Extension of the domain of applicability of the integral stability criterion (extremum property) in synchronization problems

The method of direct separation of motions is used to justify an extended formulation of the integral stability criterion which enables both "simple" and "non-simple" cases of problems of the synchronization of objects with almost uniform rotations to be considered. It is shown, by means of examples, that the results found previously by Poincare's small parameter method and by direct separation of motions, which require laborious computations, can be obtained much more simply by using an extended formulation of the integral stability criterion. (c) 2005 Elsevier Ltd. All rights reserved.