By Qingjie Cao,Alain Léger
This is the 1st publication to introduce the irrational elliptic functionality sequence, delivering a theoretical therapy for the sleek and discontinuous method and commencing a brand new department of utilized arithmetic. the invention of the graceful and discontinuous (SD) oscillator and the SD attractors mentioned during this e-book represents yet another milestone in nonlinear dynamics, following at the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963.
This specific method bears major similarities to the Duffing oscillator, displaying the normal dynamics ruled by means of the hyperbolic constitution linked to the desk bound country of the double good. in spite of the fact that, there's a mammoth departure in nonlinear dynamics from average dynamics on the discontinuous level. The built irrational elliptic functionality sequence, which bargains how to without delay procedure the character dynamics analytically for either tender and discontinuous behaviours together with the unperturbed periodic motions and the perturbed chaotic attractors with none truncation, is of specific interest.
Readers also will achieve a deeper knowing of the particular nonlinear phenomena via an easy mechanical version: the idea, technique, and the purposes in quite a few interlinked disciplines of sciences and engineering. This ebook deals a useful source for researchers, execs and postgraduate scholars in mechanical engineering, non-linear dynamics, and similar components, reminiscent of nonlinear modelling in a variety of fields of arithmetic, physics and the engineering sciences.
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A Smooth and Discontinuous Oscillator: Theory, Methodology and Applications (Springer Tracts in Mechanical Engineering) by Qingjie Cao,Alain Léger