tkinter我如何计算python中所有粒子的法向量和动能守恒？

如何解决tkinter我如何计算python中所有粒子的法向量和动能守恒？

我试图计算两个粒子 p1 和 p2 的法向量 n formula for normal vector 和切向向量 t tangential vector n=v 以求动能守恒 conservation of energy 或者这里有另一种写公式的方法：formula 2 但我真的不知道在代码中的何处以及如何实现这一点？

from tkinter import *
from random import *
from math import *
myHeight=250#400
myWidth=400#800
mySpeed=20#100

col= randint(0,255)
radius = randint(0,50)
print (col)
#x= 60 


global particules
particules = []

def initialiseParticule(dx,dy,radius,color):
    x,y = randint(0,myWidth),randint(0,myHeight) #100
    radius = randint(0,10)
    #color = randint(0,255)
    #col1=str(color)
    k = myCanvas.create_oval(x-radius,y-radius,\
                         x+radius,y+radius,\
                         width=2,fill=color)
    b = [x,y,dx,radius]
    particules.append(b)

    #print(k)


  
def updateParticules():

  N = len(particules)
  for i in range(N):  
      
      # update displacement 
      particules[i][0] += particules[i][2]
      particules[i][1] += particules[i][3]

      #xi += vxi
      #yi += vyi
      
      # collision with walls 
      if particules[i][0]<particules[i][4]or particules[i][0]>=myWidth-particules[i][4]:    
            particules[i][2] *= -1
      if particules[i][1]<particules[i][4] or particules[i][1]>=myHeight-particules[i][4]:
            particules[i][3] *= -1

      # collision with other particles 
      for j in range(N):
        if i != j:

          xi,yi = particules[i][0],particules[i][1]
          vxi,vyi = particules[i][2],particules[i][3]

          xj,yj = particules[j][0],particules[j][1]
          vxj,vyj = particules[j][2],particules[j][3]

          dij = sqrt((xi-xj)**2 + (yi-yj)**2)
          # print(dij)
          #  # collision !!!
          if dij <= particules[i][4]+particules[j][4]:
            particules[i][2] *= -1
            particules[j][2] *= -1
            particules[i][3] *= -1
            particules[j][3] *= -1


      r = particules[i][4]
      myCanvas.coords(i+1,particules[i][0]-r,particules[i][1]-r,particules[i][0]+r,particules[i][1]+r)

 
    
def animation():
    miseAJourBalles()
    myCanvas.after(mySpeed,animation)


mainWindow=Tk()
mainWindow.title('Pong')
#mainWindow.geometry(str(myWidth)+'x'+str(myHeight+100))
myCanvas=Canvas(mainWindow,bg='dark grey',height=myHeight,width=myWidth)
myCanvas.pack(side=TOP)

N = 3
for n in range(N):
#  initialiseParticules( -1,-1,'randint(0,10)') 
 initialiseParticules( -1,'pink') 



animation()

#bou=Button(mainWindow,text="Leave",command=mainWindow.destroy) 
#bou.pack() 

mainWindow.mainloop()