Three-body-problem in3d

breed [bodys body]


globals [ ; variavel global todos podem alterar
  turtle1
  turtle2
  turtle3
  force ; modulo do vetor força

; vetores do copo 1 em relação ao corpo 2
  fx1_2     ; x-component of force vector
  fy1_2     ; y-component of force vector
  fz1_2     ; z-component of force vector
; vetores do copo 1 em relação ao corpo 3
  fx1_3     ; x-component of force vector
  fy1_3     ; y-component of force vector
  fz1_3
; vetores do copo 2 em relação ao corpo 1
  fx2_1     ; x-component of force vector
  fy2_1     ; y-component of force vector
  fz2_1
; vetores do copo 2 em relação ao corpo 3
  fx2_3     ; x-component of force vector
  fy2_3     ; y-component of force vector
  fz2_3
; vetores do copo 3 em relação ao corpo 1
  fx3_1     ; x-component of force vector
  fy3_1     ; y-component of force vector
  fz3_1
; vetores do copo 3 em relação ao corpo 2
  fx3_2     ; x-component of force vector
  fy3_2     ; y-component of force vector
  fz3_2
  vx     ; x-component of velocity vector
  vy     ; y-component of velocity vector
  vz     ; z-component of velocity vector
]

to Clean

  ;; poem os valores padrao
ca
set X1 0
set Y1 0
set z1 0

set X2 5
set Y2 0
set z2 0

set X3 0
set Y3 4
set z3 0

set Mass1 1
set Mass2 1
set Mass3 1

set VelocityX1 0
set VelocityX2 0
set VelocityX3 0
set VelocityY1 0
set VelocityY2 0
set VelocityY3 0
set Velocityz1 0
set Velocityz2 0
set Velocityz3 0

  ;; plot standard position
    set-default-shape turtles "circle"
  create-turtles 1 [set turtle1 self set color green setxyz X1 Y1 Z1 set pen-size 1 pen-down ]
  create-turtles 1 [set turtle2 self set color blue setxyz X2 Y2 Z2 set pen-size 1 pen-down]
  create-turtles 1 [set turtle3 self set color white setxyz X3 Y3 z3 set pen-size 1 pen-down ]
end 

to Plot_bodies
  ca
    ;; plot standard position
    set-default-shape turtles "circle"
  create-turtles 1 [set turtle1 self set color green setxyz X1 Y1 Z1 set pen-size 1 pen-down ]
  create-turtles 1 [set turtle2 self set color blue setxyz X2 Y2 Z2 set pen-size 1 pen-down ]
  create-turtles 1 [set turtle3 self set color white setxyz X3 Y3 Z3 set pen-size 1 pen-down ]
end 

to Stable  ;; mostra um exemplo de orbita estavel dois sois e um planeta

clear-all
  ;; poem os valores padrao
ca
set X1 8
set Y1 25
set Z1 0

set X2 7
set Y2 25
set Z2 0

set X3 0
set Y3 0
set Z3 0

set VelocityX1 -0.2
set Velocityy1 0
set Velocityz1 0
set Velocityx2 -0.2
set VelocityY2 0
set Velocityz2 0.05
set Velocityx3 0
set Velocityy3 0
set VelocityZ3 0
set Mass1 0.055
set Mass2 0.0001
set Mass3 20

  ;; plot position
  set-default-shape turtles "circle"
  create-turtles 1 [set turtle1 self set color green setxyz X1 Y1 Z1 set pen-size 1 pen-down ]
  create-turtles 1 [set turtle2 self set color blue setxyz X2 Y2 Z2 set pen-size 1 pen-down]
  create-turtles 1 [set turtle3 self set color white setxyz X3 Y3 Z3 set pen-size 1 pen-down]
end 

to Stable_2
    ;; two planets and one sun
clear-all
  ;; set the default values
ca
set X1 -23
set Y1 0
set Z1 0
set X2 8
set Y2 0
set Z2 -1
set X3 0
set Y3 0
set Z3 1

set VelocityX1 0
set VelocityX2 0
set VelocityX3 0
set VelocityY1 1.5
set VelocityY2 3.5
set VelocityY3 0
set VelocityZ1 0.1
set VelocityZ2 0.6
set VelocityZ3 1

set Mass1 1
set Mass2 1
set Mass3 1000

  ;; plot position
  set-default-shape turtles "circle"
  create-turtles 1 [set turtle1 self set color green setxyz X1 Y1 Z1 set pen-size 1 pen-down ]
  create-turtles 1 [set turtle2 self set color blue setxyz X2 Y2 Z2 set pen-size 1 pen-down]
  create-turtles 1 [set turtle3 self set color white setxyz X3 Y3 Z3 set pen-size 1 pen-down]
end 

to go

; integration time an improvement that can be added in the future
;  every 0.1
;  [

  ; check if the bodies are in the field of view
  if turtle1 = nobody [ stop ]
   if turtle2 = nobody [ stop ]
   if turtle3 = nobody [ stop ]


    ;Calculate force
    ask turtle1 [
    set size 1
      update-force1_2
      update-force1_3



    ]


     ask turtle2 [
    set size 0.5
      update-force2_1
      update-force2_3


    ]


     ask turtle3 [
    set size 10
      update-force3_2
      update-force3_1



    ]



  ;; move the particles at the same time , to not influence the results
  ask turtle1 [move1]
ask turtle2 [move2]
  ask turtle3 [move3]
;
end 


