How do cats defy physics with their perfect landings?

[Phrak]

I have no idea what the "non-integrability" of a "non-holonomic" constraint is. The only thing I got out of it was the first sentence, that it is apparently possible for something to rotate while maintaining zero angular momentum, by deforming.

And it is. A fairly easy thought experiment is to replace the cat with a rather plump and metamorphosing sausage. Draw a line down one side of the sausage then divide it into 4 equal sections, one through four. Think of this as a transformer sausage. The sections can move around as long as they only push and pull one one another. No outside agents are allowed to exert any forces on the sections in this experiment.

Displace section one radially from section two. Section two and three stay attached to each other. Section four is displaced in the same direction as segment one.

Now it's best to use the symmetry of the system and just look at two sections at a time. Sections one and two have their axis separated by some rigid rod. A chain drive or belt connects the two. Now a means can be supplied to spin the two with respect to the rod without external forces or energy.

To conserve angular momentum the two segments, or disks, will need to orbit about each other. Also, important to note, the angular displacements of the line drawn on the original sausage, and now appearing on each section remains the same on each section. We can't allow one segment to turn faster than the other.

As the sections are brought back into alignment, after some number of revolutions, the line drawn down the side is displaced.

So the cat thing is reduced to two sprockets and chain, a separating rod, and some means of propulsion.

 

[Phrak]

Come to think of it, it might be fairly easy to demonstrate in a classroom, properly suspended on a string with something available from Toys R Us.

 

[sophiecentaur]

I think most people aren't thinking about something that can move its own parts, which your standard physics class probably doesn't go over when they talk about angular momentum.

The nature of an object's construction doesn't determine whether or not angular momentum is conserved. No explanation of how a cat works can do without the basic conservation laws.