Python Syntax

Claimed by Madelyn Hightower- Spring 2017

The Main Idea

This page discusses basic functioning of vPython and how the program can be used to produce models. While vPython is rather similar to the normal Python and uses the same syntax, vPython is an extension of Python and allows users to produce 3D models. It is frequently used for educational purposes, however it has also been used in research to help scientists visualize 3D models. VPython, if used correctly, can be very helpful in learning new concepts in courses like physics, or helping to further study on models that may not be easy to create in real life.

Downloading vPython

Before learning how to code vPython, the first step is to download the proper application. If interested, before downloading vPython, glow script is a great resource to practice using vPython. Glow script also creates 3D models and run programs just like vPython, so it is a great resource to try out.

To download vPython, first either install Continuum Anaconda Python Distribution. Choose from either the Anaconda with Python 3.x (this form is recommended on vypthon.org, especially if "Classic" VPython/Python 2.7 has previously been installed on the device.)

In order to access the necessary download, use this link: https://www.python.org/downloads/

For windows, then go to the Power Shell or Command Prompt and type " pip install vpython ". For macs, go to Terminal and type " pip install vypython ".

Vpython will then be successfully downloaded onto the device.

Mathematical Model

Vpython can compute any equation, but some that may be most helpful and most useful for Physics can be found below:

Always start vPython windows with: from__future__ import division from visual import*

To update momentum:

pf = pi + Fnet*deltat

To update position:

objectf.pos = objecti.pos + (pcart/mcart)*deltat

To create a vector: vector(0,0,0) -- fill in with whatever numbers the vector should be

Gravitational Force:

CONSTANTS G = 6.7e-11 mEarth = 6e24 mcraft = 15e3 deltat = 60 t = 0

Finds the change in position:

r=craft.pos-Earth.pos m=mcraft

To find the magnitude of the change in position:

rmag= mag(r)

To calculate the new magnitude of gravitational force:

Fmag=(G*mcraft*mEarth)/(rmag**2)

Calculates the direction of tbe change in position:

rhat=r/rmag

Calculates net force:

Fnet=-Fmag*rhat

Spring Force:

L0 = 0.3 Lvec = ball.pos - ceiling.pos Lhat = norm(Lvec) Lmag = mag(Lvec) Fspr = (-ks)*(Lmag - L0)*(Lhat)

Kinetic Energy:

Kinetic = (1/2)*(mball*(vel**2))

Computational Model

VPython is used to create computational models of various real world situations so that we can see how these equations used in the code can manipulate these situations.

Examples

Simple:

Creating Shapes:

Sphere:

sphere= sphere(pos=vector(-4,-2,5), radius=.4, color=color.red)

Arrow:

bt=arrow(pos=sphere.pos, axis=sphere2.pos-sphere.pos, color=color.cyan)

Vector:

vector=vector(0, 0, 0)

Trail:

trail = curve(color=sphere.color)

trail.append(pos=sphere.pos)

Setting Scene Range:

scene.range=11*sphere.radius

Helix:

spring = helix(pos=ceiling.pos, color=color.cyan, thickness=.003, coils=40, radius=0.015)

Intermediate:

Graphs:

Setup graphing windows:

gdisplay(width=500, height=250, x=600, y=1)

ygraph = gcurve(color=color.yellow)

gdisplay(width=500, height=250, x=600, y=300)

Plotting:

pgraph = gcurve(color=color.blue)

ygraph.plot(pos=(time, Fnet.y))

pgraph.plot(pos=(time, sphere.y))

Difficult:

Using Loops to update Equations:

CONSTANTS:

G = ?

mEarth = ?

mmoon = ?

mcraft = ?

deltat = ?

t = ?

OBJECTS AND INITIAL VALUES:

Earth = sphere(pos=vector(0,0,0), radius=6.4e6, color=color.cyan)

scene.range=11*Earth.radius

Moon = sphere(pos=(4e8, 0, 0), radius=1.75e6, color=color.white)

Add a radius for the spacecraft. It should be BIG, so it can be seen:

craft = sphere(pos=vector(-6.656e7,-3.648e6,0), radius= 10000, color=color.yellow) vcraft = vector(206, 2645,0) pcraft = mcraft*vcraft pArrow=arrow(color=color.green) fArrow=arrow(color=color.cyan) dpArrow=arrow(color=color.red) Fnet_tangent_arrow = arrow(color=color.yellow) Fnet_perp_arrow= arrow(color=color.magenta)

This creates a trail for the spacecraft:

trail = curve(color=craft.color)

And this prevents zooming in or out:

scene.autoscale = 0 pscale=Earth.radius/mag(pcraft) fscale=Earth.radius/((G*mEarth*mcraft)*mag(craft.pos-Earth.pos)**2) dpscale=500*Earth.radius/mag(pcraft) print("p=", pcraft)

CALCULATIONS:

Sets time for loop to run:

while t < 165240: This slows down the animation (runs faster with bigger number):

   rate(10000)   

    Add statements here for the iterative update of gravitational
   force, momentum, and position.

   r = craft.pos-Earth.pos
   rmag = sqrt(r.x**(2)+r.y**(2)+r.z**(2))
   Fmag= G*mEarth*mcraft/(rmag**2)
   rhat= r/rmag
   rmoon= craft.pos - Moon.pos
   rmoonmag= mag(rmoon)
   rmoonhat= norm(rmoon)
   Fmoonmag= G*mmoon*mcraft/(rmoonmag**2)
   Fmoon= -Fmoonmag*rmoonhat
   p_init= mag(pcraft)
   pcraft_i=pcraft+vector(0,0,0)
   Fearth= -Fmag*rhat
   Fnet= Fearth + Fmoon
   pcraft=Fnet*deltat+pcraft
   p_final=mag(pcraft)

   Fnet_tangent = (p_final-p_init)*norm(pcraft)/deltat
   Fnet_tangent_arrow.pos=craft.pos
   Fnet_tangent_arrow.axis=Fnet_tangent*fscale
   Fnet_perp = Fnet-Fnet_tangent
   Fnet_perp_arrow.pos=craft.pos
   Fnet_perp_arrow.axis=Fnet_perp*fscale
   vcraft=pcraft/mcraft
   craft.pos=vcraft*deltat+craft.pos
   pArrow.pos=craft.pos
   pArrow.axis=pcraft*pscale
   fArrow.pos=craft.pos
   fArrow.axis=Fnet*fscale
   deltap= pcraft-pcraft_i
   dpArrow.pos=craft.pos
   dpArrow.axis=deltap*dpscale
   scene.center=craft.pos
   scene.range=craft.radius*600
   

  Uncomment these two lines to exit the loop if
  the spacecraft crashes onto the Earth.

   if rmag < Earth.radius: 
       break

   trail.append(pos=craft.pos)  
   t = t+deltat

Connectedness

vPython codes are extremely useful for modeling physics situations. However, the coding skills learned in this class can be applied to almost anything. For example, Aerospace Engineers are becoming increasingly dependent on computer simulations to test ideas before prototyping to reduce costs.

History

vPython was released in 2008. It was developed by researchers at Carnegie Mellon University. It is largely used for educational purposes especially producing physics models.

References

http://vpython.org/contents/history.html