; bode1

to update-force1_2
  ;body distance 1 to 2
   let r distance turtle2
  ; avoiding infinity
  if (r < 0.5 and r > -0.5) [set r 0.5]
  ;Calculating body force  1_2
  set force 0.1 * (Mass1 * Mass2)/(r ^ 2) ;; has been multiplied by 0.1 so the particles don't leave the field of view
 ; separating the force in the components x and y
 face turtle2
 set fx1_2 force * dx
 set fy1_2 force * dy
 set fZ1_2 force * dZ
end 

to update-force1_3
  ;body distance 1 to 2
   let r distance turtle3
  ; avoiding infinity
  if (r < 0.5 and r > -0.5) [set r 0.5]
  ;Calculating body force 1_2
  set force 0.1 * (Mass1 * Mass3)/(r ^ 2)
 ; separating the force in the components x e y
 face turtle3
 set fx1_3 force * dx
 set fy1_3 force * dy
 set fZ1_3 force * dZ
end 


; bode2

to update-force2_1
  ;body distance 2 ao 1
   let r distance turtle1
  ; avoiding infinity
  if (r < 0.5 and r > -0.5) [set r 0.5]
  ;Calculating body force 2_1 (we know that is equal to - body strength 1_2, but in doubt, let's calculate)
  set force 0.1 * (Mass2 * Mass1)/(r ^ 2)
 ; separating the force in the components x and y
 face turtle1
 set fx2_1 force * dx
 set fy2_1 force * dy
 set fZ2_1 force * dZ
end 

to update-force2_3
  ;body distance 2 to 3
   let r distance turtle3
  ; avoiding infinity
  if (r < 0.5 and r > -0.5) [set r 0.5]
  ;Calculating body force 2_3
  set force 0.1 * (Mass2 * Mass3)/(r ^ 2)
 ; separating the force in the components x and y
 face turtle3
 set fx2_3 force * dx
 set fy2_3 force * dy
 set fZ2_3 force * dZ
end 

; bode3

to update-force3_1
  ;body distance 3 to 1
   let r distance turtle1
  ; avoiding infinity
  if (r < 0.5 and r > -0.5) [set r 0.5]
  ;Calculating body force 3_1 (we know that is equal to - body strength 1_3)
  set force 0.1 * (Mass3 * Mass1)/(r ^ 2)
 ; separating the force in the components x and y
 face turtle1
 set fx3_1 force * dx
 set fy3_1 force * dy
 set fZ3_1 force * dZ
end 

to update-force3_2
  ;body distance 3 to 2
   let r distance turtle2
  ; avoiding infinity
  if (r < 0.5 and r > -0.5) [set r 0.5]
  ;Calculating body force 2_3 (we know that is equal to - body strength 3_2)
  set force 0.1 * (Mass3 * Mass2)/(r ^ 2)
 ; separating the force in the components x and y
 face turtle2
 set fx3_2 force * dx
 set fy3_2 force * dy
 set fZ3_2 force * dZ
end 

to move1 ; move the particles
  ;updates particle speed and adds force;; F=m.a, then have to divide by mass
  set VelocityX1 VelocityX1 + (fx1_2 / Mass1) + (fx1_3 / Mass1)
  set VelocityY1 VelocityY1 + (fy1_2 /  Mass1) + (fy1_3 /  Mass1)
  set VelocityZ1 VelocityZ1 + (fZ1_2 /  Mass1) + (fZ1_3 /  Mass1)

  ; disappears if it goes off the edge
  if abs (ycor + vy) > max-pycor or abs (xcor + vx) > max-pxcor or abs (zcor + vz) > max-pzcor [ die ]

  ; update particle position
    set X1 X1 + VelocityX1
    set Y1 Y1 + VelocityY1
    set Z1 Z1 + VelocityZ1
    setxyz X1 Y1 Z1
end 

to move2 ;  move the particles
  ;updates particle speed and adds force
  set VelocityX2 VelocityX2 + (fx2_1 / Mass2) + (fx2_3 / Mass2)
  set VelocityY2 VelocityY2 + (fy2_1 / Mass2) + (fy2_3 / Mass2)
  set VelocityZ2 VelocityZ2 + (fZ2_1 / Mass2) + (fZ2_3 / Mass2)

  ; disappears if it goes off the edge
  if abs (ycor + vy) > max-pycor or abs (xcor + vx) > max-pxcor or abs (zcor + vz) > max-pzcor [ die ]

  ; update particle position
    set X2 X2 + VelocityX2
    set Y2 Y2 + VelocityY2
    set Z2 Z2 + VelocityZ2
    setxyz X2 Y2 Z2
end 

to move3 ;  move the particles
  ;updates particle speed and adds force
  set VelocityX3 VelocityX3 + (fx3_1 / Mass3) + (fx3_2 / Mass3)
  set VelocityY3 VelocityY3 + (fy3_1 / Mass3) + (fy3_2 / Mass3)
  set VelocityZ3 VelocityZ3 + (fZ3_1 / Mass3) + (fZ3_2 / Mass3)

  ; disappears if it goes off the edge
  if abs (ycor + vy) > max-pycor or abs (xcor + vx) > max-pxcor or abs (zcor + vz) > max-pzcor[ die ]

  ; update particle position
    set X3 X3 + VelocityX3
    set Y3 Y3 + VelocityY3
    set Z3 Z3 + VelocityZ3
    setxyz X3 Y3 Z3
end 

to setup
  clear-all
  create-turtles 3
  [
  setxy random-xcor random-ycor
  ]
end