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.