VPython Loops

Krish Katariya, Spring 2026 Editing This Page! Please don't remove.

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).

Physics Explanation: Why Loops Work for Motion

In physics, motion is usually described using continuous equations, such as Newton’s Second Law, which will relate force and momentum with:

 dP/dt = Fnet

. This equation tells us how momentum changes continuously over time.

However, in computational modeling, we cannot directly calculate continuous changes easily. To combat this, we instead approximate the process using very tiny time steps (Δt) and updating the values at each step. While this isn't continuous, if our time steps are small enough, we can approximate the process closely enough.

Using the momentum principle in discrete form, we write:

delta P = Fnet * deltat

This equation is saying that, during each small time interval (deltat), the momentum of an object changes based on the net force acting on it. After updating the momentum, we then can update position using the kinematics formulas that we are familiar with.

position = position + velocity * deltat

Now imagine we want to have many tiny steps over a long time period, writing these equations over and over in VPython would take way too long, which is why glowscript has the concept of loops. A loop allows us to repeatedly run the same lines of code many times, meaning we can apply these updates many times. Thus, using loops, we are effectively simulating continuous motion using small time steps.

The smaller the value of deltat, the closer this approximation is to real physical behavior. Large time steps can lead to inaccurate results, while very small time steps produce more realistic simulations.

Interactive Model: Why Time Step Size Matters

The embedded GlowScript model below compares falling objects simulated with different values of deltat. A larger deltat updates the motion in bigger jumps, which makes the approximation less accurate.

A smaller deltat updates the motion more frequently, so the simulated motion stays closer to the exact solution. This shows why loops are useful in VPython: they approximate continuous motion by repeatedly updating momentum and position over small time intervals. This is also why we want to use relatively small values for delta t!

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

Physics Explanation: Why Loops Work for Motion

Interactive Model: Why Time Step Size Matters

A Mathematical Model

A Computational Model

Examples

Simple

Middling

Difficult

Connectedness

History

See Also

Further Reading

External Links

References

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VPython Loops

The Main Idea

Physics Explanation: Why Loops Work for Motion

Interactive Model: Why Time Step Size Matters

A Mathematical Model

A Computational Model

Examples

Simple

Middling

Difficult

Connectedness

History

See Also

Further Reading

External Links

References

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