Mathematical Methods of Classical Mechanics

Graduate Texts in Mathematics #60

by Vladimir I. Arnold

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.

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

540 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