Bulletin of the American Mathematical Society

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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.

Ralph H. Abraham, Experimental mechanics, the first forty years, Mechanics day (Waterloo, ON, 1992) Fields Inst. Commun., vol. 7, Amer. Math. Soc., Providence, RI, 1996, pp. 1–3. MR 1365770

V. I. Arnol′d, Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian, Uspehi Mat. Nauk 18 (1963), no. 5 (113), 13–40 (Russian). MR 0163025

V. I. Arnol′d and A. Avez, Ergodic problems of classical mechanics, W. A. Benjamin, Inc., New York-Amsterdam, 1968. Translated from the French by A. Avez. MR 0232910

Stefan Banach, Mechanics, Monografie Matematyczne, Tom XXIV, Polskie Towarzystwo Matematyczne, Warszawa-Wroclaw, 1951. Translated by E. J. Scott. MR 0043607

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)

A. N. Kolmogorov, On conservation of conditionally periodic motions for a small change in Hamilton’s function, Dokl. Akad. Nauk SSSR (N.S.) 98 (1954), 527–530 (Russian). MR 0068687

Cornelius Lanczos, The Variational Principles of Mechanics, Mathematical Expositions, No. 4, University of Toronto Press, Toronto, Ont., 1949. MR 0034139

Lynn H. Loomis and Shlomo Sternberg, Advanced calculus, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1968. MR 0227327

10.

S. Mac Lane, Geometrical mechanics, mimeographed notes, Dept. of Mathematics, Chicago University, 1968.

J. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1962 (1962), 1–20. MR 147741

Jürgen Moser, Stable and random motions in dynamical systems, Annals of Mathematics Studies, No. 77, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1973. With special emphasis on celestial mechanics; Hermann Weyl Lectures, the Institute for Advanced Study, Princeton, N. J. MR 0442980

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.

Carl Ludwig Siegel and Jürgen K. Moser, Lectures on celestial mechanics, Die Grundlehren der mathematischen Wissenschaften, Band 187, Springer-Verlag, New York-Heidelberg, 1971. Translation by Charles I. Kalme. MR 0502448

17.

S. Sternberg, Celestial mechanics, 2 vols., Benjamin, New York, 1969.

J. L. Synge, Classical Dynamics, Handbuch der Physik, Bd. III/1, Springer, Berlin, 1960. MR 0117945

E. T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies: With an introduction to the problem of three bodies, Cambridge University Press, New York, 1959. 4th ed. MR 0103613

20.

A. Winter, The analytical foundatons of celestial mechanics, Princeton Univ. Press, Princeton, N. J., 1947.

1.

R. Abraham, Foundations of mechanics, Math. Physics Monograph Series, Benjamin, New York, 1967. MR 1365770

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.