Multiple Parameter Stability Theory and Its Applications: Bifurcations, Catastrophes, Instabilities (Oxford Engineering Science Series) - Tapa dura

Sinopsis

In this book, a general non-linear theory concerning the stability, instability, bifurcation, and oscillatory behaviour of autonomous systems is presented from an original engineering point of view which is conceptually simple and applicable. The emphasis is on analytical procedures which lead to construction of asymptotic solutions. Potential systems, which can only exhibit static instabilities, are treated separately. Various bifurcation phenomena and the associated imperfection-sensitivities are analysed via the multiple-parameter perturbation technique. The method leads to 'elementary catastrophes'. The emphasis, however, is on non-potential systems which may exhibit dynamic as well as static instability phenomena. This requires a new formulation which is capable of yielding information concerning periodic solutions. Thus, an intrinsic harmonic balancing technique is introduced for the analysis of the dynamic bifurcations, which parallels that of the equilibria. The approach leads to a unified treatment of both static and dynamic bifurcation phenomena within an autonomous framework.

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