Mathematical Methods of Classical Mechanics

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
** Chapter 3: Variational Principles
** Chapter 4: Lagrangian Mechanics on Manifolds
** Chapter 5: Oscillations
** Chapter 6: Rigid Bodies
* Part III: Hamiltonian Mechanics
** Chapter 7: Differential forms
** 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'' said, "The ookunder 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