Foundations of mechanics : a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the three-body problem

}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 Laplaces question of stability of the solar system. Mr. Marsdens 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 modern advanced calculus, and go on to a complete and self-contained treatment of graduate level classical mechanics.--From the Preface to the First Edition }

• Introduction
• Foreward by Tudor Ratiu and Richard Cushman
• Preliminaries
• Differential Theory
• Calculus on Manifolds
• Analytical Dynamics
• Hamiltonian and Lagrangian Systems
• Hamiltonian Systems with Symmetry
• Hamiltonian-Jacobi Theory and Mathematical Physics
• An Outline of Qualitative Dynamics
• Topological Dynamics
• Differentiable Dynamics
• Hamiltonian Dynamics
• Celestial Mechanics
• The Two-Body Problem
• The Three-Body Problem.