Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.
Part I: Preliminaries 1. Differential Theory 2. Calculus on Manifolds Part II: Analytical Dynamics 3. HamiHonlan and Lagrangian Systems 4. Hamiltonian Systems with Symmetry 5. Hamilton-Jacobi Theory and Mathematical Physics Part III: An Outline of Qualitative Dynamics 6. Topological Dynamics 7. Differentiable Dynamics 8. Hamiltonian Dynamics Part IV: Celestial Mechanics 9. The Two-Body Problem 10. The Three-Body Problem