Solved Problems in Lagrangian and Hamiltonian Mechanics

ISBN-13: 9789400791763 / Angielski / Miękka / 2014 / 464 str.

Claude Gignoux; Bernard Silvestre-Brac

Opis

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.

Recenzje

From the reviews:

"The present book fills an important gap in the scientific literature since most books on analytical mechanics concentrate on the theoretical aspects. A great number of exercises and problems are divided into eight chapters ... . In conclusion, this is an excellent source of concrete examples for students and mathematicians from several fields." (Mircea Crâsmareanu, Zentralblatt MATH, Vol. 1172, 2009)

Spis treści

Foreword Synoptic Tables. Chapter 1 : The Lagrangian formulation (1 1 problems) Chapter 2 : Lagrangian systems (14 problems) Chapter 3 : The Hamilton's principle (15 problems) Chapter 4 : The Hamiltonian formalism (17 problems) Chapter 5 : The Hamilton-Jacobi formalism (1 1 problems) Chapter 6 : Integrable systems (18 problems) Chapter 7 : Quasi-integrable systems (9 problems) Chapter 8 : From order to chaos (12 problems). Bibliography.