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'


JX00P0200C.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) 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'


JX00P0201C.jpg
... 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'


JX00P0202E.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'


JX00P0203D.jpg
... velocity (12 cycles) ...