Python Syntax: Difference between revisions

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(Created page with "====Vectors and Units==== '''The Main Idea''' This page discusses basic vPython functions and how they can be used to produce a model. vPython uses the same syntax as regular...")
 
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====Vectors and Units====
 
'''The Main Idea'''
==The Main Idea==
This page discusses basic vPython functions and how they can be used to produce a model. vPython uses the same syntax as regular Python; however, vPython also allows you to produce a 3D model simulating the equations and computations your code is producing.  
This page discusses basic vPython functions and how they can be used to produce a model. vPython uses the same syntax as regular Python; however, vPython also allows you to produce a 3D model simulating the equations and computations your code is producing.  


'''Mathematical Model'''
<!--{{spaces|2}}-->
==Mathematical Model==
Vpython can be used with any equation. However, you may find some of the following useful:
Vpython can be used with any equation. However, you may find some of the following useful:


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''''''Computational Model'''
==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)
 
trail = curve(color=craft.color)    # This creates a trail for the spacecraft
scene.autoscale = 0                # And this prevents zooming in or out
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
while t < 165240: #sets time for loop to run
    rate(10000)  # This slows down the animation (runs faster with bigger number)
 
    # 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 modeling producing physics models.
 
'''
References'''


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

Revision as of 10:32, 8 April 2017

The Main Idea

This page discusses basic vPython functions and how they can be used to produce a model. vPython uses the same syntax as regular Python; however, vPython also allows you to produce a 3D model simulating the equations and computations your code is producing.

Mathematical Model

Vpython can be used with any equation. However, you may find some of the following useful:

Momentum Update: pf = pi + Fnet*deltat

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


Gravitational Force:

  1. CONSTANTS

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

r=craft.pos-Earth.pos #finds the change in position m=mcraft rmag= mag(r) #finds the magnitude of change in position Fmag=(G*mcraft*mEarth)/(rmag**2)

# ^^Calculates the new magnitude of gravitational force

rhat=r/rmag

#^^Calculates the direction of tbe change in position

Fnet=-Fmag*rhat

  1. ^^Calculates net force

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.