Mathematical Methods of Classical Mechanics

Graduate Texts in Mathematics #60

by Vladimir I. Arnold

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 Geodesies of left-invariant metrics on Lie groups and the hydrodynamics of an ideal fluid.- Appendix 3 Symplectic structure 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 Perturbation theory of conditionally periodic motions 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.

Genres: Physics, Mathematics, Science, Textbooks, Engineering, Academic, Nonfiction

476 pages, Paperback

First published June 1, 1978

About the author

Vladimir Igorevich Arnold (alternative spelling Arnol'd, Russian: Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010)[1] was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory, including posing the ADE classification problem, since his first main result—the partial solution of Hilbert's thirteenth problem in 1957 at the age of 19.

Reviews

[Ida · Rating 5 out of 5]

I can only recommend to anyone who would like to give further thoughts to physics and mathematics, some serious but very exciting reading. I feel awfully comfortable with Arnold's writing, I must admit... and I do enjoy the fact that I finally have an excuse to include this book - only one chapter, though - in my formal studies, aka thesis.

[The Architect]

"It is this reviewer's impression that, unlike other prose on dynamics, Arnold's book is pure poetry; one does not simply read it, one enjoys it." – R. Broucke

[sara · Rating 5 out of 5]

all'unibo gli studenti di fisica si dividono tra team landau e team arnold quando devono preparare l'esame di meccanica analitica e io sono e saró per sempre team landau peró questo rimane un signor libro grazie arnold bestie

[Константин]

Много хубаво четиво. Малко стар език, но все пак ясен.

[Razvan Coca · Rating 5 out of 5]

Very clean book. Goes very deep too.

[Lulu]

Geometrical aspects of classical mechanics