Bulletin of the American Mathematical Society

MathSciNet review: 1567237
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Book Information:

Authors: Ralph Abraham and Jerrold E. Marsden
Title: Foundations of mechanics
Additional book information: Second Edition, Revised and enlarged, The Benjamin/Cummings Publishing Company, Reading, Mass., 1978, xxii + 806 pp., $39.50.

V. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 1, 319–361 (French). MR 202082

V. Arnold, Les méthodes mathématiques de la mécanique classique, Éditions Mir, Moscow, 1976 (French). Traduit du russe par Djilali Embarek. MR 0474391

Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, Mathematical Surveys, No. 14, American Mathematical Society, Providence, R.I., 1977. MR 0516965

Victor Guillemin and Shlomo Sternberg, The moment map and collective motion, Ann. Physics 127 (1980), no. 1, 220–253. MR 576424, DOI 10.1016/0003-4916(80)90155-4

D. Kazhdan, B. Kostant, and S. Sternberg, Hamiltonian group actions and dynamical systems of Calogero type, Comm. Pure Appl. Math. 31 (1978), no. 4, 481–507. MR 478225, DOI 10.1002/cpa.3160310405

Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III, Lecture Notes in Math., Vol. 170, Springer, Berlin, 1970, pp. 87–208. MR 0294568

Bertram Kostant, The solution to a generalized Toda lattice and representation theory, Adv. in Math. 34 (1979), no. 3, 195–338. MR 550790, DOI 10.1016/0001-8708(79)90057-4

Jerrold Marsden and Alan Weinstein, Reduction of symplectic manifolds with symmetry, Rep. Mathematical Phys. 5 (1974), no. 1, 121–130. MR 402819, DOI 10.1016/0034-4877(74)90021-4

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

J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970 (French). Maîtrises de mathématiques. MR 0260238

11.

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

Shlomo Sternberg, Symplectic homogeneous spaces, Trans. Amer. Math. Soc. 212 (1975), 113–130. MR 379759, DOI 10.1090/S0002-9947-1975-0379759-8

Walter Thirring, A course in mathematical physics. Vol. I. Classical dynamical systems, Springer-Verlag, New York-Vienna, 1978. Translated from the German by Evans M. Harrell. MR 507189

E. T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1988. With an introduction to the problem of three bodies; Reprint of the 1937 edition; With a foreword by William McCrea. MR 992404, DOI 10.1017/CBO9780511608797

15.

E. P. Wigner, The unreasonable effectiveness of mathematics in the natural sciences, Comm. Pure. Appl. Math. 13 (1960).

1.

V. I. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier (Grenoble) 16 (1966), 319-361. MR 0202082

2.

V. I. Arnold, Mathematical methods of classical mechanics, Graduate Texts in Math., no. 60, Springer-Verlag, Berlin and New York, 1978. MR 690288

3.

V. Guillemin and Shlomo Sternberg, Geometric asymptotics, Amer. Math. Surveys, no. 14, Amer. Math. Soc. Providence, R. I., 1977. MR 516965

4.

V. Guillemin and Shlomo Sternberg, The moment map and collective motion, Ann. Phys. (to appear). MR 576424

5.

D. Kazhdan, B. Kostant and S. Sternberg, Hamiltonian group actions and dynamical systems of Calogero type, Comm. Pure Appl. Math. 31 (1978), 481-508. MR 478225

6.

B. Kostant, Quantization and unitary representations, Lecture Notes in Math., vol. 170, Springer-Verlag, Berlin and New York, 1970. MR 294568

7.

B. Kostant, The solution to a generalized Toda lattice and representation theory (to appear). MR 550790

8.

J. Marsden and A. Weinstein, Reduction of symplectic manifolds with symmetry, Rep. Mathematical Phys. 5 (1974), 121-130. MR 402819

9.

C. L. Siegel and J. Moser, Lectures on celestial mechanics, Springer, New York, 1971. MR 502448

10.

J. M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970. MR 260238

11.

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

12.

S. Sternberg, Symplectic homogeneous spaces, Trans. Amer. Math. Soc. 212 (1975), 113-130. MR 379759

13.

W. Thirring, Classical dynamical systems, Springer-Verlag, New York, 1978. MR 507189

14.

E. T. Whittaker, A treatise of the analytical dynamics of particles and rigid bodies, Cambridge Univ. Press, London, 1904-1965. MR 992404

15.

E. P. Wigner, The unreasonable effectiveness of mathematics in the natural sciences, Comm. Pure. Appl. Math. 13 (1960).