User:Tom Allen/ta/AddendumX06P06

load 'plot'

pd 'reset'

x6Rx2   =.(0{])+((1{])-0{])*(i.@>:%])@(2{])
x6spiral=.(x6m*^@(x6q*]-x6p))(([*cos@]);[*sin@])]

x6m=.1"_
x6q=.0.01"_

x6p=.0.00p1"_
pd x6spiral x6Rx2 _150.00p1 20.10p1 15000

pd 'aspect 1'
pd 'canvas plot.html 666 500'

energy is increasing through accretion by moving inward along the spiral

pU0=:,:@(0.05 1 2 8 1 1 1 0.1 0.01"_)

vSgDd2=:pU0([([(0{])@E1cn yRef@hkyX06B),:@(S03yH{]))]

Initx =:  0.7500 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0      , 0.1"_)*%@InitInt=:8"_

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=:(0,512000"_)*InitInt
pdDG     =:vSgD@vS''

pdDG arrayPut   'pdDG'
     arrayClose 'pdDG'

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

                  arrayOpen  'pdDG'
pdDG=:4096001 8 4 arrayGet   'pdDG'   NB. ... shape required ...
                  arrayClose 'pdDG'

load 'plot'

pd 'reset'

pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDG

pd ((0.9675*cos@]"0);0.9675*sin@]"0) pTsteps _ 0p1 2p1 160
pd ((1.2832*cos@]"0);1.2832*sin@]"0) pTsteps _ 0p1 2p1 160

pd 'aspect 1'
pd 'canvas plot.html 666 500'

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 (}:@((0.1%8"_)*i.@(3072001"_));veloc)@:((S00yL{])"2) (i.@(3072001"_){]) pdDG
pd (}:@((0.1%8"_)*i.@(3072001"_));incy2)@:((S00yL{])"2) (i.@(3072001"_){]) pdDG

pd 'canvas plot.html 666 500'

load 'plot'

pd 'reset'

NB. ... plotted against the length in 4-dimensional spacetime ...
NB. ... (an equal length in 4-dimensional spacetime means the events are coincident) ...

pd (((0.1%8"_)*i.@(3072001"_));(0.1%8"_)*i.@(3072001"_))''                       NB. ... elapsed time at fixed point in empty space (blue) ...
pd (((0.1%8"_)*i.@(3072001"_));cy3"1)@:((S00yL{])"2) (i.@(3072001"_){]) pdDG     NB. ... elapsed time along the geodesic            (red ) ...
                                                                                 NB. ... (a 'fixed point' in the energy field)             ...
pd 'canvas plot.html 666 500'

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Download: File:LX06P0616C.ijs

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