Bulletin of the American Mathematical Society

Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Jerrold E. Marsden and Tudor S. Ratiu
Title: Introduction to mechanics and symmetry: A basic exposition of classical mechanical systems
Additional book information: Texts Appl. Math., vol. 17, Springer-Verlag, New York, 1994, xiv + 500 pp., ISBN 0-387-97275-7, $64.50$

Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. Second edition, revised and enlarged; With the assistance of Tudor Raţiu and Richard Cushman. MR 515141

V. I. Arnol′d, Mathematical methods of classical mechanics, 2nd ed., Graduate Texts in Mathematics, vol. 60, Springer-Verlag, New York, 1989. Translated from the Russian by K. Vogtmann and A. Weinstein. MR 997295, DOI 10.1007/978-1-4757-2063-1

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

Dynamical systems. III, 2nd ed., Encyclopaedia of Mathematical Sciences, vol. 3, Springer-Verlag, Berlin, 1993. Mathematical aspects of classical and celestial mechanics; A translation of Current problems in mathematics. Fundamental directions, Vol. 3 (Russian), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1985 [ MR0833508 (87i:58151)]; Translation by A. Iacob; Translation edited by V. I. Arnol′d. MR 1292465

Giovanni Gallavotti, The elements of mechanics, Texts and Monographs in Physics, Springer-Verlag, New York, 1983. Translated from the Italian. MR 698947, DOI 10.1007/978-3-662-00731-0

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

7.

S. Mac Lane, Geometrical mechanics, Parts I and II, Lecture Notes in Mathematics, Univ. of Chicago, 1968.

Jerrold E. Marsden, Lectures on mechanics, London Mathematical Society Lecture Note Series, vol. 174, Cambridge University Press, Cambridge, 1992. MR 1171218, DOI 10.1017/CBO9780511624001

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

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

11.

S. Sternberg, Celestial mechanics, Parts I and II, Benjamin, New York, 1969.

12.

W. Thirring, Classical dynamical systems, second ed., Springer-Verlag, New York, 1991.

C. Truesdell, An idiot’s fugitive essays on science, Springer-Verlag, New York, 1984. Methods, criticism, training, circumstances. MR 769106, DOI 10.1007/978-1-4613-8185-3

C. Truesdell, Great scientists of old as heretics in “the scientific method”, University Press of Virginia, Charlottesville, VA, 1987. MR 915762

1.

R. Abraham and J. E. Marsden, Foundations of mechanics, second ed., Benjamin/Cummings, Reading, MA, 1978. MR 0515141

2.

V. I. Arnold, Mathematical methods of classical mechanics, second ed., Springer-Verlag, New York, 1989. MR 0997295

3.

V. I. Arnold and A. Avez, Ergodic problems of classical mechanics, Benjamin, New York, 1968. MR 0232910

4.

V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical aspects of classical and celestial mechanics, Encyclopedia of Mathematical Sciences, vol. 3 (R. V. Gamkrelidze, editor-in-chief; Dynamical Systems III, V. I. Arnold, ed.), Springer-Verlag, Berlin, 1988; second ed., 1993. MR 1292465

5.

G. Gallavotti, The elements of mechanics, Springer-Verlag, New York, 1983. MR 0698947

6.

L. H. Loomis and S. Sternberg, Advanced calculus, Addison-Wesley, Reading, MA, 1968. MR 0227327

7.

S. Mac Lane, Geometrical mechanics, Parts I and II, Lecture Notes in Mathematics, Univ. of Chicago, 1968.

8.

J. E. Marsden, Lectures on mechanics, London Math. Soc. Lecture Note Series, vol. 174, Cambridge Univ. Press, Cambridge, 1992. MR 1171218

9.

J. K. Moser, Stable and random motions in dynamical systems, with special emphasis on celestial mechanics, Ann. of Math. Stud., No. 77, Princeton Univ. Press, Princeton, NJ, 1973. MR 0442980

10.

C. L. Siegel and J. K. Moser, Lectures on celestial mechanics, Springer-Verlag, Berlin, 1971. MR 0502448

11.

S. Sternberg, Celestial mechanics, Parts I and II, Benjamin, New York, 1969.

12.

W. Thirring, Classical dynamical systems, second ed., Springer-Verlag, New York, 1991.

13.

C. Truesdell, An idiot's fugitive essays on science: Methods, criticism, training, circumstances, Springer-Verlag, New York, 1984. MR 0769106

14.

------, Great scientists of old as heretics in ``The Scientific Method'', Univ. of Virginia Press, Charlottesville, VA, 1987. MR 0915762