Bulletin (New Series) of the American Mathematical Society

Review: V. I. Arnold, Mathematical methods of classical mechanics, and Walter Thirring, A course in mathematical physics, vol. 1: Classical dynamical systems

Ian N. Sneddon
Source: Bull. Amer. Math. Soc. (N.S.) Volume 2, Number 2 (1980), 346-352.
First Page: Show Hide

Reviewed Works:

V. I. Arnold, Mathematical methods of classical mechanics. 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.

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

Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.bams/1183546243

References

1. R. Abraham, Foundations of mechanics, Math. Physics Monograph Series, Benjamin, New York, 1967.
Zentralblatt MATH: 0158.42901
Mathematical Reviews (MathSciNet): MR1365770
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.
Zentralblatt MATH: 0129.16606
Mathematical Reviews (MathSciNet): MR163025
3. V. I. Arnold and A. Avez, Ergodic problems of classical mechanics. Math. Physics Monograph Series, Benjamin, New York, 1968.
Zentralblatt MATH: 0715.70004
Mathematical Reviews (MathSciNet): MR232910
4. S. Banach, Mechanics, (English translation by E. J. Scott), Monografie Mat., P.W.N., Warszawa, 1951.
Zentralblatt MATH: 0043.18101
Mathematical Reviews (MathSciNet): MR43607
5. G. D. Birkhoff, Dynamical systems, Amer. Math. Soc. Colloq. Publ., vol. 9, Amer. Math. Soc., New York, 1927.
Jahrbuch database (Zbl): 53.0732.01
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.
Zentralblatt MATH: 0056.31502
Mathematical Reviews (MathSciNet): MR68687
8. C. Lanczos, The variational principles of mechanics, Univ. of Toronto Press, Toronto, 1949.
Zentralblatt MATH: 0138.19705
Mathematical Reviews (MathSciNet): MR34139
9. L. H. Loomis and S. Sternberg, Advanced calculus, Addison-Wesley, Reading, Mass., 1968.
Zentralblatt MATH: 0162.35301
Mathematical Reviews (MathSciNet): MR227327
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.
Zentralblatt MATH: 0107.29301
Mathematical Reviews (MathSciNet): MR147741
12. J. Moser, Stable and random motions in dynamical systems, Ann. of Math. Studies, no. 77, Princeton Univ. Press, Princeton, N. J., 1973.
Zentralblatt MATH: 0271.70009
Mathematical Reviews (MathSciNet): MR442980
13. E. Noether, Invariante Variationsproblem, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. 2 (1918), 235.
Jahrbuch database (Zbl): 46.0770.01
14. L. A. Pars, A treatise on analytical dynamics, Heinemann, London, 1965.
Zentralblatt MATH: 0125.12004
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.
Zentralblatt MATH: 0817.70001
Mathematical Reviews (MathSciNet): MR502448
17. S. Sternberg, Celestial mechanics, 2 vols., Benjamin, New York, 1969.
Zentralblatt MATH: 0194.56702
18. J. L. Synge, Classical dynamics, Handbuch der Physik, III/1, Springer-Verlag, Berlin, 1960, pp. 1-225.
Mathematical Reviews (MathSciNet): MR117945
19. E. T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, 4th ed., Cambridge Univ. Press, London, 1927.
Zentralblatt MATH: 0091.16406
Mathematical Reviews (MathSciNet): MR103613
20. A. Winter, The analytical foundatons of celestial mechanics, Princeton Univ. Press, Princeton, N. J., 1947.
Jahrbuch database (Zbl): 67.0785.01

2012 © American Mathematical Society

Bulletin (New Series) of the American Mathematical Society

Bulletin (New Series) of the American Mathematical Society

Turn MathJax Off
What is MathJax?