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Nonlinear Dynamics - Between Linear and Impact Limits (Paperback, 2010 ed.)
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Nonlinear Dynamics - Between Linear and Impact Limits (Paperback, 2010 ed.)
Series: Lecture Notes in Applied and Computational Mechanics, 52
Expected to ship within 10 - 15 working days
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Nonlinear Dynamics represents a wide interdisciplinary area of
research dealing with a variety of "unusual" physical phenomena by
means of nonlinear differential equations, discrete mappings, and
related mathematical algorithms. However, with no real substitute
for the linear superposition principle, the methods of Nonlinear
Dynamics appeared to be very diverse, individual and technically
complicated. This book makes an attempt to find a common ground for
nonlinear dynamic analyses based on the existence of strongly
nonlinear but quite simple counterparts to the linear models and
tools. It is shown that, since the subgroup of rotations, harmonic
oscillators, and the conventional complex analysis generate linear
and weakly nonlinear approaches, then translations and reflections,
impact oscillators, and hyperbolic (Clifford's) algebras must give
rise to some "quasi impact" methodology. Such strongly nonlinear
methods are developed in several chapters of this book based on the
idea of non-smooth time substitutions. Although most of the
illustrations are based on mechanical oscillators, the area of
applications may include also electric, electro-mechanical,
electrochemical and other physical models generating strongly
anharmonic temporal signals or spatial distributions. Possible
applications to periodic elastic structures with non-smooth or
discontinuous characteristics are outlined in the final chapter of
the book.
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