Version 2 of Sketchpad had already proven itself a powerful tool for modeling situations from physics, including motion, optics, vectors, electrostatics, simple harmonic motion, and waves. Version 3 makes construction of these models easier and, in some cases, possible.

The sketches on this page are available individually (below) or can be downloaded as a package.

Projectile Path
This sketch shows the path of a projectile computed iteratively. Buttons give you control over showing the focus and directrix and over an illustration of how to find the focus of the parabolic path using light rays. An animation button allows you to animate a ball along the path. A Time Trace button shows a dynamic locus of the balls at uniform time intervals.

The construction was accomplished with a four-step recursive script.

Projectile Script
1. Point p(0)
2. Point v(origin)
3. Point v(0)
4. Point Delta_v

   1. Let [p'(0)] = Image of Point p(0) translated by vector v(origin)->v(0).
   2. Let [m] = Segment between Point [p'(0)] and Point p(0).
   3. Let [v'(0)] = Image of Point v(0) translated by vector v(origin)->Delta_v.
   4. Recurse on [p'(0)], v(origin), [v'(0)] and Delta_v.

This sketch shows the path of a particle in a fixed, inverse square force field, using discrete integration. The particle's initial velocity is given by a vector v0. The strength of the force field and its center may be varied, and changing the strength to negative changes the force from attractive to repulsive.

As with the projectile sketch (above), construction of this sketch required a recursive script. In addition, computation of the force at any point, and applying that force to the particle, was done with Version 3's dynamic transformation based on calculated quantities.

The quantity dt controls the increment of time used in the numerical integration. If the path is not smooth, decrease dt. If the path is too short, increase dt.

A button moves the givens to simulate launching a projectile on the surface of the earth.

This sketch requires a fast machine with FPU for reasonable response. You may also need to increase Sketchpad's memory partition.

The Two Body Problem
This sketch is similar to the orbit sketch above, but now there are two particles, each free to move in the field created by the other. Each particle has mass, so you can experiment with the limiting cases of one mass much greater than the other. The Simulation button takes dt down to zero and then gradually increases it, showing, in effect, the motion of the two particles as an animation.

This sketch requires a fast machine with FPU for reasonable response. You may also need to increase Sketchpad's memory partition.

Return to the Foyer.

Sketches, scripts, and web pages by Bill Finzer and Nick Jackiw.