 
Summary: Optimal Rotations of Deformable Bodies and Orbits in Magnetic Fields
J. E. Avron,* O. Gat, O. Kenneth, and U. Sivan
Department of Physics, Technion, Haifa 32000, Israel
(Received 4 August 2003; published 28 January 2004)
Deformations can induce rotation with zero angular momentum where dissipation is a natural ``cost
function.'' This gives rise to an optimization problem of finding the most effective rotation with zero
angular momentum. For certain plastic and viscous media in two dimensions the optimal path is the
orbit of a charged particle on a surface of constant negative curvature with a magnetic field whose total
flux is half a quantum unit.
DOI: 10.1103/PhysRevLett.92.040201 PACS numbers: 02.40.k, 83.50.v, 07.10.Cm
Rotations with zero angular momentum are intriguing.
The most celebrated phenomenon of this kind is the
rotation of a falling cat. A mechanical model [1] replac
ing the cat by two rigid bodies that can rotate relative to
each other has been studied extensively; see [2,3], and
references therein. Here we address rotations with zero
angular momentum under linear deformations. Our mo
tivation comes from nanomechanics: Imagine an elastic
or plastic material with its own energy source and ask
what is the most efficient way of turning it through an
