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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?)

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  • 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. Victor Guillemin and Shlomo Sternberg, The moment map and collective motion, Ann. Physics 127 (1980), no. 1, 220–253. MR 576424, https://doi.org/10.1016/0003-4916(80)90155-4
  • 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. Bertram Kostant, The solution to a generalized Toda lattice and representation theory, Adv. in Math. 34 (1979), no. 3, 195–338. MR 550790, https://doi.org/10.1016/0001-8708(79)90057-4
  • 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. 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
  • 14. 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
  • 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