|
|
| Line 1: |
Line 1: |
| ====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: |
|
| |
|
| Line 45: |
Line 46: |
|
| |
|
|
| |
|
| ''''''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. |
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:
- 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
- ^^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.