# Introduction

ROMP movement is controlled by three types of forces - gravity, magnetic, and friction. The level of observed chaos is basically a function of the number and placement of magnets. While ROMP trajectories may seem very complicated, the underlying physics is fundamental.

We will look at this problem in terms of energy hills and valleys.* So, the pendulum moves slowly at the top of a hill and quickly in a valley. As friction and vibration transfer reduce it“s energy, the pendulum comes to rest in a valley.

# No magnets

If you don“t add any magnets to the base, the pendulum swings like one would expect. Gravity pulls down as it does on any pendulum.

The pendulum moves as if in a smooth energy valley.** A picture of this gravity bowl is shown below. (Click image to enlarge.)

A short video clip of a ROMP sans magnets may be viewed by clicking on the image corresponding to your choice of video file type.

 Mpeg video - 0.69 Mb. Wmv video - 114 Kb.

# Central repelling magnet

Let“s put a magnet in the center of the ROMP base. We will set this magnet so that it repels the pendulum magnet.

Ignoring gravity, the effect of this magnet is a hill in the center as depicted in the sketch below. (Click on the image to enlarge.)

Putting this together with the ROMP gravity bowl, we find that the repelling magnet introduces a hill in the bowl as in the diagrams that follow.

The hill is small and thus difficult to see. Let's cut away a bit of our gravity bowl so we can see the magnetic hill.

The video clip shows that the pendulum avoids the gravity hill area. Eventually, the pendulum comes to rest at the hill bottom.

 Mpeg video - 1.28 Mb. Wmv video - 186 Kb.

# An attractive magnet

Ok, so the magnet may not be all that good-looking. However, if we turn over a formerly repelling magnet and place it on a ROMP base, the pendulum wants to cozy up with it.

The magnetic attraction energy picture, sans gravity, is given below. We have moved the magnet position off to one side to better illustrate what is going on. (Click on the image to enlarge.)

An attracting magnet puts a dent in the original gravity bowl. The bowl now looks like this. (Click on either image to view an enlargement.)

A short mpg video of ROMP with a single attracting magnet can be viewed by clicking on the photograph below. The pendulum settles such that it points toward the attracting magnet after the video ends.

 Mpeg video - 1.81 Mb. Wmv video - 236 Kb.

# Nine repelling magnets

As a final example, we consider the case of nine repelling magnets. The energy plot for these magnetics alone looks a it like a small mountain range. It is displayed below. To view a larger picture, click on the graph.

ROMP's energy picture is complete when gravity is included. The pendulum has lots of hills and valleys with which to contend. This makes for one very neat deak toy!

To see a short video of ROMP negotiating the nine magnet obstacle course, click on one of the photos that follow.

 Mpeg video - 1.27 Mb. Wmv video - 183 Kb.

* For illustrative purposes, the half-widths of the individual magnetic potentials have been reduced.

** Since the base is metallic, there is a small added magnetic attraction toward the base itself. The size of this attraction to the base is very small when compared to gravity, so we will not consider it here.