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Mathematical Methods of Classical Mechanics
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<h2 id="contents">Contents</h2> <ul><li>Part I: Newtonian Mechanics <ul><li>Chapter 1: Experimental Facts</li> <li>Chapter 2: Investigation of the Equations of Motion</li></ul></li> <li>Part II: <a href="/facts/Lagrangian_mechanics/sTxyqWz8">Lagrangian Mechanics</a> <ul><li>Chapter 3: <a href="/facts/Calculus_of_variations/Ya5Lsma3">Variational Principles</a></li> <li>Chapter 4: Lagrangian Mechanics on Manifolds</li> <li>Chapter 5: Oscillations</li> <li>Chapter 6: <a href="/facts/Rigid_body/THezBlq2">Rigid Bodies</a></li></ul></li> <li>Part III: <a href="/facts/Hamiltonian_mechanics/2ReerlNA">Hamiltonian Mechanics</a> <ul><li>Chapter 7: <a href="/facts/Differential_form/T9gyHtMv">Differential forms</a></li> <li>Chapter 8: Symplectic Manifolds</li> <li>Chapter 9: Canonical Formalism</li> <li>Chapter 10: Introduction to Perturbation Theory</li></ul></li> <li>Appendices <ul><li>Riemannian curvature</li> <li>Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids</li> <li>Symplectic structures on algebraic manifolds</li> <li>Contact structures</li> <li>Dynamical systems with symmetries</li> <li>Normal forms of quadratic Hamiltonians</li> <li>Normal forms of Hamiltonian systems near stationary points and closed trajectories</li> <li>Theory of perturbations of conditionally period motion and Kolmogorov's theorem</li> <li>Poincaré's geometric theorem, its generalizations and applications</li> <li>Multiplicities of characteristic frequencies, and ellipsoids depending on parameters</li> <li>Short wave asymptotics</li> <li>Lagrangian singularities</li> <li>The <a href="/facts/Korteweg%25E2%2580%2593de_Vries_equation/w8W3YDRK">Kortweg-de Vries equation</a></li> <li>Poisson structures</li> <li>On elliptic coordinates</li> <li>Singularities of ray systems</li></ul></li></ul> <h2 id="russian-original-and-translations">Russian original and translations</h2> <p>The original Russian first edition <i>Математические методы классической механики</i> was published in 1974 by <a href="/facts/Nauka_(publisher)/3RL2DQMQ">Наука</a>. A second edition was published in 1979, and a third in 1989. The book has since been translated into a number of other languages, including French, German, Japanese and Mandarin. </p> <h2 id="reviews">Reviews</h2> <p>The <i><a href="/facts/Bulletin_of_the_American_Mathematical_Society/8ER5KY5z">Bulletin of the American Mathematical Society</a></i> said, "The [book] under review [...] written by a distinguished mathematician [...is one of] the first textbooks [to] successfully to present to students of mathematics and physics, [sic] classical mechanics in a modern setting."<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> </p><p>A book review in the journal <i>Celestial Mechanics</i> 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."<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/List_of_textbooks_on_classical_and_quantum_mechanics/9VgL77nA">List of textbooks in classical and quantum mechanics</a></li></ul> <h2 id="bibliography">Bibliography</h2> <ul><li><a href="/facts/Vladimir_Igorevich_Arnold/IMBhyfMS">Arnold, Vladimir I.</a> (16 May 1989) [First published in 1974]. Mathematical Methods of Classical Mechanics Математические методы классической механики. <a href="/facts/Graduate_Texts_in_Mathematics/VTIfY29j">Graduate Texts in Mathematics</a>. Vol. 60. Translated by <a href="/facts/Karen_Vogtmann/vD1vYSVE">Vogtmann, Karen</a>; <a href="/facts/Alan_David_Weinstein/QM8cP0pb">Weinstein, Alan D.</a> (2nd ed.). New York: Springer-Verlag. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-387-96890-2. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/18681352">18681352</a>.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles. Springer Science & Business Media. 2010. p. 211. ISBN 9783642136061. <a href="9783642136061" target="_blank">9783642136061</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Sneddon, Ian N. (March 1980). "Book Review of Mathematical methods of classical mechanics and A course in mathematical physics, vol. 1: Classical dynamical systems". Bulletin of the American Mathematical Society. 2 (2): 346–352. doi:10.1090/S0273-0979-1980-14755-2 – via Project Euclid. <a href="/wiki/Ian_Sneddon" target="_blank">/wiki/Ian_Sneddon</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Broucke, R (1982). "Book-Review - Mathematical Methods of Classical Mechanics". Celestial Mechanics. 28: 345. Bibcode:1982CeMec..28..345A. doi:10.1007/bf01243742. S2CID 189830621 – via SAO/NASA ADS. <a href="/wiki/Roger_A._Broucke" target="_blank">/wiki/Roger_A._Broucke</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> </ol>