Abraham R., Marsden J.E. Foundations of Mechanics

Redwood City: Addison-Wesley Publishing Company. -1987. - 838 p. In the Spring of 1966, I gave a series of lectures in the Princeton University Department of Physics, aimed at recent mathematical results in mechanics, especially the work of Kolmogorov, Arnold, and Moser and its application to Laplace's question of the stability of the solar system. Mr. Marsden's notes of the lectures, with some revision and expansion by both of us became this book. Although the lectures were attended equally by mathematicians and physicists, our goal was to make the subject available to the nonspecialists. Therefore, the mathematical background assumed was dictated by the physics graduate students in the audience. Hoping this would be typical of the people interested in this subject. I have made the same assumptions in the book. Thus, we take for granted basic undergraduate calculus and linear algebra, and a limited amount of classical analysis, point set topology, and elementary mechanics. Then we begin with modem advanced calculus, and go on to a complete and self-contained treatment of graduate level classical mechanics.Preface to the Second Edition
Preface to the First Edition
MuseumPreview.
PRELIMINARIES
Differential Theory
Calculus on Manifolds
ANALYTICAL DYNAMICS
Hamiltonian and Lagrangian Systems
Hamiltonian Systems with Symmetry
Hamilton-Jacobi Theory and Mathematical Physics
AN OUTLINE OF QUALITATIVE DYNAMICS
Topological Dynamics
Differentiable Dynamics
Hamiltonian Dynamics
CELESTIAL MECHANICS
The Three-Body Problem
AppendixGlossary of Symbols.
Inside front cover