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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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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.

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

  • 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 202082
  • 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).

Review Information:

Reviewer: Shlomo Sternberg
Journal: Bull. Amer. Math. Soc. 2 (1980), 378-387
DOI: https://doi.org/10.1090/S0273-0979-1980-14771-0
American Mathematical Society