

Availability

All items



Record Format

Book



Shelf Number

517.938 STE







Author

Stetz, Albert W., 1940



Title

Lectures in nonlinear mechanics and chaos theory / Albert W. Stetz.



Imprint

Singapore : World Scientific, c2016.



Collation

ix, 130 pages : illustrations ; 24 cm.



Bibliography Note

Includes bibliography (p. 125126) and index.



Contents

Contents: Lagrangian dynamics  Canonical transformations  Abstract transformation theory  Canonical perturbation theory Introduction to chaos  Computational projects  Appendix A. Measure theory and the ergodic hypothesis.



Description

"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 Poincaré 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 Poincaré sections. This leads to the two great landmarks of chaos theory, the Poincaré–Birkhoff theorem and the socalled 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."Publisher.







Subjects

Nonlinear mechanics.




Nonlinear systems.




Chaotic behavior in systems.



ISBN

9789813143029 paperback



Record Number

000112428







Digital Object 
cover 





