Central potentials with closed cruise orbits

A particle will be said to be in cruise motion if it is nonholonomically constrained to have constant speed. When the particle is placed in a central force field, the resulting mechanical system is known to be integrable. Cruise orbits in a central force field may be closed (periodic in time) or not, depending on the potential and on the speed. Here we give a constructive characterization of all central potentials for which all cruise motions of a given speed are closed. As a consequence, we also give a new proof of the fact that for any such potential the set of speeds for which all cruise motions are closed has always empty interior. (C) 2009 Elsevier Inc. All rights reserved.