Intermediate Axis Theory: Simulating Fun

Sunday. October 27, 2019 - 1 min

While wandering around youtube, I ran into this video:

So I asked myself a lot of questions, one of those was: can we capture this phenomenon in simulation?. To answer this question, I had to understand more about the physics of the problem, to know whether it is due to imperfections, or it occurs because of a mathematical error in nature

After reading some articles and papers, starting with Wikipedia, I understood that when a body has 3 different moments of inertia, the rotation about the intermediate inertia axis is always unstable und causes reversal in rotation axes as seen in the video. I will not write an article explaining the theorem, available literature is enough. I am only concerned with simulating the phenomenon.

Further resources:

After that, I went to my favorite dynamics simulation software, built a very simple model with a body with looking like letter T, with 3 different moments of inertia. The body is driven with a pulse moment around the intermediate axis (the trunk of T), then left free to rotate, without any external effects, i.e. no gravity, friction, other excitations, etc.

Here is my simulation:

So the simulation is able to capture this mathematical beauty (or instability, call it whatever you want).

Omar Kamel

Not only an engineer