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Book Review

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Book Information:

Author: V. I. Arnold
Title: Mathematical methods of classical mechanics
Additional book information: translated from the 1974 Russian edition by K. Vogtmann and A. Weinstein, Graduate Texts in Math., Vol. 60, Springer-Verlag, New York and Berlin, 1978, x + 462 pp.

Author: Walter Thirring
Title: A course in mathematical physics, vol. 1: Classical dynamical systems
Additional book information: translated from German by Evans M. Harrel, Springer-Verlag, New York and Berlin, 1978, xii + 258 pp., $19.80.

References [Enhancements On Off] (What's this?)

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  • 2. V. I. Arnold, Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian, Uspehi Mat. Nauk 18 (1963), no. 5 (113), 13-40; English transl., Russian Math. Surveys 18 (1963), no. 5, 9-36. MR 163025
  • 3. V. I. Arnold and A. Avez, Ergodic problems of classical mechanics. Math. Physics Monograph Series, Benjamin, New York, 1968. MR 232910
  • 4. S. Banach, Mechanics, (English translation by E. J. Scott), Monografie Mat., P.W.N., Warszawa, 1951. MR 43607
  • 5. G. D. Birkhoff, Dynamical systems, Amer. Math. Soc. Colloq. Publ., vol. 9, Amer. Math. Soc., New York, 1927.
  • 6. A. N. Kolmogorov, General theory of dynamical systems, Proc. Internat. Congr. Math. (Amsterdam, 1954), vol. 1, North-Holland, Amsterdam, 1957, p. 315. (Russian)
  • 7. A. N. Kolmogorov, On the conservation of quasi-periodic motions for a small change in the Hamiltonian function, Dokl. Akad. Nauk. SSSR 98 (1954), 527. MR 68687
  • 8. C. Lanczos, The variational principles of mechanics, Univ. of Toronto Press, Toronto, 1949. MR 34139
  • 9. L. H. Loomis and S. Sternberg, Advanced calculus, Addison-Wesley, Reading, Mass., 1968. MR 227327
  • 10. S. Mac Lane, Geometrical mechanics, mimeographed notes, Dept. of Mathematics, Chicago University, 1968.
  • 11. J. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. (1962), 1. MR 147741
  • 12. J. Moser, Stable and random motions in dynamical systems, Ann. of Math. Studies, no. 77, Princeton Univ. Press, Princeton, N. J., 1973. MR 442980
  • 13. E. Noether, Invariante Variationsproblem, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. 2 (1918), 235.
  • 14. L. A. Pars, A treatise on analytical dynamics, Heinemann, London, 1965.
  • 15. H. Poincaré, Les méthodes nouvelles de la mécanique celeste, 3 vols., reprint, Dover, New York, 1957.
  • 16. C. L. Siegel and J. Moser, Lectures on celestial mechanics, (English transl. by C. I. Kalme), Springer-Verlag, New York, 1971. MR 502448
  • 17. S. Sternberg, Celestial mechanics, 2 vols., Benjamin, New York, 1969.
  • 18. J. L. Synge, Classical dynamics, Handbuch der Physik, III/1, Springer-Verlag, Berlin, 1960, pp. 1-225. MR 117945
  • 19. E. T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, 4th ed., Cambridge Univ. Press, London, 1927. MR 103613
  • 20. A. Winter, The analytical foundatons of celestial mechanics, Princeton Univ. Press, Princeton, N. J., 1947.

Review Information:

Reviewer: Ian N. Sneddon
Journal: Bull. Amer. Math. Soc. 2 (1980), 346-352
DOI: https://doi.org/10.1090/S0273-0979-1980-14755-2
American Mathematical Society