This is the first book to introduce the irrational elliptic function series providing a
theoretical treatment for the smooth and discontinuous system and opening a new branch of
applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD
attractors discussed in this book represents a further milestone in nonlinear dynamics
following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963.This
particular system bears significant similarities to the Duffing oscillator exhibiting the
standard dynamics governed by the hyperbolic structure associated with the stationary state of
the double well. However there is a substantial departure in nonlinear dynamics from standard
dynamics at the discontinuous stage. The constructed irrational elliptic function series which
offers a way to directly approach the nature dynamics analytically for both smooth and
discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic
attractors without any truncation is of particular interest.Readers will also gain a deeper
understanding of the actual nonlinear phenomena by means of a simple mechanical model: the
theory methodology and the applications in various interlinked disciplines of sciences and
engineering. This book offers a valuable resource for researchers professionals and
postgraduate students in mechanical engineering non-linear dynamics and related areas such
as nonlinear modelling in various fields of mathematics physics and the engineering sciences.
