Descriptions: Throw a rectangular object with sides of three different lengths (such as a cereal box), into the air. You can get the box to tumble stably about its longest axis, or about its shortest axis. But if you try to make it tumble about it middle axis, you will find the motion is unstable. The model of the angular momentum is a nonlinear system of three differential equations. There are six critical points: the four corresponding to the long and short axes are stable; the two corresponding to the middle axis are unstable.
Instructor: Cleve Moler