Nonlinear Stability and Bifurcation Theory

This study aims to make progress in the field of stability theory available to scientists and engineers. A treatment of the different types of loss of stability of equilibrium positions of static and dynamic systems and of periodic solutions of dynamic systems is given by means of the methods of bifurcation and singuality theory. The reader needs only a background in mathematics. Among others, concepts such as centre manifold theory, the method of Ljapunov-Schmidt, normal form theory, unfolding theory, bifurcation diagrams, classifications and bifurcations in symmetric systems are discussed, as far as they are relevant in applications. Most important for the whole representation is a set of examples taken from mechanics and engineering showing the usefulness of the above mentioned concepts. These examples include buckling problems of rods, plates and shells, the loss of stability of the motion of road and rail vehicles, of a simple robot, and of fluid conveying elastic tubes. With these examples, questions like symmetry breaking, pattern formation, imperfection sensitivity, transition to chaos and correct modelling of systems are explored. Finally, a number of selected FORTRAN-routines should encourage readers to apply these theories to their own individual problems.