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03315aam a22003858i 4500 001 5BD9EABE8B8A11E6A6C758ADDAD10320 003 SILO 005 20161006010101 008 160219t20162016si b 001 0 eng c 010 $a 2016008403 020 $a 9813141352 020 $a 9789813141353 035 $a (OCoLC)940796016 040 $a OU/DLC $b eng $e rda $c OSU $d DLC $d OCLCF $d YDXCP $d BTCTA $d SILO 042 $a pcc 050 00 $a QA805 $b .S724 2016 082 00 $a 531 $2 23 100 1 $a Stetz, Albert W., $d 1940- $e author. 245 10 $a Lectures on nonlinear mechanics and chaos theory / $c Albert W. Stetz, Oregon State University, USA. 263 $a 1604 264 1 $a Singapore ; $b World Scientific Publishing Co. Pte. Ltd., $c [2016] 300 $a pages cm 504 $a Includes bibliographical references and index. 505 0 $a Lagrangian dynamics -- Noether's theorem -- Hamiltonian formulation -- Hamilton's principle function -- Hamilton's characteristic function -- Action-angle variables -- Abstract transformation theory -- Poisson brackets -- Liouville's theorem -- Preturbation theory -- The Henon-Heiles oscillator -- Discrete maps -- Lyapunov exponents -- The PoincarÌÆ°e-Birkoff theorem -- The KAM theorem -- Ergodic hypothesis -- Measure theory. 520 $a "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 pathology. 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 PoincarÌÆ°e 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 PoincarÌÆ°e sections. This leads to the two great landmarks of chaos theory, the PoincarÌÆ°e-Birkoff 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"-- $c Provided by publisher. 650 0 $a Nonlinear mechanics. 650 0 $a Nonlinear systems. 650 0 $a Chaotic behavior in systems. 650 7 $a Chaotic behavior in systems. $2 fast $0 (OCoLC)fst00852171 650 7 $a Nonlinear mechanics. $2 fast $0 (OCoLC)fst01038793 650 7 $a Nonlinear systems. $2 fast $0 (OCoLC)fst01038810 941 $a 1 952 $l USUX851 $d 20180403015739.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=5BD9EABE8B8A11E6A6C758ADDAD10320 994 $a 92 $b IWAInitiate Another SILO Locator Search