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'


JX00P0300C.jpg
... geodesics ...


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'


JX00P0301C.jpg
... velocity (12 cycles) ...


... 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'


JX00P0302D.jpg


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'


JX00P0303D.jpg


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'


JX00P0304C.jpg