Reorganization of the configuration manifold and critical systems

When the dynamics of holonomic mechanical systems are described in redundan t coordinates with parameter-dependent constraints, some special features a rise. At certain (critical) values of the parameters, the configuration man ifold of the system may have, for example, self-intersections; in the neigh bourhood of such a singular submanifold one cannot introduce Lagrangian coo rdinates of the system and it becomes difficult (even impossible) to define the orbits of the "critical" system correctly by taking limits with respec t to the parameter. In such cases the classical Poincare theory of bifurcat ion of equilibria in conservative systems also needs some adjustment. As an example, a crank-gear mechanism is considered. (C) 2000 Elsevier Science L td. Ail rights reserved.