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Lectures On Nonlinear Mechanics And Chaos Theory (Hardcover)
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Lectures On Nonlinear Mechanics And Chaos Theory (Hardcover)
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This elegant book presents a rigorous introduction to the theory of
nonlinear mechanics and chaos. It turns out that many simple
mechanical systems suffer from a peculiar malady. They are
deterministic in the sense that their motion can be described with
partial differential equations, but these equations have no proper
solutions and the behavior they describe can be wildly
unpredictable. This is implicit in Newtonian physics, and although
it was analyzed in the pioneering work of Poincare in the 19th
century, its full significance has only been realized since the
advent of modern computing. This book follows this development in
the context of classical mechanics as it is usually taught in most
graduate programs in physics. It starts with the seminal work of
Laplace, Hamilton, and Liouville in the early 19th century and
shows how their formulation of mechanics inevitably leads to
systems that cannot be 'solved' in the usual sense of the word. It
then discusses perturbation theory which, rather than providing
approximate solutions, fails catastrophically due to the problem of
small denominators. It then goes on to describe chaotic motion
using the tools of discrete maps and Poincare sections. This leads
to the two great landmarks of chaos theory, the Poincare-Birkhoff
theorem and the so-called KAM theorem, one of the signal results in
modern mathematics. The book concludes with an appendix discussing
the relevance of the KAM theorem to the ergodic hypothesis and the
second law of thermodynamics.Lectures on Nonlinear Mechanics and
Chaos Theory is written in the easy conversational style of a great
teacher. It features numerous computer-drawn figures illustrating
the behavior of nonlinear systems. It also contains homework
exercises and a selection of more detailed computational projects.
The book will be valuable to students and faculty in physics,
mathematics, and engineering.See Press Release: Problems in
mechanics open the door to the orderly world of chaos
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