User:Tom Allen/ta/AddendumX00P02
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... 8 cycles (example) ...
gX0=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
gX1=:,:@(0.15 1 2 8 1 1 8 8 0 0"_)
vSgDd2=:''([-@([(0{])@E1cn yRef@([hkxX00C zfxc"_ 1)),:@(S03yH{]))]
Initx =: 0.823 , 0.5p1 , (0.25p1%8"_) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@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=:(0,15000"_)*InitInt
pdD0823 =:vSgD@vS''
pdD0823 arrayPut 'pdD0823'
arrayClose 'pdD0823'
Initx =: 0.930 , 0.5p1 , (0.25p1%8"_) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@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=:(0,15000"_)*InitInt
pdD0930 =:vSgD@vS''
pdD0930 arrayPut 'pdD0930'
arrayClose 'pdD0930'
Initx =: 0.999 , 0.5p1 , (0.25p1%8"_) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@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=:(0,15000"_)*InitInt
pdD0999 =:vSgD@vS''
pdD0999 arrayPut 'pdD0999'
arrayClose 'pdD0999'
NB. ... execute (ijx) ...
arrayOpen 'pdD0823'
pdD0823=:15001 8 4 arrayGet 'pdD0823' NB. ... shape required ...
arrayClose 'pdD0823'
arrayOpen 'pdD0930'
pdD0930=:15001 8 4 arrayGet 'pdD0930' NB. ... shape required ...
arrayClose 'pdD0930'
arrayOpen 'pdD0999'
pdD0999=:15001 8 4 arrayGet 'pdD0999' NB. ... shape required ...
arrayClose 'pdD0999'
load 'plot'
pd 'reset'
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdD0823
pd ((0.823*cos@]"0);0.823*sin@]"0) pTsteps (_,0p1,((0.25p1%8"_)*2"_),160"_)''
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdD0999
pd ((0.999*cos@]"0);0.999*sin@]"0) pTsteps (_,0p1,((0.25p1%8"_)*2"_),160"_)''
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdD0930
pd ((0.930*cos@]"0);0.930*sin@]"0) pTsteps (_,0p1,((0.25p1%8"_)*2"_),160"_)''
pd 'aspect 1'
pd 'pdf'
pd 'show'
... 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) pdD0823
pd (}:@:(cy3"1);incy2)@:((S00yL{])"2) pdD0823 NB. ... incy2 is zero ...
pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdD0999
pd (}:@:(cy3"1);incy2)@:((S00yL{])"2) pdD0999 NB. ... incy2 is zero ...
pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdD0930
pd (}:@:(cy3"1);incy2)@:((S00yL{])"2) pdD0930 NB. ... incy2 is zero ...
pd 'pdf'
pd 'show'
... velocity (8 cycles) ...
... 12 cycles (example) ...
gX0=:,:@(0.15 1 2 8 1 1 12 _12 0 0"_)
gX1=:,:@(0.15 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 , 0.04"_)*%@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=:(0,15000"_)*InitInt
pdD0890 =:vSgD@vS''
pdD0890 arrayPut 'pdD0890'
arrayClose 'pdD0890'
Initx =: 1.010 , 0.5p1 , (0.25p1%12"_) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@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=:(0,15000"_)*InitInt
pdD1010 =:vSgD@vS''
pdD1010 arrayPut 'pdD1010'
arrayClose 'pdD1010'
Initx =: 0.960 , 0.5p1 , (0.25p1%12"_) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@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=:(0,15000"_)*InitInt
pdD0960 =:vSgD@vS''
pdD0960 arrayPut 'pdD0960'
arrayClose 'pdD0960'
NB. ... execute (ijx) ...
arrayOpen 'pdD0890'
pdD0890=:15001 8 4 arrayGet 'pdD0890' NB. ... shape required ...
arrayClose 'pdD0890'
arrayOpen 'pdD0960'
pdD0960=:15001 8 4 arrayGet 'pdD0960' NB. ... shape required ...
arrayClose 'pdD0960'
arrayOpen 'pdD1010'
pdD1010=:15001 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'
... 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'
... velocity (12 cycles) ...
