Mathematical Methods of Classical Mechanics

Vladimir I. Arnold - Collection Graduate Texts in Mathematics

520 pages, parution le 01/01/1989 (2^eme édition)

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Résumé

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.

Written for: Graduate Students

L'auteur - Vladimir I. Arnold

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Sommaire

Newtonian Mechanics
- Experimental facts Investigation of the equations of motion
Lagrangian mechanics
- Variational principles
- Lagrangian mechanics on manifolds
- Oscillations
- Rigid Bodies
Hamiltonian Mechanics
- Differential forms
- Symplectic manifolds
- Canonical formalism
- Introduction to perturbation theory
- Appendices

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Vladimir I. Arnold
Collection	Graduate Texts in Mathematics
Parution	01/01/1989
Édition	2^eme édition
Nb. de pages	520
Format	16 x 24
Couverture	Relié
Poids	890g
Intérieur	Noir et Blanc
EAN13	9780387968902
ISBN13	978-0-387-96890-2