1.25 _ _ )"_ yCpts=:0.3 2 50,(0.1,(1p1-0.1),28),0 2p1 50,:1 8 50"_ (gXT(([Phicndx hkAy)(((2^_22);2^_14)qteq[;])"2(0|:[:(gXT([Phicn hkAy)])D.1])"_ 1)]) (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 (gXT(([Phicndxdx hkAy)(((2^_18);2^_14)qteq[;])"3(0|:[:(gXT([Phicndx hkAy)])D.1])"_ 1)]) (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
NB. ... script torsiontensor.ijs ... Omgcv=:Omgdx+-@(ch2k smx"3 1 Omg) Omgcvdxt1=:Omgdxdx Omgcvdxt2=:ch2k -@(( [)smx 0|:])"3 2 Omgdx Omgcvdxt3=:ch2kdx-@((2|:[)smx ])"4 1 Omg Omgcvdx =:Omgcvdxt1+Omgcvdxt2+Omgcvdxt3 Omgcvdxdxt1=:Omgdxdxdx Omgcvdxdxt2=:ch2k -@(( [)smx 0|:])"3 3 Omgdxdx Omgcvdxdxt3=:ch2kdx -@(2|:])@((2|:[)smx 0|:])"4 2 Omgdx Omgcvdxdxt4=:ch2kdx -@((2|:[)smx 0|:])"4 2 Omgdx Omgcvdxdxt5=:ch2kdxdx -@((2|:[)smx ])"5 1 Omg Omgcvdxdx =:Omgcvdxdxt1+Omgcvdxdxt2+Omgcvdxdxt3+Omgcvdxdxt4+Omgcvdxdxt5
NB. ... execute (ijx) ... gXcme =:( 1.5 0.45 0.754 )"_ gXpAll=:( 6 _1.4 1.7 )"_ gXqAll=:( 1 1 _1 )"_ gXwAll=:( 1.25 _ _ )"_ yCpts=:0.3 2 50,(0.1,(1p1-0.1),28),0 2p1 50,:1 8 50"_ NB. ... Omgcv is a tensor ... OmgcvBox=:([Omgcv hkAx);([(0|:])"2@:ycdx xfromy);[Omgcv hkAy OmgcvChk=:[(>@(0{])(((2^_44);2^_44)qteq[;])"2>@(1{])([smx"2 smx"2)>@(2{]))OmgcvBox (gXT OmgcvChk]) (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 NB. ... derivatives ... (gXT(([Omgcvdx hkAy)(((2^_23);2^_18)qteq[;])"3(0|:[:(gXT([Omgcv hkAy)])D.1])"_ 1)]) (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 (gXT(([Omgcvdxdx hkAy)(((2^_19);2^_14)qteq[;])"4(0|:[:(gXT([Omgcvdx hkAy)])D.1])"_ 1)]) (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
NB. ... script torsiontensor.ijs ... Ups =:(( 0|:])-])"2@Omgcv Upsdx =:(( 1 0 2|:])-])"3@Omgcvdx Upsdxdx=:((1 0 2 3|:])-])"4@Omgcvdxdx
NB. ... execute (ijx) ... gXcme =:( 1.5 0.45 0.754 )"_ gXpAll=:( 6 _1.4 1.7 )"_ gXqAll=:( 1 1 _1 )"_ gXwAll=:( 1.25 _ _ )"_ yCpts=:0.3 2 50,(0.1,(1p1-0.1),28),0 2p1 50,:1 8 50"_ NB. ... Ups is a tensor ... UpsBox=:([Ups hkAx);([(0|:])"2@:ycdx xfromy);[Ups hkAy UpsChk=:[(>@(0{])(((2^_44);2^_44)qteq[;])"2>@(1{])([smx"2 smx"2)>@(2{]))UpsBox (gXT UpsChk]) (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 NB. ... derivatives ... (gXT(([Upsdx hkAy)(((2^_24);2^_22)qteq[;])"3(0|:[:(gXT([Ups hkAy)])D.1])"_ 1)]) (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 (gXT(([Upsdxdx hkAy)(((2^_24);2^_22)qteq[;])"4(0|:[:(gXT([Upsdx hkAy)])D.1])"_ 1)]) (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
NB. ... script torsiontensor.ijs ... S=:Ups*/"2 1 Phicn Sdxt1=:Ups (*/)"2 2 Phicndx Sdxt2=:Upsdx(2|:])@(*/)"3 1 Phicn Sdx =:Sdxt1+Sdxt2 Sdxdxt1=:Ups (*/)"2 3 Phicndxdx Sdxdxt2=:Upsdx ( 2|:])@(*/)"3 2 Phicndx Sdxdxt3=:Upsdx (2 4|:])@(*/)"3 2 Phicndx Sdxdxt4=:Upsdxdx(2 3|:])@(*/)"4 1 Phicn Sdxdx =:Sdxdxt1+Sdxdxt2+Sdxdxt3+Sdxdxt4
NB. ... execute (ijx) ... gXcme =:( 1.5 0.45 0.754 )"_ gXpAll=:( 6 _1.4 1.7 )"_ gXqAll=:( 1 1 _1 )"_ gXwAll=:( 1.25 _ _ )"_ yCpts=:0.3 2 50,(0.1,(1p1-0.1),28),0 2p1 50,:1 8 50"_ NB. ... S is a tensor ... SBox=:([S hkAx);xcdy;([(0|:])"2@:ycdx xfromy);[S hkAy SChk=:[(>@(0{])(((2^_44);2^_44)qteq[;])"3>@(2{])([smx"2 3 smx"2 3)>@(1{])smx"2 3>@(3{]))SBox (gXT SChk]) (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 NB. ... example ... NB. NB. ... S in frame of reference which is not rotating ... NB. ... S in frame of reference which is rotating ... (gXT(([S hkAy),:([S hkAx))]) (1 yCrandom yCpts)'' 0 0 0 0 0 0 0 0 0 0 0 0 _25.9184 0 0 11.9925 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 25.9184 0 0 _11.9925 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 _25.9184 0 _14.9906 11.9925 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 25.9184 0 14.9906 _11.9925 0 0 0 0 0 0 0 0 0 0 0 0 NB. ... derivatives ... (gXT(([Sdx hkAy)(((2^_19);2^_14)qteq[;])"4(0|:[:(gXT([S hkAy)])D.1])"_ 1)]) (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 (gXT(([Sdxdx hkAy)(((2^_16);2^_14)qteq[;])"5(0|:[:(gXT([Sdx hkAy)])D.1])"_ 1)]) (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
NB. ... script torsiontensor.ijs ... Gam =:ch2k +0.5*S Gamdx =:ch2kdx +0.5*Sdx Gamdxdx=:ch2kdxdx+0.5*Sdxdx
NB. ... execute (ijx) ... gXcme =:( 1.5 0.45 0.754 )"_ gXpAll=:( 6 _1.4 1.7 )"_ gXqAll=:( 1 1 _1 )"_ gXwAll=:( 1.25 _ _ )"_ yCpts=:0.3 2 50,(0.1,(1p1-0.1),28),0 2p1 50,:1 8 50"_ (gXT(([Gamdx hkAy)(((2^_20);2^_14)qteq[;])"4(0|:[:(gXT([Gam hkAy)])D.1])"_ 1)]) (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 (gXT(([Gamdxdx hkAy)(((2^_17);2^_14)qteq[;])"5(0|:[:(gXT([Gamdx hkAy)])D.1])"_ 1)]) (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:LTT0300C.txt
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Download: File:LTT0302C.txt
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Download: File:LTT0304C.txt
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Contributed by Tom Allen