Disaster machine. Drawing, description

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Disaster machine. Children's Science Lab

Children's Science Lab

This simple device can be made by anyone. You need to take a board and, having cut out a disk from cardboard, attach it with a needle in the center to the board so that the disk can rotate freely. Another needle sticks only into the disk at its edge, and the third one only into the board. To complete the assembly of the machine, you need two more bands of easily stretchable rubber (you can take apothecary rubber bands), a pencil and a sheet of paper.

Disaster Machine

After the needle at the edge of the disk is connected to the stationary needle and pencil with rubber bands, we place the point of the pencil at some point on the sheet of paper and thereby stretch the rubber bands. The disc is installed in a certain position. Now, as the pencil moves across the sheet of paper, the disk will rotate, and it turns out that for certain positions of the pencil point, a small change in its position can cause a "catastrophe", that is, an abrupt rotation of the disk. If we mark the places of all such catastrophes on a piece of paper, we get a "catastrophe curve".

It also turns out that the resulting "catastrophe curve" itself has four cusp points. Interestingly, when crossing the catastrophe curve, a jump may or may not occur, depending on which path the pencil took around the cusps.

By experimenting with the catastrophe machine and analyzing its behavior (movement, as physicists and mathematicians say, representing points along the equilibrium surface), one can be convinced in detail how the theory of singularities predicts the geometry of catastrophes - jumps from one equilibrium state to another.

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