User:Tom Allen/ta/AddendumX04P05

... for these calculations ...
... the spacetime coordinates of the geodesic ...
... do not coincide with ...
... the spacetime coordinates of the electromagnetic wave ...

uQ0=:,:@(0.05 1 2 8 1 1 1 _0.1 0"_)

vSgDd2=:uQ0([-@([(0{])@E1cn yRef@hkyX04B),:@(S03yH{]))]

Initx =:  1.0000 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0.01   , 0.1"_)*%@InitInt=:512"_

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=:(0,700"_)*InitInt
pdDM     =:vSgD@vS''

pdDM arrayPut   'pdDM'
     arrayClose 'pdDM'

NB. ... execute (ijx) ...

                 arrayOpen  'pdDM'
pdDM=:358401 8 4 arrayGet   'pdDM'   NB. ... shape required ...
                 arrayClose 'pdDM'

load 'plot'

pd 'reset'

pd ((1*cos@]"0);1*sin@]"0) pTsteps (_,0.25p1,(0.25p1+2p1*10),1600"_)''

pd ((1*cos@]"0);1*sin@]"0) pTsteps (_,0.25p1,(0.25p1+2p1-0.01392),160"_)''

pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) (i.@(321136"_){]) pdDM

pd 'aspect 1'
pd 'pdf'

... match on time coordinates ...
... (space coordinates don't match) ...

NB. ... execute (ijx) ...

NB. ... spacetime coordinate at the end of the geodesic (spherical) ...

   zfxc@{.@{:@(i.@(321136"_){]) pdDM
1.16039 1.5708 0.791762 62.8319
   
NB. ... time coordinate at the end of the electromagnetic wave after 10 cycles ...

   1*2p1*10
62.8319

...
...
...

load 'plot'

pd 'reset'

pd ((1*cos@]"0);1*sin@]"0) pTsteps (_,0.25p1,(0.25p1+2p1*10),1600"_)''

pd ((1*cos@]"0);1*sin@]"0) pTsteps (_,0.25p1,(0.25p1+2p1-0.01392),160"_)''

pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) (i.@(319986"_){]) pdDM

pd 'aspect 1'
pd 'pdf'

... match on space coordinates ...
... (time coordinates don't match) ...

NB. ... execute (ijx) ...

NB. ... spacetime coordinate at the end of the geodesic (spherical) ...

   zfxc@{.@{:@(i.@(319986"_){]) pdDM
1.0001 1.5708 0.77148 62.6072

NB. ... x2 coordinate at the end of the electromagnetic wave (spherical) ...

   arctan@{:@(0|:])@:>@((1*cos@]"0);1*sin@]"0) pTsteps (_,0.25p1,((0.25p1+2p1*10)-0.01392),1600"_)''
0.771478

NB. ... time coordinate at the end of the electromagnetic wave ...

   1*(2p1*10)-0.01392
62.8179