Institute for Mathematics and Its Applications
Jerry Marsden, California Institute of Technology
We will present a new proof of Richard Montgomery's beautiful ``Falling Cat Theorem'' which relates optimal reorientation of the falling cat to the dynamics of particles in Yang-Mills fields (governed by Wong's equations). We will begin by putting the theorem in the general context of optimal control problems as studied by Brockett. The new proof involves ideas of Lagrangian reduction for which there has been much activity lately (Scheurle, Weinstein, Koon, Ratiu, Bloch, Krishnaprasad, Murray, Cendra, Holm, etc. etc.). We shall also present generalizations of the Falling Cat Theorem to the context of nonholonomic locomotion problems.