Lectures on nonlinear mechanics and chaos theory:
"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...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
[2016]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "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 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-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"... |
| Beschreibung: | ix, 130 Seiten Diagramme |
| ISBN: | 9789813141353 9813141352 9789813143029 |
Internformat
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| 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 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-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"... | ||
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Datensatz im Suchindex
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| adam_text | LECTURES ON NONLINEAR MECHANICS AND CHAOS THEORY
/ STETZ, ALBERT W.YYD1940-YYEAUTHOR
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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 POINCARE-BIRKOFF THEOREM
THE KAM THEOREM
ERGODIC HYPOTHESIS
MEASURE THEORY
DIESES SCHRIFTSTCK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Stetz, Albert W. 1940- |
| author_GND | (DE-588)1120421004 |
| author_facet | Stetz, Albert W. 1940- |
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| building | Verbundindex |
| bvnumber | BV043856492 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA805 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | UG 3900 UF 1950 SK 950 |
| ctrlnum | (OCoLC)961315544 (DE-599)BVBBV043856492 |
| dewey-full | 531 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531 |
| dewey-search | 531 |
| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV043856492 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:36:52Z |
| institution | BVB |
| isbn | 9789813141353 9813141352 9789813143029 |
| language | English |
| lccn | 016008403 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029266688 |
| oclc_num | 961315544 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-11 |
| owner_facet | DE-703 DE-29T DE-11 |
| physical | ix, 130 Seiten Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Stetz, Albert W. 1940- Verfasser (DE-588)1120421004 aut Lectures on nonlinear mechanics and chaos theory Albert W. Stetz New Jersey World Scientific [2016] ix, 130 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier "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 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-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"... Nonlinear mechanics Nonlinear systems Chaotic behavior in systems Nichtlineare Mechanik (DE-588)4042095-4 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Nichtlineare Mechanik (DE-588)4042095-4 s Chaotisches System (DE-588)4316104-2 s DE-604 LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029266688&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stetz, Albert W. 1940- Lectures on nonlinear mechanics and chaos theory Nonlinear mechanics Nonlinear systems Chaotic behavior in systems Nichtlineare Mechanik (DE-588)4042095-4 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4042095-4 (DE-588)4316104-2 |
| title | Lectures on nonlinear mechanics and chaos theory |
| title_auth | Lectures on nonlinear mechanics and chaos theory |
| title_exact_search | Lectures on nonlinear mechanics and chaos theory |
| title_full | Lectures on nonlinear mechanics and chaos theory Albert W. Stetz |
| title_fullStr | Lectures on nonlinear mechanics and chaos theory Albert W. Stetz |
| title_full_unstemmed | Lectures on nonlinear mechanics and chaos theory Albert W. Stetz |
| title_short | Lectures on nonlinear mechanics and chaos theory |
| title_sort | lectures on nonlinear mechanics and chaos theory |
| topic | Nonlinear mechanics Nonlinear systems Chaotic behavior in systems Nichtlineare Mechanik (DE-588)4042095-4 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Nonlinear mechanics Nonlinear systems Chaotic behavior in systems Nichtlineare Mechanik Chaotisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029266688&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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