User:Tom Allen/ta/AddendumX00P03
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... 12 cycles (example) ...
...
... the amplitude of the standing wave can be varied ...
... the initial velocity of the geodesic can be varied ...
gX0=:,:@(0.23 1 2 8 1 1 12 _12 0 0"_) gX1=:,:@(0.23 1 2 8 1 1 12 12 0 0"_) vSgDd2=:''([-@([(0{])@E1cn yRef@([hkxX00C zfxc"_ 1)),:@(S03yH{]))] Initx =: 0.890 , 0.5p1 , (0.25p1%12"_) , 0p1 "_ Initdx=: (0 , 0 , 0.001 , 0.038"_)*%@InitInt=:1"_ Inity =:zfyc@Initx Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy vS00yL =:Inity vS01dyL =:0,0,0,0: vS02d1L =:Initdy%Initds vS06ds =:Initds vS07count=:(0,120000"_)*InitInt pdD0890 =:vSgD@vS'' pdD0890 arrayPut 'pdD0890' arrayClose 'pdD0890' Initx =: 1.010 , 0.5p1 , (0.25p1%12"_) , 0p1 "_ Initdx=: (0 , 0 , 0.001 , 0.038"_)*%@InitInt=:1"_ Inity =:zfyc@Initx Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy vS00yL =:Inity vS01dyL =:0,0,0,0: vS02d1L =:Initdy%Initds vS06ds =:Initds vS07count=:(0,120000"_)*InitInt pdD1010 =:vSgD@vS'' pdD1010 arrayPut 'pdD1010' arrayClose 'pdD1010' Initx =: 0.960 , 0.5p1 , (0.25p1%12"_) , 0p1 "_ Initdx=: (0 , 0 , 0.001 , 0.038"_)*%@InitInt=:1"_ Inity =:zfyc@Initx Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy vS00yL =:Inity vS01dyL =:0,0,0,0: vS02d1L =:Initdy%Initds vS06ds =:Initds vS07count=:(0,120000"_)*InitInt pdD0960 =:vSgD@vS'' pdD0960 arrayPut 'pdD0960' arrayClose 'pdD0960'
NB. ... execute (ijx) ... arrayOpen 'pdD0890' pdD0890=:120001 8 4 arrayGet 'pdD0890' NB. ... shape required ... arrayClose 'pdD0890' arrayOpen 'pdD0960' pdD0960=:120001 8 4 arrayGet 'pdD0960' NB. ... shape required ... arrayClose 'pdD0960' arrayOpen 'pdD1010' pdD1010=:120001 8 4 arrayGet 'pdD1010' NB. ... shape required ... arrayClose 'pdD1010'
load 'plot' pd 'reset' pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdD0890 pd ((0.890*cos@]"0);0.890*sin@]"0) pTsteps (_,0p1,((0.25p1%12"_)*2"_),160"_)'' pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdD1010 pd ((1.010*cos@]"0);1.010*sin@]"0) pTsteps (_,0p1,((0.25p1%12"_)*2"_),160"_)'' pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdD0960 pd ((0.960*cos@]"0);0.960*sin@]"0) pTsteps (_,0p1,((0.25p1%12"_)*2"_),160"_)'' pd 'aspect 1' pd 'pdf' pd 'show'
load 'plot' pd 'reset' incy0=:(2-~/\])@:(cy0"1) incy1=:(2-~/\])@:(cy1"1) incy2=:(2-~/\])@:(cy2"1) incy3=:(2-~/\])@:(cy3"1) veloc=:(((incy0^2:)+incy1^2:)^0.5"_)%incy3 pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdD0890 pd (}:@:(cy3"1);incy2)@:((S00yL{])"2) pdD0890 NB. ... incy2 is zero ... pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdD1010 pd (}:@:(cy3"1);incy2)@:((S00yL{])"2) pdD1010 NB. ... incy2 is zero ... pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdD0960 pd (}:@:(cy3"1);incy2)@:((S00yL{])"2) pdD0960 NB. ... incy2 is zero ... pd 'pdf' pd 'show'
... patterns can be generated ...
... examples (compare TensorExperimentsR23) ...
load 'plot' pd 'reset' pd (cy3"1;(((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)"1)@:((S00yL{])"2) ((103000+i.@(08000"_)){]) pdD0890 NB. ... for this geodesic cy2 is zero ... pd 'show'
load 'plot' pd 'reset' pd (cy3"1;(((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)"1)@:((S00yL{])"2) ((107100+i.@(9780"_)){]) pdD1010 NB. ... for this geodesic cy2 is zero ... pd 'show'
load 'plot' pd 'reset' pd (cy3"1;(((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)"1)@:((S00yL{])"2) ((105000+i.@(10260"_)){]) pdD0960 NB. ... for this geodesic cy2 is zero ... pd 'show'