Foundations of Mechanics

Ralph Abraham, University of California, Santa Cruz, CA, and Jerrold E. Marsden, California Institute of Technology, Pasadena, CA

• PreliminariesChapter 1. Differential theoryChapter 2. Calculus on manifoldsAnalytical dynamicsChapter 3. Hamiltonian and Lagrangian systemsChapter 4. Hamiltonian systems with symmetryChapter 5. Hamilton-Jacobi theory and mathematical physicsAn outline of qualitative dynamicsChapter 6. Topological dynamicsChapter 7. Differentiable dynamicsChapter 8. Index of IllustrationsChapter 9. Hamiltonian dynamicsCelestial mechanicsChapter 10. The two-body problemChapter 11. The three-body problemAppendix. The general theory of dynamical systems and classical mechanics by A. N. Kolmogorov

Undoubtedly [the book] will be for years the standard reference on symplectic geometry, analytical mechanics and symplectic methods in mathematical physics."" —Zentralblatt fur Mathematik