Dr. Claude Gignoux, Dr. Bernard Silvestre-Brac (auth.)9048123925, 9789048123926, 9048123933, 9789048123933
The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader.
This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.
Table of contents :
Front Matter….Pages I-8
The Lagrangian Formulation….Pages 9-50
Lagrangian Systems….Pages 51-109
Hamilton’s Principle….Pages 111-164
Hamiltonian Formalism….Pages 165-231
Hamilton–Jacobi Formalism….Pages 233-280
Integrable Systems….Pages 281-339
Quasi-Integrable Systems….Pages 341-384
From Order to Chaos….Pages 385-455
Back Matter….Pages 457-464
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