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?
THIS COLLOQUIUM IS JOINTLY SPONSORED BY FIELDS INSTITUTE RESEARCH IN MATHEMATICAL SCIENCES AND THE DEPARTMENT OF PHYSICS.
Prof. Ruina will also be giving a talk on "Some Issues in Bipedal locomotion" at Fields Institute on Wednesday, March 9 th at 3:10 p.m.
For details, please visit http://www.fields.utoronto.ca/programs/scientific/10-11/physics/index.html