VPython Loops

An introduction to creating and using loops in VPython.

The Main Idea

The most commonly used loop structures in VPython are the 'for' loop and the 'while' loop. In Physics modeling, the 'for' loop is useful when one wants to check a condition before running the code in the 'for' loop. For example, the code following the statement -- 'for i in range(0,3):' -- will only run when i is within the specified range. The 'while' loop is useful when one wants to run a code for a specified interval or while a condition is true. For example, the code following the statement -- 'while t < 100:' -- will run until t is greater than or equal to 100 (1,2,3).

A Mathematical Model

When computing iterations for physics problems, using the iterative method with small delta t increments can produce near accurate results. To have truly small delta t increments, however, computational modeling is necessary for computation.

In a problem that requires use of the momentum principle and a specific number of time steps for iteration, we update momentum for each time step using the following equation:

delta P = Fnet * deltat

With this equation, the final momentum is updated after each time step (deltat) up to a time (t). We can only manually do this with a small number of increments, however, and as a result, with less accuracy than if our delta t increments were smaller. This is where computational modeling and VPython loops come in.

A Computational Model

With computational modeling using VPython, we can reduce the size of delta t and increase the number of time steps in the approximation of an iteration. Instead of two or three time steps, VPython loops make it possible to test infinitely small time steps, making the final result more accurate. For example, to calculate an approximation from t = 0 to t = 2 using two time steps, one could write the following time update:

deltat = 1
t = 0
while t < 2:
    t += deltat

However, loops can be used to test much smaller time steps than deltat = 1; the smaller the time step, the more accurate the iteration.

Examples

The following examples cover a range of loops that can be created in VPython from the simplest 'for' loops to more complicated 'for' and 'while' loops.

Simple

The simplest example is a basic 'for' loop. The following code will print each integer in a range:

for i in range(0,10):
    print i

The same thing can be accomplished with a 'while' loop as well. See the following:

i = 0
while i < 10:
    print i
    i += 1

When modeling momentum updates, using a 'while' loop allows the code to run until Tfinal has been reached by adding deltat to t each time the loop runs.

Middling

To solve more complex problems, we need to create values and objects before the loop that will then be updated within the loop until a certain time, t. In the following example, the final position and final velocity of object ball is updated until t = 10 using a time step of deltat = 1.

t = 0
deltat = 1

while t < 10:
    Fgrav = vector(0,-ball.m*g,0)
    Fdrag=(.5)*dragCoeff*airDensity*areaBall*mag(ball.p/ball.m)**2*norm(ball.p)
    Fnet = Fgrav - Fdrag

    ball.p = ball.p + Fnet*deltat
    ball.pos = ball.pos + (ball.p/ball.m)*deltat  

    t += deltat

print(ball.pos)    #prints final ball position
print(ball.p/mball)    #prints final ball velocity

Difficult

The following code calculates the final position and velocity of a ball attached to a string mounted to a ceiling. After code is written listing the constants, creating the objects, and setting an initial value of t = 0, the following statements update the position and velocity values until t = 10 seconds.

t = 0
deltat = 1

while t < 10:   
    L = ball.pos - ceiling.pos
    s=mag(L) - L0
    Lhat = L/mag(L)
    Fs = -(ks)*s*Lhat
    Fg = vector(0,-g*mball,0)
    Fdrag = (-1)*b*(ball.p/mball)
    Fnet = Fg + Fs + Fdrag
    ball.p = ball.p + Fnet*deltat
    ball.pos = ball.pos + (ball.p/(mball))*deltat
    spring.axis = ball.pos - ceiling.pos 
    
    t += deltat

print(ball.pos)    #prints final ball position
print(ball.p/mball)    #prints final ball velocity

Connectedness

Understanding the basics of VPython creates a framework for more easily learning to write in coding languages other than Python. Additionally, understanding the basics of the 'for' loop and the 'while' loop enables one to write more complex code using both 'for' and 'while' loops, even nesting both types of loops in creating complex conditionals. In more advanced Physics modeling, being able to write more complex conditional statements enables these more complex equations and relationships to be solved via computational modeling.

Even for non-computing majors, coding experience is a highly valuable trait employers are increasingly looking for in candidates. In 2016, analytics firm Burning Glass reported that programming jobs were growing 12% faster than the market average. Additionally, half of the projected job openings looking for programming experience are in non-technology fields such as 'finance, manufacturing, and healthcare' (4). In 2017, Forbes ranked Python as the top-ranked in-demand coding language among the top five: 'Python, Java, JavaScript, C#, and PHP' (5).

History

Python is an interpreted language that originated in the 1980s and was released from development in the 1990s. Because it is interpreted, compiling is not required to convert lines of code into machine-understandable instructions (6). In 1998, David Scherer saw a need for a better 2D and 3D graphics programming environment and created the idea for Visual (a.k.a. VPython), a Python module (7).

VPython Loops

Contents

The Main Idea

A Mathematical Model

A Computational Model

Examples

Simple

Middling

Difficult

Connectedness

History

See Also

Further Reading

External Links

References

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