Mathematical Methods of Classical Mechanics is a classic graduate textbook by the mathematician
Vladimir I. Arnold. It was originally written in Russian, but was translated into English by
A. Weinstein and
K. Vogtmann.
Contents
* Part I: Newtonian Mechanics
** Chapter 1: Experimental Facts
** Chapter 2: Investigation of the Equations of Motion
* Part II:
Lagrangian Mechanics
In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph- ...
** Chapter 3:
Variational Principles
** Chapter 4: Lagrangian Mechanics on Manifolds
** Chapter 5: Oscillations
** Chapter 6:
Rigid Bodies
In physics, a rigid body (also known as a rigid object) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external fo ...
* Part III:
Hamiltonian Mechanics
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta ...
** Chapter 7:
Differential forms
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, ...
** Chapter 8: Symplectic Manifolds
** Chapter 9: Canonical Formalism
** Chapter 10: Introduction to Perturbation Theory
* Appendices
** Riemannian curvature
** Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids
** Symplectic structures on algebraic manifolds
** Contact structures
** Dynamical systems with symmetries
** Normal forms of quadratic Hamiltonians
** Normal forms of Hamiltonian systems near stationary points and closed trajectories
** Theory of perturbations of conditionally period motion and Kolmogorov's theorem
** Poincaré's geometric theorem, its generalizations and applications
** Multiplicities of characteristic frequencies, and ellipsoids depending on parameters
** Short wave asymptotics
** Lagrangian singularities
** The
Kortweg-de Vries equation
** Poisson structures
** On elliptic coordinates
** Singularities of ray systems
Russian Original and Translations
*The original Russian first edition ''Математические методы классической механики'' was published in 1974 by
Наука, a second one was published in 1979, and a third - in 1989.
*The first French translation, ''Les Méthodes mathématiques de la mécanique classique'', was published in 1976.
*The first Bulgarian translation, ''Математически методи на класическата механика'', was published in 1978. А second translation of the second Russian edition appeared in 1985.
*The first Japanese translation, ''古典力学の数学的方法'', was published in 1980. А second translation was published in 2003
*The first Romanian translation, ''Metodele matematice ale mecanicii clasice'', was published in 1980.
*The first Polish translation, "Metody matematyczne mechaniki klasycznej", was published in 1981.
*The first Spanish translation, ''Mecánica clásica. Métodos matemáticos'', was published in 1983.
*The first Hungarian translation, ''A mechanika matematikai módszerei'', was published in 1985. А second translation appeared in 2013.
*The first Portuguese translation, ''Métodos matemáticos da mecânica clássica'', was published in 1987.
*The first German translation, ''Mathematische Methoden der klassischen Mechanik'', was published in 1988.
*The first Italian translation, ''Metodi matematici della meccanica classica'', was published in 1992.
*The first Chinese translation, ''经典力学的数学方法'', was published in 1992.
Reviews
The ''
Bulletin of the American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society.
Scope
It publishes surveys on contemporary research topics, written at a level accessible to non-experts. I ...
'' said, "The
ook
Ook, OoK or OOK may refer to:
* Ook Chung (born 1963), Korean-Canadian writer from Quebec
* On-off keying, in radio technology
* Toksook Bay Airport (IATA code OOK), in Alaska
* Ook!, an esoteric programming language based on Brainfuck
* Ook, th ...
under review
..written by a distinguished mathematician
..is one ofthe first textbooks
osuccessfully to present to students of mathematics and physics,
icclassical mechanics in a modern setting."
A book review in the journal ''Celestial Mechanics'' said, "In summary, the author has succeeded in producing a mathematical synthesis of the science of dynamics. The book is well presented and beautifully translated
..Arnold's book is pure poetry; one does not simply read it, one enjoys it."
See also
*
List of textbooks in classical and quantum mechanics
References
Bibliography
*
External links
pdf version
1974 non-fiction books
Classical mechanics
Mathematics textbooks
Physics textbooks