January 21, 2011, 1100 Webb

It is well known that a system with zero angular momentum can, by appropriate deformations, rotate while always maintaining the condition of zero angular momentum. This effect explains how a cat that is dropped while upside down can turn over and of how certain gymnastic maneuvers are performed. These rotations are taken as a demonstration of the “non-integrability” of a “non-holonomic” constraint. There is a simple demonstration of this rotation-with-zero-angular-momentum effect with a rotating platform. But the demonstration often doesn’t work because most floors are not perfectly flat. I found a simple better demonstration experiment. Unfortunately, the experiment came out all wrong for different reasons. But I figured out why and did a second demonstration experiment. And that came out wrong exactly in the opposite way. The talk presents the four puzzles: a) how can you turn while having zero angular momentum? b) Why does a rotating platform demonstration often not work. c) Why does a simple demonstration not work? d) Why does almost exactly the same demonstration not work in the opposite way? The talk starts with various personal stories about non-holonomic constraints and their relation to locomotion — that’s bikes skates and walking — and then gets into the 4 rotation puzzles.

Andy Ruina has worked at Cornell University since Monday August 25, 1980. He has studied friction, fracture, collisions, bicycles and the mechanics of walking. His lab made the most energy stingy walking robot and also a robot that walked 14.3 miles without human contact or refueling. He spends his summers in on an island in SouthWest Finland near Stockholm where his wife studies wasps that lay eggs in baby butterflies.