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Books > Science & Mathematics > Physics > Classical mechanics > Sound, vibration & waves (acoustics)
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A Smooth and Discontinuous Oscillator - Theory, Methodology and Applications (Hardcover, 1st ed. 2017)
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A Smooth and Discontinuous Oscillator - Theory, Methodology and Applications (Hardcover, 1st ed. 2017)
Series: Springer Tracts in Mechanical Engineering
Expected to ship within 12 - 17 working days
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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.
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