Mathematical Methods of Classical Mechanics 2nd Ed. by V. I. Arnold HC 1989

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Book Title
Mathematical Methods of Classical Mechanics (Graduate Texts in Ma
Personalized
Yes
ISBN
9780387968902
Kategorie

Über dieses Produkt

Product Identifiers

Publisher
Springer New York
ISBN-10
0387968903
ISBN-13
9780387968902
eBay Product ID (ePID)
977999

Product Key Features

Number of Pages
Xvi, 520 Pages
Publication Name
Mathematical Methods of Classical Mechanics
Language
English
Publication Year
1989
Subject
Mechanics / General, Physics / Mathematical & Computational, Mathematical Analysis
Features
Revised
Type
Textbook
Author
V. I. Arnold
Subject Area
Mathematics, Science
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover

Dimensions

Item Height
0.5 in
Item Weight
72.3 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Edition Number
2
Intended Audience
Scholarly & Professional
LCCN
88-039823
Dewey Edition
21
Reviews
Second EditionV.I. Arnol'dMathematical Methods of Classical Mechanics"The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising . . . The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview." -AMERICAN MATHEMATICAL MONTHLY, Second Edition V.I. Arnol'd Mathematical Methods of Classical Mechanics "The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising . . . The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview." --AMERICAN MATHEMATICAL MONTHLY, Second Edition V.I. Arnol'd Mathematical Methods of Classical Mechanics "The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising . . . The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview." -AMERICAN MATHEMATICAL MONTHLY
Series Volume Number
60
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
531/.01515
Edition Description
Revised edition
Table Of Content
I Newtonian Mechanics.- 1 Experimental facts.- 2 Investigation of the equations of motion.- II Lagrangian Mechanics.- 3 Variational principles.- 4 Lagrangian mechanics on manifolds.- 5 Oscillations.- 6 Rigid bodies.- III Hamiltonian Mechanics.- 7 Differential forms.- 8 Symplectic manifolds.- 9 Canonical formalism.- 10 Introduction to perturbation theory.- Appendix 1 Riemannian curvature.- Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids.- Appendix 3 Symplectic structures on algebraic manifolds.- Appendix 4 Contact structures.- Appendix 5 Dynamical systems with symmetries.- Appendix 6 Normal forms of quadratic hamiltonians.- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories.- Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov's theorem.- Appendix 9 Poincaré's geometric theorem, its generalizations and applications.- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters.- Appendix 11 Short wave asymptotics.- Appendix 12 Lagrangian singularities.- Appendix 13 The Korteweg-de Vries equation.- Appendix 14 Poisson structures.- Appendix 15 On elliptic coordinates.- Appendix 16 Singularities of ray systems.
Synopsis
This text begins with the basic facts of classical mechanics and proceeds to examine many important questions in dynamics. This modern approach, based on the theory of the geometry of manifolds, distinguishes itself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout., In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance., This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. The author emphasizes geometrical considerations throughout and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
LC Classification Number
QA299.6-433

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