Simulating physics with VPython

In the physical sciences, simplifications and approximate values ​​are often allowed: the orbits are always circular, the projectiles fly without air resistance, and the pendulum is deflected only by a small angle. 

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Pypi, pip:

pip install vpython

3D Cylinder ():

import vpython as vpvp.cylinder()

, :

vp.cylinder(pos=vp.vector( 4, 0, 0), size=vp.vector(4,4,4), color = vp.color.red)

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, :

import vpython as vp
vp.scene.title = "Modeling the motion of planets with the gravitational force"
vp.scene.height = 600
vp.scene.width = 800
      
      

        
        
        
      

    
        
        
        
      
      

        
        
        
      

    
    

( ):

planet = vp.sphere(pos=vp.vector(1,0,0), radius=0.05, color=vp.color.green,
               mass = 1, momentum=vp.vector(0,30,0), make_trail=True )

star = vp.sphere(pos=vp.vector(0,0,0), radius=0.2, color=vp.color.yellow,
               mass = 2.0*1000, momentum=vp.vector(0,0,0), make_trail=True)
      
      

        
        
        
      

    
        
        
        
      
      

        
        
        
      

    
    

, :

def gravitationalForce(p1,p2):
	G = 1 #real-world value is : G = 6.67e-11
	rVector = p1.pos - p2.pos
	rMagnitude = vp.mag(rVector)
	rHat = rVector / rMagnitude
	F = - rHat * G * p1.mass * p2.mass /rMagnitude**2
	return F
      
      

        
        
        
      

    
        
        
        
      
      

        
        
        
      

    
    

, — , :

t = 0
dt = 0.0001 #The step size. This should be a small number
      
      

        
        
        
      

    
        
        
        
      
      

        
        
        
      

    
    

, t



.

: rate()



, , sleep()

while True:
	vp.rate(500)
  #calculte the force using gravitationalForce function
	star.force = gravitationalForce(star,planet)
	planet.force = gravitationalForce(planet,star)
  #Update momentum, position and time
	star.momentum = star.momentum + star.force*dt
	planet.momentum = planet.momentum + planet.force*dt
	star.pos = star.pos + star.momentum/star.mass*dt
	planet.pos = planet.pos + planet.momentum/planet.mass*dt
	t+= dt
      
      

        
        
        
      

    
        
        
        
      
      

        
        
        
      

    
    

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: RGB :

star = vp.sphere(pos=vp.vector(0,0,0), radius=0.2, color=vp.color.yellow,
               mass = 1000, momentum=vp.vector(0,0,0), make_trail=True)

planet1 = vp.sphere(pos=vp.vector(1,0,0), radius=0.05, color=vp.color.green,
               mass = 1, momentum=vp.vector(0,30,0), make_trail=True)

planet2 = vp.sphere(pos=vp.vector(0,3,0), radius=0.075, color=vp.vector(0.0,0.82,0.33),#RGB color
                  mass = 2, momentum=vp.vector(-35,0,0), make_trail=True)
                  
planet3  = vp.sphere(pos=vp.vector(0,-4,0), radius=0.1, color=vp.vector(0.58,0.153,0.68),
                  mass = 10, momentum=vp.vector(160,0,0), make_trail=True)
      
      

        
        
        
      

    
        
        
        
      
      

        
        
        
      

    
    

:

while (True):
    vp.rate(500)
    
 	#Calculte the force using gravitationalForce function
    star.force = gravitationalForce(star,planet1)+gravitationalForce(star,planet2)+gravitationalForce(star,planet3)
    planet1.force = gravitationalForce(planet1,star)+gravitationalForce(planet1,planet2)+gravitationalForce(planet1,planet3)
    planet2.force = gravitationalForce(planet2,star)+gravitationalForce(planet2,planet1)+gravitationalForce(planet2,planet3)
    planet3.force = gravitationalForce(planet3,star)+gravitationalForce(planet3,planet1)+gravitationalForce(planet3,planet2)

    #Update momentum, position and time
    star.momentum = star.momentum + star.force*dt
    planet1.momentum = planet1.momentum + planet1.force*dt
    planet2.momentum = planet2.momentum + planet2.force*dt
    planet3.momentum = planet3.momentum + planet3.force*dt

    star.pos = star.pos + star.momentum/star.mass*dt
    planet1.pos = planet1.pos + planet1.momentum/planet1.mass*dt
    planet2.pos = planet2.pos + planet2.momentum/planet2.mass*dt
    planet3.pos = planet3.pos + planet3.momentum/planet3.mass*dt
    
    t += dt
      
      

        
        
        
      

    
        
        
        
      
      

        
        
        
      

    
    

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VPython 3D- , .